# Solved papers for JEE Main & Advanced Physics Electrostatics & Capacitance JEE PYQ-Electrostatics and Capacitance

### done JEE PYQ-Electrostatics and Capacitance Total Questions - 156

• question_answer1) On moving a charge of 20 C by 2 cm, 2 J of work is done, then the potential difference between the points is                [AIEEE 2002]

A)
$0.1$ V

B)
8V

C)
2 V

D)
3V

• question_answer2)  A charged particle g is placed at the centre O of cube of length L (ABCDEFGH). Another same charge q is placed at a distance L from 0. Then, the electric flux through ABCD is [AIEEE 2002]

A)
$q/4\pi {{\varepsilon }_{0}}L$

B)
zero

C)
$q/2\pi {{\varepsilon }_{0}}L$

D)
None of these

• question_answer3) If there are n capacitors in parallel connected to V volt source, then the energy stored is equal to [AIEEE 2002]

A)
CV

B)
$\frac{1}{2}nC{{V}^{2}}$

C)
$C{{V}^{2}}$

D)
$\frac{1}{2n}C{{V}^{2}}$

• question_answer4) If a charge q is placed at the centre of the line joining two equal charges Q such that the system is in equilibrium, then the value of q is [AIEEE 2002]

A)
$Q/2$

B)
$-Q/2$

C)
$Q/4$

D)
$-Q/4$

• question_answer5) Capacitance (in F) of a spherical conductor having radius 1 m, is                 [AIEEE 2002]

A)
$1.1\times {{10}^{-10}}$

B)
${{10}^{-6}}$

C)
$9\times {{10}^{-9}}$

D)
${{10}^{-3}}$

• question_answer6) A light string passing over a smooth light pulley connects two blocks of masses ${{m}_{1}}$ and ${{m}_{2}}$ (vertically). If the acceleration of the system is g/8, then the ratio of the masses is [AIEEE 2002]

A)
$8:1$

B)
$9:7$

C)
$4:3$

D)
$5:3$

• question_answer7) If the electric flux entering and leaving an enclosed surface respectively is ${{\phi }_{1}}$ and ${{\phi }_{2}}$, the electric charge inside the surface will be [AIEEE 2003]

A)
$({{\phi }_{1}}-{{\phi }_{2}}){{\varepsilon }_{0}}$

B)
$({{\phi }_{1}}+{{\phi }_{2}})/{{\varepsilon }_{0}}$

C)
$({{\phi }_{1}}-{{\phi }_{2}})/{{\varepsilon }_{0}}$

D)
$({{\phi }_{1}}+{{\phi }_{2}}){{\varepsilon }_{0}}$

• question_answer8) A sheet of aluminium foil of negligible thickness is introduced between the plates of a capacitor. The capacitance of the capacitor [AIEEE 2003]

A)
decreases

B)
remains unchanged

C)
becomes' infinite

D)
increases

• question_answer9) A thin spherical conducting shell of radius R has a charge q. Another charge 0 is placed at the centre of the shell. The electrostatic potential at a point P at a distance R/2 from the centre of the shell is [AIEEE 2003]

A)
$\frac{2Q}{4\pi {{\varepsilon }_{0}}R}$

B)
$\frac{2Q}{4\pi {{\varepsilon }_{0}}R}-\frac{2q}{4\pi {{\varepsilon }_{0}}R}$

C)
$\frac{2Q}{4\pi {{\varepsilon }_{0}}R}+\frac{q}{4\pi {{\varepsilon }_{0}}R}$

D)
$\frac{(q+Q)}{4\pi {{\varepsilon }_{0}}R}\frac{2}{R}$

• question_answer10) The work done in placing a charge of $8\times {{10}^{-18}}C$ on a condenser of capacity $100\mu F$ is [AIEEE 2003]

A)
$16\times {{10}^{-32}}$ J

B)
$3.1\times {{10}^{-26}}$ J

C)
$4\times {{10}^{-10}}$ J

D)
$32\times {{10}^{-32}}$ J

• question_answer11)  Three charges $-{{q}_{1}},+{{q}_{2}}$ and $-{{q}_{3}}$ are placed as shown in the figure. The x-component of the force on $-{{q}_{1}}$ is proportional to   [AIEEE 2003]

A)
$\frac{{{q}_{2}}}{{{b}^{2}}}-\frac{{{q}_{3}}}{{{a}^{2}}}\cos \theta$

B)
$\frac{{{q}_{2}}}{{{b}^{2}}}+\frac{{{q}_{3}}}{{{a}^{2}}}\sin \theta$

C)
$\frac{{{q}_{2}}}{{{b}^{2}}}+\frac{{{q}_{3}}}{{{a}^{2}}}\cos \theta$

D)
$\frac{{{q}_{2}}}{{{b}^{2}}}-\frac{{{q}_{3}}}{{{a}^{2}}}\sin \theta$

• question_answer12) Two spherical conductors B and C having equal radii and carrying equal charges in them repel each other with a force F when kept apart at some distance. A third spherical conductor having same radius as that of B but uncharged, is brought in contact with B, then brought in contact with C and finally removed away from both. The new force of repulsion between B and C is                                               [AIEEE 2004]

A)
$\frac{F}{4}$

B)
$\frac{3F}{4}$

C)
$\frac{F}{8}$

D)
$\frac{3F}{8}$

• question_answer13)  A charged particle q is shot towards another charged particle$Q$which is fixed, with a speed v. It approaches$Q$upto a closest distance r and then returns. If q was given a speed 2 v, the closest distance of approach would be [AIEEE 2004]

A)
r

B)
2r

C)
r/2

D)
r/4

• question_answer14) Four charges equal to $-Q$ are placed at the four comers of a square and a charge q is at its centre. If the system is in equilibrium, the value of q is                                     [AIEEE 2004]

A)
$-\frac{Q}{4}(1+2\sqrt{2})$

B)
$\frac{Q}{4}(1+2\sqrt{2})$

C)
$-\frac{Q}{2}(1+2\sqrt{2})$

D)
$\frac{Q}{2}(1+2\sqrt{2})$

• question_answer15) A charged oil drop is suspended in uniform field of$3\times {{10}^{4}}V/m,$so that it neither falls nor rises. The charge on the drop will be (take the mass of the charge                           [AIEEE 2004] $=9.9\times {{10}^{-15}}kg\text{ }and\text{ }g=10\text{ }m/{{s}^{2}}$)

A)
$3.3\times {{10}^{-18}}C$

B)
$3.2\times {{10}^{-18}}C$

C)
$1.6\times {{10}^{-18}}C$

D)
$4.8\times {{10}^{-18}}C$

• question_answer16) A fully charged capacitor has a capacitance C. It is discharged through a small coil of resistance wire embedded in a thermally insulated block of specific heat capacity s and mass m. If the temperature of the block is raised by AT, the potential difference V across the capacitance is [AIEEE 2005]

A)
$\sqrt{\frac{2mC\Delta T}{s}}$

B)
$\frac{mC\Delta T}{s}$

C)
$\frac{ms\Delta T}{C}$

D)
$\sqrt{\frac{2ms\Delta T}{C}}$

• question_answer17) A charged ball B hangs from a silk thread S, which makes an angle $\theta$ with a large charged conducting sheet as shown in the figure. The surface charge density o of the sheet is proportional to                  [AIEEE 2005]

A)
$\cos \theta$

B)
$\cot \theta$

C)
$\sin \theta$

D)
$\tan \theta$

• question_answer18) Two point charges $+8q$ and $-2q$ are located at$x=0$and$x=L$respectively. The location of a point on the x-axis at which the net electric field due to these two point charges is zero, is [AIEEE 2005]

A)
2L

B)
L/4

C)
8L

D)
4L

• question_answer19)  Two thin wire rings each having a radius R are placed at a distance d apart with their axes coinciding. The charges on the two rings are $+\text{ }q$and$-\text{ }q$. The potential difference between the centres of the two rings is                                 [AIEEE 2005]

A)
$\frac{qR}{4\pi {{\varepsilon }_{0}}{{d}^{2}}}$

B)
$\frac{q}{2\pi {{\varepsilon }_{0}}}\left[ \frac{1}{R}-\frac{1}{\sqrt{{{R}^{2}}+{{d}^{2}}}} \right]$

C)
zero

D)
$\frac{q}{4\pi {{\varepsilon }_{0}}}\left[ \frac{1}{R}-\frac{1}{\sqrt{{{R}^{2}}+{{d}^{2}}}} \right]$

• question_answer20) A parallel plate capacitor is made by stacking n equally spaced plates connected alternatively. If the capacitance between any two adjacent plates is C, then the resultant capacitance is [AIEEE 2005]

A)
$(n-1)C$

B)
$(n+1)C$

C)
C

D)
$nC$

• question_answer21) An electric dipole is placed at an angle of $30{}^\circ$to a non-uniform electric field. The dipole will experience                                  [AIEEE 2006]

A)
a translational force only in the direction of the field

B)
a translational force only in a direction normal to the direction of the field

C)
a torque as well as a translational force

D)
a torque only

• question_answer22)  Two insulating plates are both uniformly charged in such a way that the potential difference between them is${{V}_{2}}-{{V}_{1}}=20\,V$ (i.e., plate 2 is at a higher potential). The plates are separated by$d=0.1\text{ }m$and can be treated as infinitely large. An electron is released from rest on the inner surface of plate 1. What is its speed when it hits plate 2? $(e=1.6\times {{10}^{-19}}C,{{m}_{0}}=9.11\times {{10}^{-31}}kg)$ [AIEEE 2006]

A)
$2.65\times {{10}^{6}}\text{ }m/s$

B)
$7.02\times {{10}^{12}}\text{ }m/s$

C)
$1.87\times {{10}^{6}}m/s$

D)
$32\times {{10}^{-19}}m/s$

• question_answer23) Two spherical conductors A and B of radii 1 mm and 2 mm are separated by a distance of 5 cm and are uniformly charged. If the spheres are connected by a conducting wire, the in equilibrium condition, the ratio of the magnitude of the electric fields at the surfaces of spheres A and B is                                    [AIEEE 2006]

A)
4 : 1

B)
1 : 2

C)
2 : 1

D)
1 : 4

• question_answer24) An electric charge${{y}^{2}}={{x}^{2}}-2xy\frac{dy}{dx}$is placed at the origin (0, 0) of xy-coordinate system. Two points A and B are situated at${{p}^{2}}+{{q}^{2}}=1,$and (2, 0) respectively. The potential difference between the points A and B will be          [AIEEE 2007]

A)
9V

B)
zero

C)
2V

D)
4.5V

• question_answer25) A battery is used to charge a parallel plate capacitor till the potential difference between the plates becomes equal to the electromotive force of the battery. The ratio of the energy stored in the capacitor and the work done by the battery, will be                                           [AIEEE 2007]

A)
1

B)
2

C)
$(p+q)$

D)
$\frac{1}{2}$

• question_answer26)  Charges are placed on the vertices of a square     as shown. Let E be the electric field and V be the potential at the centre. If the charges on A and B are interchanged with those on D and C respectively, then             [AIEEE 2007]

A)
E remains unchanged, V changes

B)
both E and V change

C)
E and V remain unchanged

D)
E changes, V remains unchanged

• question_answer27) The potential at a point x (measured in${{e}^{-\frac{1}{2}}}$due to some charges situated on the x-axis is given by${{e}^{+\frac{1}{2}}}$volt.            The electric field E at $2u\times 3v$urn is given by [AIEEE 2007]

A)
${{\tan }^{-1}}\frac{b}{ac}$and in the -ve$45{}^\circ$direction

B)
${{\tan }^{-1}}\frac{bc}{a(c-a)}$and in the +ve${{\tan }^{-1}}\frac{bc}{a}$direction

C)
${{y}^{2}}=8x$and in the -ve$y=x+2$direction

D)
${{x}^{2}}+{{y}^{2}}+{{z}^{2}}-6x-12y-2\text{ }z+20=0,$and in the +ve$a=\hat{i}+\hat{j}+\hat{k},b=\hat{i}-\hat{j}+2\hat{k}$direction

• question_answer28) A parallel plate ' condenser with a dielectric of dielectric constant K between the plates has a capacity C and is charged to a potential V volts. The dielectric slab is slowly removed from between the plates and then reinserted. The net work done by the system in this process is   [AIEEE 2007]

A)
${{y}^{2}}=x$

B)
$y=|\text{ }x|$

C)
$\frac{2}{3}$

D)
zero

• question_answer29)  Directions: are based on the following paragraph Consider a block of conducting material of resistivity   $\rho$ shown in the figure. Current I enters at A and leaves from D. We apply superposition principal to find voltage $\Delta V$ developed between B and C. The calculation is done in the following steps: (i) Take current I entering from A and assume it to spread over a hemispherical surface in the block. (ii) Calculate field E(r) at distance r from A by using Ohms law $E=\rho j$, where j is the current per unit area at r. (iii) From the r  dependence of E(r), obtain the potential V(r) at r. (iv)  Repeat (i), (ii) and (iii) for current I leaving D and superpose results for A and D. $\Delta V$ measured between B and C is [AIEEE 2008]

A)
$\frac{\rho I}{2\pi a}-\frac{\rho I}{2\pi \left( a+b \right)}$

B)
$\frac{\rho I}{2\pi \left( a-b \right)}$

C)
$\frac{\rho I}{\pi a}-\frac{\rho I}{\pi \left( a+b \right)}$

D)
$\frac{\rho I}{a}-\frac{\rho I}{\left( a+b \right)}$

• question_answer30)  Directions: are based on the following paragraph Consider a block of conducting material of resistivity   $\rho$ shown in the figure. Current I enters at A and leaves from D. We apply superposition principal to find voltage $\Delta V$ developed between B and C. The calculation is done in the following steps: (i) Take current I entering from A and assume it to spread over a hemispherical surface in the block. (ii) Calculate field E(r) at distance r from A by using Ohms law $E=\rho j$, where j is the current per unit area at r. (iii) From the r  dependence of E(r), obtain the potential V(r) at r. (iv)  Repeat (i), (ii) and (iii) for current I leaving D and superpose results for A and D. For current entering at A, the electric field at a distance r from A is             [AIEEE 2008]

A)
$\frac{\rho I}{2\pi {{r}^{2}}}$

B)
$\frac{\rho I}{4\pi {{r}^{2}}}$

C)
$\frac{\rho I}{8\pi {{r}^{2}}}$

D)
$\frac{\rho I}{{{r}^{2}}}$

• question_answer31) A thin spherical shell of radius R has charge Q spread uniformly over its surface. Which of the following graphs most closely represents the electric field E(r) produced by the shell in the range $0\le r<\infty$, where r is the distance from the centre of the shell?                [AIEEE 2008]

A)

B)

C)

D)

• question_answer32) A parallel plate capacitor with air between the plates has a capacitance of 9 pF. The separation between its plates is d. The space between the plates is now filled with two dielectrics. One of the dielectric has dielectric constant ${{\kappa }_{1}}=3$ and thickness $\frac{d}{3}$ while the other one has dielectric constant ${{\kappa }_{2}}=6$ and thickness $\frac{2d}{3}$. Capacitance of the capacitor is now                                                         [AIEEE 2008]

A)
40.5 pF

B)
20.25 pF

C)
1.8 pF

D)
45 pF

• question_answer33)  Direction: The question contains Statement-I and Statement-II of the four Choices given after the statements, choose the one that best describe the two statements. STATEMENT - 1 For a charged particle moving from point P to point Q, the net work done by an electrostatic field on the particle is independent of the path connected point P to point Q. STATEMENT - 2 The net work done by a conservative force on an object moving along a closed loop is zero. [AIEEE 2009]

A)
Statement - 1 is True, Statement - 2 is False.

B)
Statement - 1 is True, Statement - 2 is True; Statement - 2 is a correct explanation for Statement - 1.

C)
Statement - 1 is True, Statement - 2 is True; Statement - 2 is not the correct explanation for Statement - 1.

D)
Statement - 1 is False, Statement - 2 is true.

• question_answer34) Let$p(r)=\frac{Q}{\pi {{R}^{4}}}r$be the charge density distribution for a solid sphere of radius R and total charge Q. For a point 'p' inside the sphere at distance${{r}_{1}}$from the centre of sphere, the magnitude of electric field is        [AIEEE 2009]

A)
0

B)
$\frac{Q}{4\pi {{\varepsilon }_{0}}r_{1}^{2}}$

C)
$\frac{Qr_{1}^{2}}{4\pi {{\varepsilon }_{0}}{{R}^{4}}}$

D)
$\frac{Qr_{1}^{2}}{3\pi {{\varepsilon }_{0}}{{R}^{4}}}$

• question_answer35) Two points P and Q are maintained at the potentials of 10V and -4V, respectively. The work done in moving 100 electrons from P to Q is                                               [AIEEE 2009]

A)
$9.60\times {{10}^{17}}J$

B)
$9.60\times {{10}^{17}}J$

C)
$2.24\times {{10}^{16}}J$

D)
$2.24\times {{10}^{16}}J.$

• question_answer36) A charge Q is placed at each of the opposite corners of a square. A charge q is placed at each of the other two corners. If the net electrical force on Q is zero, then Q/q equals:     [AIEEE 2009]

A)
$-2\sqrt{2}$

B)
- 1

C)
1

D)
$-\frac{1}{\sqrt{2}}$

• question_answer37)  A thin semi-circular ring of radius r has a positive charge q distributed uniformly over it. The net field$\overrightarrow{E}$at the centre O is -           [AIEEE 2010]

A)
$\frac{q}{2{{\pi }^{2}}{{\varepsilon }_{0}}{{r}^{2}}}\hat{j}$

B)
$\frac{q}{4{{\pi }^{2}}{{\varepsilon }_{0}}{{r}^{2}}}\hat{j}$

C)
$-\frac{q}{4{{\pi }^{2}}{{\varepsilon }_{0}}{{r}^{2}}}\hat{j}$

D)
$-\frac{q}{2{{\pi }^{2}}{{\varepsilon }_{0}}{{r}^{2}}}\hat{j}$

• question_answer38) Let there be a spherically symmetric charge distribution with charge density varying as$\rho (r)={{\rho }_{0}}\left( \frac{5}{4}-\frac{r}{R} \right)$upto$r=R,$and$\rho (r)=0$for$r>R,$where r is the distance from the origin. The electric field at a distance $r(r<R)$from the origin is given by -                    [AIEEE 2010]

A)
$\frac{{{\rho }_{0}}r}{3{{\varepsilon }_{0}}}\left( \frac{5}{4}-\frac{r}{R} \right)$

B)
$\frac{4\pi {{\rho }_{0}}r}{3{{\varepsilon }_{0}}}\left( \frac{5}{3}-\frac{r}{R} \right)$

C)
$\frac{{{\rho }_{0}}r}{4{{\varepsilon }_{0}}}\left( \frac{5}{3}-\frac{r}{R} \right)$

D)
$\frac{4{{\rho }_{0}}r}{3{{\varepsilon }_{0}}}\left( \frac{5}{4}-\frac{r}{R} \right)$

• question_answer39) Let C be the capacitance of a capacitor discharging through a resistor R. Suppose${{t}_{1}}$is the time taken for the energy stored in the capacitor to reduce to half its initial value and ${{t}_{2}}$is the time taken for the charge to reduce to one-fourth its initial value. Then the ratio ${{t}_{1}}/{{t}_{2}}$will be - [AIEEE 2010]

A)
2

B)
1

C)
$\frac{1}{2}$

D)
$\frac{1}{4}$

• question_answer40) Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of$30{}^\circ$with each other. When suspended in a liquid of density$0.8\text{ }g\text{ }c{{m}^{3}},$ the angle remains the same. If density of the material of the sphere is$1.6\text{ }g\text{ }c{{m}^{3}},$ the dielectric constant of the liquid is -                            [AIEEE 2010]

A)
1

B)
4

C)
3

D)
2

• question_answer41) Two identical charged spheres suspended from a common point by two massless strings of length l are initially a distance $d(d<<l)$ apart because of their mutual repulsion. The charge begins to leak from both the spheres at a constant rate. As a result the charges approach each other with a velocity v. Then as a function of distance $x$ between them                              [AIEEE 2011]

A)
$\upsilon \propto x$

B)
$\upsilon \propto {{x}^{-\frac{1}{2}}}$

C)
$\upsilon \propto {{x}^{-1}}$

D)
$\upsilon \propto {{x}^{\frac{1}{2}}}$

• question_answer42) The electrostatic potential inside a charged spherical ball is given by $\phi =an{{r}^{2}}+b$ where r is the distance from the centre; a, b are constants. Then the charge density inside the ball is                                             [AIEEE 2011]

A)
$-6\,\,a{{\varepsilon }_{0}}$

B)
$-24\,\pi \,a{{\varepsilon }_{0}}\gamma$

C)
$-6\,a{{\varepsilon }_{0}}\gamma$

D)
$-24\,\,\pi \,a{{\varepsilon }_{0}}\gamma$

• question_answer43) Two positive charges of magnitude 'q' are placed at the ends of a side (side 1) of a square of side '2a'. Two negative charges of the same magnitude are kept at the other corners. Starting from rest, if a charge Q moves from the middle of side 1 to the centre of square, its kinetic energy at the centre of square is : [AIEEE 11-05-2011]

A)
zero

B)
$\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{2qQ}{a}\left( 1+\frac{1}{\sqrt{5}} \right)$

C)
$\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{2qQ}{a}\left( 1-\frac{2}{\sqrt{5}} \right)$

D)
$\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{2qQ}{a}\left( 1-\frac{1}{\sqrt{5}} \right)$

• question_answer44) In a uniformly charged sphere of total charge Q and radius R, the electric field E is plotted as function of distance from the centre. The graph which would correspond to the above will be: [AIEEE 2012]

A)

B)

C)

D)

• question_answer45) If a simple pendulum has significant amplitude (up to a factor of 1/e of original) only in the period between $t=0s$ to $t=\tau s$, then $\tau$ may be called the average life of the pendulum. When the spherical bob of the pendulum suffers a retardation (due to viscous drag) proportional to its velocity, with 'b' as the constant of proportionality, the averatge life time of the pendulum is (assuming damping is small) in seconds:                     [AIEEE 2012]

A)
$\frac{0.693}{b}$

B)
b

C)
$\frac{1}{b}$

D)
$\frac{2}{b}$

• question_answer46)  This questions has statement-1 and statement-2. Of the four choices given after the statements, choose the one that best describe the two statements. An insulating solid sphere of radius R has a uniformly positive charge density $\rho$.As a result of this uniform charge distribution there is a finite value of electric potential at the centre of the sphere, at the surface of the sphere and also at a point outside the sphere. The electric potential at infinite is zero. Statement-1: When a charge q is take from the centre of the surface of the sphere its potential energy changes by $\frac{q\rho }{3{{\varepsilon }_{0}}}$. Statement-2: The electric field at a distance r $(r A) Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation of statement-1. B) Statement 1 is true Statement 2 is false. C) Statement 1 is false Statement 2 is true. D) Statement 1 is true, Statement 2 is true, and Statement 2 is the correct explanation of Statement 1. View Answer play_arrow • question_answer47)  Two circuits and have charged capacitors of capacitance C, 2C and 3C with open switches. Charges on each of the capacitor are as shown in the figures. On closing the switches [JEE ONLINE 07-05-2012] A) No charge flows in [a] but charge flows from R to L in [b] B) Charges flow from L to R in both and [b] C) Charges flow from R to L in [a] and from L to R in [b] D) No charge flows in [a] but charge flows from L to R in [b] View Answer play_arrow • question_answer48) The electric potential V(x) in a region around the origin is given by \[V(x)=4{{x}^{2}}$volts. The electric charge enclosed in a cube of 1 m side with its centre at the origin is (in coulomb). [JEE ONLINE 07-05-2012]

A)
$8{{\varepsilon }_{0}}$

B)
$-4{{\varepsilon }_{0}}$

C)
0

D)
$-8{{\varepsilon }_{0}}$

• question_answer49) A series combination of${{n}_{1}}$ capacitors, each of capacity ${{C}_{1}}$ is charged by source of potential difference 4 V. When another parallel combination of ${{n}_{2}}$capacitors each of capacity ${{C}_{2}}$ is charged by a source of potential difference V, it has the same total energy stored in it as the first combination has. The value of ${{C}_{2}}$ in terms of ${{C}_{1}}$is then         [JEE ONLINE 12-05-2012]

A)
$16\frac{{{n}_{2}}}{{{n}_{1}}}{{C}_{1}}$

B)
$\frac{2{{C}_{1}}}{{{n}_{1}}{{n}_{2}}}$

C)
$2\frac{{{n}_{2}}}{{{n}_{1}}}{{C}_{1}}$

D)
$\frac{16{{C}_{1}}}{{{n}_{1}}{{n}_{2}}}$

• question_answer50) A charge of total amount Q is distributed over two concentric hollow spheres of radii r and R             (R > r) such that the surface charge densities on the two spheres are equal. The electric potential at the common centre is          [JEE ONLINE 19-05-2012]

A)
$\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{\left( R-r \right)Q}{\left( {{R}^{2}}+{{r}^{2}} \right)}$

B)
$\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{\left( R+r \right)Q}{2\left( {{R}^{2}}+{{r}^{2}} \right)}$

C)
$\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{\left( R+r \right)Q}{\left( {{R}^{2}}+{{r}^{2}} \right)}$

D)
$\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{\left( R-r \right)Q}{\left( {{R}^{2}}+{{r}^{2}} \right)}$

• question_answer51)  The flat base of a hemisphere of radius a with no charge inside it lies in a horizontal plane. A uniform electric field E is applied at an angle$\frac{\pi }{4}$with the vertical direction. The electric flux through the curved surface of the hemisphere is [JEE ONLINE 19-05-2012]

A)
$\pi {{a}^{2}}E$

B)
$\frac{\pi {{a}^{2}}E}{\sqrt{2}}$

C)
$\frac{\pi {{a}^{2}}E}{2\sqrt{2}}$

D)
$\frac{\left( \pi +2 \right)\pi {{a}^{2}}E}{{{\left( 2\sqrt{2} \right)}^{2}}}$

• question_answer52) Three positive charges of equal value q are placed at vertices of an equilateral triangle. The resulting lines of force should be sketched as in [JEE ONLINE 26-05-2012]

A)

B)

C)

D)

• question_answer53)  This question has Statement 1 and Statement 2. [JEE ONLINE 26-05-2012] Of the four choices given after the Statements, choose the one that best describes the two Statements. Statement 1: It is not possible to make a sphere of capacity 1 farad using a conducting material. Statement 2: It is possible for earth as its radius is$6.4\times {{10}^{6}}m.$

A)
Statement 1 is true, Statement 2 is true, and Statement 2 is the correct explanation of Statement 1.

B)
Statement 1 is false, Statement 2 is true.

C)
Statement 1 is true, Statement 2 is true, and Statement 2 is not the correct explanation of Statement 1.

D)
Statement 1 is true, Statement 2 is false.

• question_answer54)  The capacitor of an oscillatory circuit is enclosed in a container. When the container is evacuated the resonance frequency of the circuit is 10 kHz. When the container is filled with a gas the resonance frequency changes by 50 Hz. The dielectric constant of the gas is            [JEE ONLINE 26-05-2012]

A)
1.001

B)
2.001

C)
1.01

D)
3.01

• question_answer55) Two capacitors${{C}_{1}}$and${{C}_{2}}$are charged to 120 V and 200 V respectively. It is found that by connecting them together the potential on each one can be made zero. Then: [JEE MAIN 2013]

A)
$5{{C}_{1}}=3{{C}_{2}}$

B)
$3{{C}_{1}}=5{{C}_{2}}$

C)
$3{{C}_{1}}+5{{C}_{2}}=0$

D)
$9{{C}_{1}}=4{{C}_{2}}$

• question_answer56) Two charges, each equal to q, are kept at $x=-a$ and$x=a$ on the x−axis. A particle of mass m and charge${{q}_{0}}=\frac{q}{2}$ is placed at the origin. If charge${{q}_{0}}$is given a small displacement$(y<<a)$ along the y−axis, the net force acting on the particle is proportional to: [JEE MAIN 2013]

A)
y

B)
− y

C)
$\frac{1}{y}$

D)
$-\frac{1}{y}$

• question_answer57)  A charge Q is uniformly distributed over a long rod AB of length L as shown in the figure. The electric potential at the point O lying at a distance L from the end A is:  [JEE MAIN 2013]

A)
$\frac{Q}{8\pi {{\varepsilon }_{0}}L}$

B)
$\frac{3Q}{4\pi {{\varepsilon }_{0}}L}$

C)
$\frac{Q}{4\pi {{\varepsilon }_{0}}L\ell n2}$

D)
$\frac{Q\ell n2}{4\pi {{\varepsilon }_{0}}L}$

• question_answer58) A uniform electric field $\vec{E}$ exists between the plates of a charged condenser. A charged particle enters the space between the plates and perpendicular to $\vec{E}$. The path of the particle between the plates is a: [JEE ONLINE 09-04-2013]

A)
straight line

B)
hyperbola

C)
parabola

D)
circle

• question_answer59) Two point dipoles of dipole moment $\overset{\to }{\mathop{{{\operatorname{P}}_{1}}}}\,$ and $\overset{\to }{\mathop{{{\operatorname{P}}_{2}}}}\,$ are at a distance $x$ from each other and $\overset{\to }{\mathop{{{\operatorname{P}}_{2}}}}\,||\overset{\to }{\mathop{{{\operatorname{P}}_{2}}}}\,$ The force between the dipoles is:                          [JEE ONLINE 09-04-2013]

A)
$\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{4{{\operatorname{p}}_{1}}{{\operatorname{p}}_{2}}}{{{x}^{4}}}$

B)
$\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{3{{\operatorname{p}}_{1}}{{\operatorname{p}}_{2}}}{{{x}^{3}}}$

C)
$\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{6{{\operatorname{p}}_{1}}{{\operatorname{p}}_{2}}}{{{x}^{4}}}$

D)
$\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{8{{\operatorname{p}}_{1}}{{\operatorname{p}}_{2}}}{{{x}^{4}}}$

• question_answer60) Two balls of same mass and carrying equal charge are hung from a fixed support of length $l$. At electrostatic equilibrium, assuming that angles made by each thread is small, the separation, $x$ between the balls is proportional to:                     [JEE ONLINE 09-04-2013]

A)
$l$

B)
${{l}^{2}}$

C)
${{l}^{2/3}}$

D)
${{l}^{1/3}}$

• question_answer61) A point charge of magnitude + $1\mu C$ is fixed at (0, 0, 0). An isolated uncharged spherical conductor, is fixed with its center at (4, 0, 0). The potential and the induced electric field at the sphere is: [JEE ONLINE 22-04-2013]

A)
$1.8\times {{10}^{5}}$ and $-5.625\times {{10}^{6}}\,V/m$

B)
$0\operatorname{V}$ and $0\operatorname{V}/\operatorname{m}$

C)
$2.25\times {{10}^{5}}\operatorname{V}$ and $-5.625\times {{10}^{6}}\operatorname{V}/\operatorname{m}$

D)
$2.25\times {{10}^{5}}\operatorname{V}$ and V/m

• question_answer62) To establish an instantaneous current of 2 A through a $1\mu \operatorname{F}$ capacitor; the potential difference across the capacitor plates should be changed at the rate of: [JEE ONLINE 22-04-2013]

A)
$2\times {{10}^{4}}\operatorname{V}/s$

B)
$4\times {{10}^{6}}\operatorname{V}/s$

C)
$2\times {{10}^{6}}\operatorname{V}/s$

D)
$4\times {{10}^{4}}\operatorname{V}/s$

• question_answer63) Two small equal point charges of magnitude q are suspended from a common point on the ceiling by insulating massless strings of equal lengths. They come to equilibrium with each string making angle $\theta$ from the vertical. If the mass of each charge is m, then the electrostatic potential at the centre of line joining them will be $\left( \frac{1}{4\pi {{\in }_{0}}}=\operatorname{k} \right).$     [JEE ONLINE 22-04-2013]

A)
$2\sqrt{\operatorname{k}\operatorname{mg}\tan \theta }$

B)
$\sqrt{\operatorname{k}\operatorname{mg}\tan \theta }$

C)
$4\sqrt{\operatorname{k}\operatorname{mg}/\tan \theta }$

D)
$4\sqrt{\operatorname{k}\operatorname{mg}\,\,\tan \theta }$

• question_answer64) Consider a finite insulated, uncharged conductor placed near a finite positively charged conductor. The uncharged body must have a potential:             [JEE ONLINE 23-04-2013]

A)
less than the charged conductor more than at infinity

B)
more than the charged conductor and less  than at infinity.

C)
more than the charged conductor and more than at infinity.

D)
less than the charged conductor and less than at infinity

• question_answer65) A liquid drop having 6 excess electrons is kept stationary under a uniform electric field of $25.5{{\operatorname{KVm}}^{-1}}$. The density of liquid is$1.26\times {{10}^{3}}$. The radius of the drop is (neglect buoyancy) [JEE ONLINE 23-04-2013]

A)
$4.3\times {{10}^{-7}}\operatorname{m}$

B)
$7.8\times {{10}^{-7}}\operatorname{m}$

C)
$0.078\times {{10}^{-7}}\operatorname{m}$

D)
$3.4\times {{10}^{-7}}\operatorname{m}$

• question_answer66)  This question has Statement-1 and that Statements-2. Of the four choice given after the Statements, choose the one that best describes the two Statements. [JEE ONLINE 25-04-2013] Statement 1: No work is required to be done to move a fest charge between any two pints on an equipotential surface. Statement 2: Electric lines of force at the equipotential surfaces are mutually perpendicular to each other

A)
Statement 1 is true, Statement 2 is true, Statement 2 is the correct explanation of Statement 1

B)
Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation of Statement 1.

C)
Statement 1 is true, Statement 2 is false.

D)
Statement 1 is false, Statement 2 is true.

• question_answer67) The surface charge density of a thin charge disc of radius R is $\sigma$. The value of the electric field at the centre of the disc is $\frac{\sigma }{2{{\in }_{0}}}.$ With respect to the field at the centre, the electric field along the axis at a distance R From the centre of the disc:     [JEE ONLINE 25-04-2013]

A)
reduces by 70.7%

B)
reduces by 29.3%

C)
reduces by 9.7%

D)
reduces by 14.6%

• question_answer68) A parallel plate capacitor having a separation between the plates d, plate area A and material with dielectric constant K has capacitance${{C}_{0}}$. Now one-third of the material is replaced by another material with dielectric constant 2K, so that effectively there are two capacitors one with area $\frac{1}{3}\operatorname{A},$ dielectric constant 2 K and another with area $\frac{2}{3}\operatorname{A},$ and dielectric constant K. If the capacitance of this new capacitor is C then $C/{{C}_{0}}$is: [JEE ONLINE 25-04-2013]

A)
$1$

B)
$\frac{4}{3}$

C)
$\frac{2}{3}$

D)
$\frac{1}{3}$

• question_answer69) A parallel plate capacitor is made of two circular plates separated by a distance of 5 mm and with a dielectric of dielectric constant 2.2 between them. When the electric field in the dielectric is$3\times {{10}^{4}}V/m,$the charge density of the positive plate will be close to:            [JEE MAIN 2014]

A)
$3\times {{10}^{4}}C/{{m}^{2}}$

B)
$6\times {{10}^{4}}C/{{m}^{2}}$

C)
$6\times {{10}^{-7}}C/{{m}^{2}}$

D)
$3\times {{10}^{-7}}C/{{m}^{2}}$

• question_answer70) Assume that an electric field $\vec{E}=30{{x}^{2}}\hat{i}$exists in space. Then the potential difference ${{V}_{A}}-{{V}_{O}},$where ${{\text{V}}_{\text{O}}}$is the potential at the origin and ${{\text{V}}_{\text{A}}}$ the potential at x = 2 m is: [JEE MAIN 2014]

A)
80 J

B)
80 J

C)
120 J

D)
−120 J

• question_answer71) The magnitude of the average electric field normally present in the atmosphere just above the surface of the Earth is about 150 N/C, directed inward towards the center of the Earth. This gives the total net surface charge carried by the Earth to be:    [JEE ONLINE 09-04-2014] [Given${{\varepsilon }_{o}}=8.85\times {{10}^{-12}}{{C}^{2}}/N-{{m}^{2}},$${{R}_{E}}=6.37\times {{10}^{6}}m$]

A)
+ 670 kC

B)
- 670 kC

C)
680 kC

D)
+ 680 kC

• question_answer72) Three capacitors, each of $3\mu F,$are provided. These cannot be combined to provide the resultant capacitance of:  [JEE ONLINE 09-04-2014]

A)
$1\mu F$

B)
$2\mu F$

C)
$4.5\mu F$

D)
$6\mu F$

• question_answer73) A cone of base radius R and height h is located in a uniform electric field $\overset{\to }{\mathop{E}}\,$ parallel to its base. The electric flux entering the cone is: [JEE ONLINE 11-04-2014]

A)
$\frac{1}{2}EhR$

B)
her

C)
2 E h R

D)
4 E h R

• question_answer74)  A parallel plate capacitor is made of two plates of length l, width w and separated by distance d. A dielectric slab (dielectric constant K) that fits exactly between the plates is held near the edge of the plates. It is pulled into the capacitor by a force$F=-\frac{\partial U}{\partial x}$where U is the energy of the capacitor when dielectric is inside the capacitor up to distance x (See figure). If the charge on the capacitor is Q then the force on the dielectric when it is near the edge is:       [JEE ONLINE 11-04-2014]

A)
$\frac{{{Q}^{2}}d}{2\omega {{1}^{2}}{{\varepsilon }_{o}}}K$

B)
$\frac{{{Q}^{2}}\omega }{2d{{1}^{2}}{{\varepsilon }_{o}}}\left( K-1 \right)$

C)
$\frac{{{Q}^{2}}d}{2w{{1}^{2}}{{\varepsilon }_{o}}}\left( K-1 \right)$

D)
$\frac{{{Q}^{2}}w}{2d{{1}^{2}}{{\varepsilon }_{o}}}K$

• question_answer75)  A spherically symmetric charge distribution is characterized by a charge density having the following variations: $\rho (r)={{\rho }_{o}}\left( 1-\frac{r}{R} \right)$for r < R$\rho (r)=0$for $r\ge R$ Where r is the distance from the centre of the charge distribution ${{\rho }_{o}}$is a constant. The electric field at an internal point (r < R) is:[JEE ONLINE 12-04-2014]

A)
$\frac{{{\rho }_{o}}}{4{{\varepsilon }_{0}}}\left( \frac{r}{3}-\frac{{{r}^{2}}}{4R} \right)$

B)
$\frac{{{\rho }_{o}}}{{{\varepsilon }_{o}}}\left( \frac{r}{3}-\frac{{{r}^{2}}}{4R} \right)$

C)
$\frac{{{\rho }_{o}}}{3{{\varepsilon }_{o}}}\left( \frac{r}{3}-\frac{{{r}^{2}}}{4R} \right)$

D)
$\frac{{{\rho }_{o}}}{12{{\varepsilon }_{o}}}\left( \frac{r}{3}-\frac{{{r}^{2}}}{4R} \right)$

• question_answer76)  The space between the plates of a parallel plate capacitor is filled with a dielectric whose dielectric constant varies with distance as per the relation: $K(x)={{K}_{o}}+\lambda x$ ($\lambda =$ a constant) The capacitance C, of the capacitor, would be related to its vacuum capacitance Co for the relation:                    [JEE ONLINE 12-04-2014]

A)
$C=\frac{\lambda d}{\ln (1+{{K}_{o}}\lambda d)}{{C}_{o}}$

B)
$C=\frac{\lambda }{d.ln(1+{{K}_{o}}\lambda d)}{{C}_{o}}$

C)
$C=\frac{\lambda d}{ln(1+\lambda d/{{K}_{o}})}{{C}_{o}}$

D)
$C=\frac{\lambda }{d.ln(1+{{K}_{o}}/\lambda d)}{{C}_{o}}$

• question_answer77) The electric field in a region of space is given by, $\vec{E}={{E}_{o}}\hat{i}+2{{E}_{o}}\hat{j}$where ${{E}_{o}}=100N/C.$The flux of the field through a circular surface of radius 0.02 m parallel to the YZ plane is nearly:            [JEE ONLINE 19-04-2014]

A)
0.125 Nm2/C

B)
0.02 Nm2/C

C)
0.005 Nm2/C

D)
3.14 Nm2/C

• question_answer78) The gap between the plates of a parallel plate capacitor of area A and distance between plates d, is filled with a dielectric whose permittivity varies linearly from ${{\in }_{1}}$ at one plate to ${{\in }_{2}}$at the other. The capacitance of capacitor is:        [JEE ONLINE 19-04-2014]

A)
${{\in }_{0}}\left( {{\in }_{1}}+{{\in }_{2}} \right)A/d$

B)
${{\in }_{0}}\left( {{\in }_{2}}+{{\in }_{1}} \right)A/2d$

C)
${{\in }_{0}}A/\left[ d/n\left( {{\in }_{2}}+{{\in }_{1}} \right) \right]$

D)
${{\in }_{0}}A/\left( {{\in }_{2}}-{{\in }_{1}} \right)A/\left[ d/n\left( {{\in }_{2}}/{{\in }_{1}} \right) \right]$

• question_answer79)  In the given circuit, charge ${{Q}_{2}}$ on the $2\mu F$ capacitor changes as C is varied from $1\mu F$ to $3\mu F.{{Q}_{2}}$ as a function of C is given properly by : (figures are drawn schematically and are not to scale)  [JEE MAIN 2015]

A)

B)

C)

D)

• question_answer80) A uniformly charged solid sphere of radius R has potential ${{V}_{0}}$(measured with respect to$\infty$) on its surface. For this sphere the equipotential surfaces with potentials $\frac{3{{V}_{0}}}{2},\frac{5{{V}_{0}}}{4},\frac{3{{V}_{0}}}{4}$and $\frac{{{V}_{0}}}{4}$have radius ${{R}_{1}},{{R}_{2}},{{R}_{3}}$ and${{R}_{4}}$ respectively. Then [JEE MAIN 2015]

A)
${{R}_{1}}=0$and${{R}_{2}}<\left( {{R}_{4}}-{{R}_{3}} \right)$

B)
$2R<{{R}_{4}}$

C)
${{R}_{1}}=0$and${{R}_{2}}>\left( {{R}_{4}}-{{R}_{3}} \right)$

D)
${{R}_{1}}\ne 0$and$\left( {{R}_{2}}-{{R}_{1}} \right)>\left( {{R}_{4}}-{{R}_{3}} \right)$

• question_answer81) A long cylinderal shell carries positive surface charge $\sigma$ in the upper half and negative surface charge $-\sigma$in the lower half. The electric field lines around the cylinder will looke like figure given in:        [JEE MAIN 2015] (Figures are schematic and not drawn to scale)

A)

B)

C)

D)

• question_answer82)  A thin disc of radius b = 2a has a concentric hole of radius $'\sigma '$ in it (see figure). It carries uniform surface charge 'w' on it. If the electric field on its axis at height 'h' (h<

A)
$\frac{\sigma }{a{{\varepsilon }_{0}}}$

B)
$\frac{\sigma }{4a{{\varepsilon }_{0}}}$

C)
$\frac{\sigma }{2a{{\varepsilon }_{0}}}$

D)
$\frac{\sigma }{8a{{\varepsilon }_{0}}}$

• question_answer83)  A wire, of length L(=20 cm), is bent into a semi-circular arc. If the two equal halves, of the arc, were each to be uniformly charged with charges $\pm Q.[|Q|={{10}^{3}}{{\varepsilon }_{0}}$Coulomb where ${{\varepsilon }_{0}}$is the permittivity (in SI units) of free space] the net electric field at the centre 0 of the semi-circular arc would be :             [JEE MAIN 11-04-2015]

A)
$(50\times {{10}^{3}}N/C)\hat{J}$

B)
$(25\times {{10}^{3}}N/C)\hat{i}$

C)
$(25\times {{10}^{3}}N/C)\hat{j}$

D)
$(50\times {{10}^{3}}N/C)\hat{i}$

• question_answer84) An electric field $\overset{\to }{\mathop{E}}\,=\left( 25\,\hat{i}+30\hat{j} \right)N{{C}^{-1}}$ exists in a region of space. If the potential at the origin is taken to be zero then the potential at x = 2 m, y = 2 m is:             [JEE MAIN 11-04-2015]

A)
- 130J

B)
- 12.0J

C)
- 140J

D)
- 110J

• question_answer85)  In figure is shown a system of four capacitors connected across a 10 V battery. Charge that will flow from switch S when it is closed is:              [JEE MAIN 11-04-2015]

A)
$5\mu C$ from b to a

B)
$20\mu C$ from a to b

C)
$5\mu C$ from a to b

D)
zero

• question_answer86)  A combination of capacitors is set up as shown in the figure. The magnitude of the electric field, due to a point charge Q (having a charge equal to the sum of the charges on the $4\mu F$ and $9\mu F$capacitors), at a point 30 m from it , would equal:                      [JEE MAIN - I 3-4-2016]

A)
480 N/C

B)
240 N/C

C)
360 N/C

D)
420 N/C

• question_answer87)  The region between two concentric spheres of radii 'a' and 'b', respectively (see figure), has volume charge density $\rho =\frac{A}{r},$where A is a constant and r is the distance from the centre. At the centre of the spheres is a point charge Q. The value of A such that the electric field in the region between the spheres will be constant, is :- [JEE MAIN - I 3-4-2016]

A)
$\frac{2Q}{\pi {{a}^{2}}}$

B)
$\frac{Q}{2\pi {{a}^{2}}}$

C)
$\frac{Q}{2\pi ({{b}^{2}}-{{a}^{2}})}$

D)
$\frac{2Q}{\pi ({{a}^{2}}-{{b}^{2}})}$

• question_answer88)  The potential (in volts) of a charge distribution is given by $V(z)=30-5{{z}^{2}}$for$|z|\le 1m$ $V(z)=35-10|z|$for$|z|\ge 1m.$ V(z) does not depend on x and y . If this potential is generated by a constant charge per unit volume ${{\rho }_{0}},$(in units of ${{\varepsilon }_{0}}$) which is spread over certain region ,then choose the correct statement. [JEE ONLINE 09-04-2016]

A)
${{\rho }_{0}}=40{{\varepsilon }_{0}}$in the entire region

B)
${{\rho }_{0}}=20{{\varepsilon }_{0}}$ in the entire region

C)
${{\rho }_{0}}=20{{\varepsilon }_{0}}$ for $|z|$in$\le 1m$and ${{\rho }_{0}}=0$else where

D)
(d${{\rho }_{0}}=10{{\varepsilon }_{0}}$for $|z|$in $\le 1m$and${{\rho }_{0}}=0$ else where

• question_answer89) Three capacitors each of $4\mu F$are to be connected in such a way that the effective capacitance is $6\mu F.$ This can be done by connecting them: [JEE ONLINE 09-04-2016]

A)
all in series

B)
two in parallel and one in series

C)
two in series and one in parallel

D)
all in parallel

• question_answer90)  Figure shows a network of capacitors where the number indicates capacitances in micro Farad. The value of capacitance C if the equivalent capacitance between point A and B is to be $1\mu F$ is: [JEE ONLINE 10-04-2016]

A)
$\frac{33}{23}\mu F$

B)
$\frac{31}{23}\mu F$

C)
$\frac{32}{23}\mu F$

D)
$\frac{34}{23}\mu F$

• question_answer91) Within a spherical charge distribution of charge density$\rho (r)$, N equipotential surfaces of potential${{V}_{0}},\,{{V}_{0}}+\Delta V,{{V}_{0}}+2\Delta v$, .... ${{V}_{0}}+N\Delta V(\Delta V<0)$ are drawn and have increasing radii ${{r}_{0}},{{r}_{1}}{{r}_{2}},.......{{r}_{N}}$, respectively. If the difference in the radii of the surface is constant for all values of ${{V}_{0}}$ and $\Delta V$ then:                                      [JEE ONLINE 10-04-2016]

A)
$\rho (r)\alpha r$

B)
$\rho (r)\alpha \frac{1}{{{r}^{2}}}$

C)
$\rho (r)\alpha \frac{1}{r}$

D)
$\rho (r)$= constant

• question_answer92) An electric dipole has a fixed dipole moment$\vec{p},$, which makes angle $\theta$ with respect to x-axis. When subjected to an electric${{\vec{E}}_{1}}=E\hat{i},$ field It experiences a torque $\vec{T}=\tau \hat{k}.$ When subjected to another electric field ${{\vec{E}}_{2}}=\sqrt{3}{{E}_{1}}\hat{j}$ it experiences torque${{\vec{T}}_{2}}=-{{\vec{T}}_{1}}.$ The angle $\theta$ is: [JEE Main 2017]

A)
${{60}^{o}}$

B)
${{90}^{o}}$

C)
${{30}^{o}}$

D)
${{45}^{o}}$

• question_answer93)  A capacitance of $2\mu F$is required in an electrical circuit across a potential difference of 1.0 kV.  A large number of$1\mu F$capacitors are available which can withstand a potential difference of not more than 300 V. The minimum number of capacitors required to achieve this is:                            [JEE Main 2017]

A)
24

B)
32

C)
2

D)
16

• question_answer94) The energy stored in the electric field produced by a metal sphere is 4.5 J. If the sphere contains $4\mu C$ charge, its radius will be: [Take :$\frac{1}{4\pi {{\varepsilon }_{0}}}=9\times {{10}^{9}}N-{{m}^{2}}/{{C}^{2}}$] [JEE Online 08-04-2017]

A)
32 mm

B)
16 mm

C)
28 mm

D)
20 mm

• question_answer95) There is a uniform electrostatic field in a region. The potential at various points on a small sphere centred at P, in the region, is found to vary between in limits 589.0V to 589.8 V. What is the potential at a point on the sphere whose radius vector makes an angle of 60° with the direction of the field? [JEE Online 08-04-2017]

A)
589.4 V

B)
589.5 V

C)
589.2 V

D)
589.6 V

• question_answer96)  Four closed surfaces and corresponding charge distributions are shown below - Let the respective electric fluxes through the surfaces be ${{\Phi }_{1}},\,{{\Phi }_{2}},\,{{\Phi }_{3}}$ and ${{\Phi }_{4}}$. Then - [JEE Online 09-04-2017]

A)
${{\Phi }_{1}}>{{\Phi }_{2}}>{{\Phi }_{3}}>{{\Phi }_{4}}$

B)
${{\Phi }_{1}}<{{\Phi }_{2}}={{\Phi }_{3}}>{{\Phi }_{4}}$

C)
${{\Phi }_{1}}>{{\Phi }_{3}};\,\,{{\Phi }_{2}}>{{\Phi }_{4}}$

D)
${{\Phi }_{1}}={{\Phi }_{2}}={{\Phi }_{3}}={{\Phi }_{4}}$

• question_answer97)  A combination of parallel plate capacitors is maintained at a certain potential difference. When a 3 mm thick slab is introduced between all the plates, in order to maintain the same potential difference, the distance between the plates is increased by 2.4 mm. Find the dielectric constant of the slab. [JEE Online 09-04-2017]

A)
6

B)
4

C)
3

D)
5

• question_answer98) A parallel plate capacitor of capacitance $\text{90 pF}$ is connected to a battery of$\text{emf 20 V}$. If a dielectric material of dielectric constant $\text{K=}\frac{5}{3}$is inserted between the plates, the magnitude of the induced charge will be: [JEE Main Online 08-04-2018]

A)
$\text{2}\text{.4 n C}$

B)
$\text{0}\text{.9 n C}$

C)
$\text{1}\text{.2 n C}$

D)
$\text{0}\text{.3 n C}$

• question_answer99) Three concentric metal shells A, B and C of respective radii a, b and c (a < b < c) have surface charge densities $\text{+ }\sigma$, $\text{- }\sigma$ and $\text{+ }\sigma$ respectively. The potential of shell B is: [JEE Main Online 08-04-2018]

A)
$\frac{\sigma }{{{\in }_{\text{O}}}}\left[ \frac{{{b}^{2}}-{{c}^{2}}}{b}+a \right]$

B)
$\frac{\sigma }{{{\in }_{\text{O}}}}\left[ \frac{{{b}^{2}}-{{c}^{2}}}{c}+a \right]$

C)
$\frac{\sigma }{{{\in }_{\text{O}}}}\left[ \frac{{{a}^{2}}-{{b}^{2}}}{a}+c \right]$

D)
$\frac{\sigma }{{{\in }_{\text{O}}}}\left[ \frac{{{a}^{2}}-{{b}^{2}}}{b}+c \right]$

• question_answer100)  The equivalent capacitance between A and B  in the circuit given below is: [JEE Online 15-04-2018]

A)
$4.9\mu F$

B)
$3.6\mu F$

C)
$5.4\mu F$

D)
$2.4\mu F$

• question_answer101) A body of mass $M$ and charge $q$ is connected to a spring of spring constant$k$. It is oscillating along x-direction about its equilibrium position, taken to be at $x=0$, with an amplitude $A$. An electric field $E$ is applied along the x-direction. Which of the following statements is correct? [JEE Online 15-04-2018]

A)
The total energy of the system is $\frac{1}{2}m{{\omega }^{2}}{{A}^{2}}+\frac{1}{2}\frac{{{q}^{2}}{{E}^{2}}}{k}$

B)
The new equilibrium position is at a distance: $\frac{2qE}{k}$ from $x=0$

C)
The new equilibrium position is at a distance:$\frac{qE}{2k}$  from $x=0$

D)
The total energy of the system is $\frac{1}{2}m{{\omega }^{2}}{{A}^{2}}-\frac{1}{2}\frac{{{q}^{2}}{{E}^{2}}}{k}$

• question_answer102)  A charge $Q$ is placed at a distance $a/2$ above the centre of the square surface of edge $a$ as shown in the figure. The electric flux through the square surface is: [JEE Online 15-04-2018]

A)
$\frac{Q}{3{{\in }_{0}}}$

B)
$\frac{Q}{6{{\in }_{0}}}$

C)
$\frac{Q}{2{{\in }_{0}}}$

D)
$\frac{Q}{{{\in }_{0}}}$

• question_answer103) A parallel plate capacitor with area $200c{{m}^{2}}$ and separation between the plates$1.5cm$, is connected across a battery of emf V. If the force of attraction between the plates is $25\times {{10}^{-6}}N$,  the value of $V$ is approximately:      [JEE Online 15-04-2018 (II)] $\left( {{\in }_{0}}=8.85\times {{10}^{-12}}\frac{{{C}^{2}}}{N.{{m}^{2}}} \right)$

A)
$150V$

B)
$100V$

C)
$250V$

D)
$300V$

• question_answer104) A solid ball of radius R has a charge density $\rho$ given by $\rho ={{\rho }_{o}}\left( 1-\frac{r}{R} \right)$ for $0\le r\le R$. The electric field outside the ball is: [JEE Online 15-04-2018 (II)]

A)
$\frac{{{\rho }_{0}}{{R}^{3}}}{{{\in }_{0}}{{r}^{2}}}$

B)
$\frac{4{{\rho }_{0}}{{R}^{3}}}{3{{\in }_{0}}{{r}^{2}}}$

C)
$\frac{3{{\rho }_{0}}{{R}^{3}}}{4{{\in }_{0}}{{r}^{2}}}$

D)
$\frac{{{\rho }_{0}}{{R}^{3}}}{12{{\in }_{0}}{{r}^{2}}}$

• question_answer105)  A capacitor ${{C}_{1}}=10\mu F$ is charged up to a voltage $V=60V$ by connecting it to battery $B$ through switch (1), Now ${{C}_{1}}$ is disconnected from battery and connected to a circuit consisting of two uncharged capacitors ${{C}_{2}}=3.0\mu F$ and $P{{C}_{3}}=6.0\mu F$ through a switch (2) as shown in the figure. The sum of final charges on ${{C}_{2}}$and ${{C}_{3}}$is: [JEE Online 15-04-2018 (II)]

A)
$36\mu C$

B)
$20\mu C$

C)
$54\mu C$

D)
$40\mu C$

• question_answer106) Two identical conducting spheres A and B, carry equal charge. They are separated by a distance much larger than their diameter, and the force between them is F. A third identical conducting sphere C is uncharged. Sphere C is first touched to A then to B, and the removed. As a result, the force between A and B would be equal to     [JEE Main Online 16-4-2018]

A)
$\frac{3F}{4}$

B)
$\frac{F}{2}$

C)
F

D)
$\frac{3F}{8}$

• question_answer107) For a uniformly charged ring of radius R, the electric field on its axis has the largest magnitude at a distance h from its centre. Then value of h is:             [JEE Main 09-Jan-2019 Morning]

A)
$R\sqrt{2}$

B)
R

C)
$\frac{R}{\sqrt{5}}$

D)
$\frac{R}{\sqrt{2}}$

• question_answer108)  A parallel plate capacitor is made of two square plates of side a, separated by a distance$d\left( d< A) \[\frac{K{{\in }_{0}}{{a}^{2}}}{2d\,(K+1)}$

B)
$\frac{K{{\in }_{0}}{{a}^{2}}}{d\,(K-1)}\,\,In\,\,K$

C)
$\frac{K{{\in }_{0}}{{a}^{2}}}{d}\,\,In\,\,K$

D)
$\frac{1}{2}\,\,\,\frac{K{{\in }_{0}}{{a}^{2}}}{d}$

• question_answer109) Three charges +Q, q, +Q are placed respectively, at distance, 0, $d/2$ and d from the origin, on the x-axis. If the net force experienced $by+Q$, placed at $x=0$, is zero then value of q is: [JEE Main 09-Jan-2019 Morning]

A)
+Q/2

B)
-Q/4

C)
+Q/4

D)
-Q/2

• question_answer110)  A parallel plate capacitor with square plates is filled with four dielectrics of dielectric constants ${{K}_{1}},\text{ }{{K}_{2}},\text{ }{{K}_{3}},\text{ }{{K}_{4}}$ arranged as shown in the figure. The effective dielectric constant K will be: [JEE Main 09-Jan-2019 Evening]

A)
$K\,\,=\,\,\frac{({{K}_{1}}+{{K}_{2}})({{K}_{2}}+{{K}_{4}})}{{{K}_{1}}+{{K}_{2}}+{{K}_{3}}+{{K}_{4}}}$

B)
$K\,\,=\,\,\frac{({{K}_{1}}+{{K}_{2}})({{K}_{2}}+{{K}_{4}})}{2({{K}_{1}}+{{K}_{2}}+{{K}_{3}}+{{K}_{4}})}$

C)
$K\,\,=\,\,\frac{({{K}_{1}}+{{K}_{2}})({{K}_{3}}+{{K}_{4}})}{({{K}_{1}}+{{K}_{2}}+{{K}_{3}}+{{K}_{4}})}$

D)
None of these

• question_answer111) Charge is distributed within a sphere of radius R with a volume charge density$\rho (r)=\frac{A}{{{r}^{2}}}{{e}^{{}^{-2r}/{}_{a}}}$, where A and a are constants. If Q is the total charge of this charge distribution, the radius R is: [JEE Main 09-Jan-2019 Evening]

A)
$\frac{a}{2}\,\log \,\left( 1-\frac{Q}{2\,\pi \,a\,A} \right)$

B)
$\frac{a}{2}\,\log \,\left( 1-\frac{1}{\frac{Q}{2\,\pi \,a\,A}} \right)$

C)
$a\,\,\log \,\,\left( \frac{1}{1-\frac{Q}{2\,\pi \,a\,A}} \right)$

D)
$a\,\,\log \,\,\left( 1-\frac{Q}{2\,\pi \,a\,A} \right)$

• question_answer112) Two point charges ${{q}_{1}}\,(\sqrt{10}\,\mu C)$and ${{q}_{2}}(-25\,\,\mu C)$ are placed on the x-axis at $x=1\,m$ and $x=4\,m$respectively. The electric field (in V/m) at a point $y=3$m on y-axis is, [take$\frac{1}{4\pi {{\in }_{0}}}\,\,=\,\,9\,\times {{10}^{9}}\,N{{m}^{2}}{{C}^{-}}^{2}$ [JEE Main 09-Jan-2019 Evening]

A)
$(-81\widehat{i}\,\,+\,\,81\widehat{j})\,\,\times \,{{10}^{2}}$

B)
$(81\widehat{i}-81\widehat{j})\times {{10}^{2}}$

C)
$(63\widehat{i}\,\,-\,\,27\widehat{j})\,\,\times \,{{10}^{2}}$

D)
$(-63\widehat{i}+27\widehat{j})\times {{10}^{2}}$

• question_answer113)  A parallel plate capacitor is of area $6\text{ }c{{m}^{2}}$ and a separation 3 mm. The gap is filled with three dielectric materials of equal thickness (see figure) with dielectric constants ${{K}_{1}}=10,\text{ }{{K}_{2}}=12$ and${{K}_{3}}=14$. The dielectric constant of a material which when fully inserted in above capacitor, gives same capacitance would be - [JEE Main 10-Jan-2019 Morning]

A)
12

B)
36

C)
14

D)
4

• question_answer114)  Two electric dipoles, A, B with respective dipole moments ${{\overrightarrow{d}}_{A}}=-4qa\widehat{i}$ and ${{\overrightarrow{d}}_{B}}=-2qa\widehat{i}$ are placed on the x-axis with a separation R, as shown in the figure. The distance from A at which both of them produce the same potential is -              [JEE Main 10-Jan-2019 Morning]

A)
$\frac{\sqrt{2}\,R}{\sqrt{2}+1}$

B)
$\frac{\,R}{\sqrt{2}+1}$

C)
$\frac{\,\sqrt{2}\,R}{\sqrt{2}-1}$

D)
$\frac{\,\,R}{\sqrt{2}-1}$

• question_answer115) An insulating thin rad of length l has a linear charge density $\rho (x)\,\,=\,\,{{\rho }_{0}}\,\frac{x}{l}$on it. The rod is rotated about an axis passing through the origin $(x\,\,=\,\,0)$and perpendicular to the rod. If the rod makes n rotations per second, then the time averaged magnetic moment of the rod is- [JEE Main 10-Jan-2019 Morning]

A)
$\frac{\pi }{3}\,n\,\,\rho {{l}^{3}}$

B)
$\frac{\pi }{4}\,n\,\,\rho {{l}^{3}}$

C)
$n\,\,\rho {{l}^{3}}$

D)
$\pi n\,\,\rho {{l}^{3}}$

• question_answer116) A charge Q is distributed over three concentric spherical shells of radii a, b, c $\left( a<b<c \right)$ such that their surface charge densities are equal to one another. The total potential at a point at distance r from their common centre, where $r<a$, would be- [JEE Main 10-Jan-2019 Morning]

A)
$\frac{Q({{a}^{2}}+{{b}^{2}}+{{c}^{2}})}{{{4}_{\pi {{\varepsilon }_{0}}}}({{a}^{3}}+{{b}^{3}}+{{c}^{3}})}$

B)
$\frac{Q}{{{4}_{\pi {{\varepsilon }_{0}}}}(a+b+c)}$

C)
$\frac{Q}{{{12}_{\pi \varepsilon {{\,}_{0}}}}}\,\,\frac{ab+bc+ca}{abc}$

D)
$\frac{Q(a+b+c)}{{{4}_{\pi \varepsilon {{\,}_{0}}}}({{a}^{2}}+{{b}^{2}}+{{c}^{2}})}$

• question_answer117)  Four equal point charges Q each are placed in the xy plane at $\left( 0,\text{ }2 \right),\text{ }\left( 4,\text{ }2 \right),\text{ }\left( 4,\,-2 \right)\text{ }and\text{ }\left( 0,-\,2 \right)$. The work required to put a fifth charge Q at the origin of the coordinate system will be-[JEE Main 10-Jan-2019 Evening]

A)
$\frac{{{Q}^{2}}}{4\pi {{\varepsilon }_{0}}}$

B)
$\frac{{{Q}^{2}}}{2\sqrt{2}\pi {{\varepsilon }_{0}}}$

C)
$\frac{{{Q}^{2}}}{4\pi {{\varepsilon }_{0}}}\left( 1+\frac{1}{\sqrt{3}} \right)$

D)
$\frac{{{Q}^{2}}}{4\pi {{\varepsilon }_{0}}}\left( 1+\frac{1}{\sqrt{5}} \right)$

• question_answer118)  Charges -q and +q located at A and B. respectively, constitute an electric dipole. Distance $AB=2a$, 0 is the mid-point of the dipole and OP is perpendicular to AB. A charge Q is placed at P where $OP=y$ and $y\,\,>\,\,>\,\,2a$. The charge Q experiences an electrostatic force F. If Q is now moved along the equatorial line to P such that $OP'=\left( \frac{y}{3} \right)$,  the force on Q will be close to- $\left( \frac{y}{3}>>2a \right)$ [JEE Main 10-Jan-2019 Evening]

A)
9F

B)
3F

C)
F/3

D)
27F

• question_answer119) A   parallel   plate   capacitor   having capacitance 12 pF is charged by a battery to a potential difference of 10 V between its plates. The charging battery is now disconnected and a porcelain slab of dielectric constant 6.5 is slipped between the plates. The work done by the capacitor on the slab is: [JEE Main 10-Jan-2019 Evening]

A)
508 pJ

B)
692 pJ

C)
560 pJ

D)
600 pJ

• question_answer120)  Three charges $Q,+q$and $+q$ are placed at the vertices of a right-angle isosceles triangle as shown below. The net electrostatic energy of the configuration is zero, if the value of Q is- [JEE Main 11-Jan-2019 Morning]

A)
$+q$

B)
$-2q$

C)
$\frac{-\sqrt{2}q}{\sqrt{2}+1}$

D)
$\frac{-q}{1+\sqrt{2}}$

• question_answer121)  The given graph shows variation (with distance r from centre) of-       [JEE Main 11-Jan-2019 Morning]

A)
Electric field of a uniformly charged spherical shell

B)
Electric field of a uniformly charged sphere

C)
Potential of a uniformly charged spherical shell

D)
Potential of a uniformly charged sphere

• question_answer122) A particle is moving along a circular path with a constant speed of $10m{{s}^{-1}}$. What is the magnitude of the change in velocity of the particle, when it moves through an angle of $60{}^\circ$ around the centre of the circle? [JEE Main 11-Jan-2019 Morning]

A)
zero

B)
$10\sqrt{2}m/s$

C)
$10\sqrt{3}m/s$

D)
$10\,m/s$

• question_answer123) An electric field of 1000 V/m is applied to an electric dipole at angle of $45{}^\circ$. The value of electric dipole moment is ${{10}^{-29}}Cm.$What is the potential energy of the electric dipole?       [JEE Main 11-Jan-2019 Evening]

A)
$-10\times {{10}^{-29}}J$

B)
$-7\times {{10}^{-27}}J$

C)
$-20\times {{10}^{-18}}J$

D)
$-9\times {{10}^{-20}}J$

• question_answer124) Seven capacitors, each of capacitance $2\mu F,$are to be connected in a configuration to obtain an effective capacitance of $\left( \frac{6}{13} \right)\mu F,$Which of the combinations, shown in figures below, will achieve the desired value? [JEE Main 11-Jan-2019 Evening]

A)

B)

C)

D)

• question_answer125) There is a uniform spherically symmetric surface charge density at a distance ${{R}_{0}}$ from the origin. The charge distribution is initially at rest and starts expanding because of mutual repulsion. The figure that represents best the speed V(R(t)) of the distribution as a function of its instantaneous radius R(t) is- [JEE Main 12-Jan-2019 Morning]

A)

B)

C)

D)

• question_answer126)  Determine the electric dipole moment of the system of three charges, placed on the vertices of an equilateral triangle, as shown in the figure. [JEE Main 12-Jan-2019 Morning]

A)
$2ql\,\hat{j}$

B)
$(ql)\,\frac{\hat{i}+\,\hat{j}}{\sqrt{2}}$

C)
$\sqrt{3}ql\,\frac{\,\hat{j}-\hat{i}}{\sqrt{2}}$

D)
$-\sqrt{3}ql\,\hat{j}$

• question_answer127) The bob of a simple pendulum has mass 2g and a charge of $5.0\mu C.$It is at rest in a uniform horizontal electric field of intensity 2000 V/m. At equilibrium, the angle that the pendulum makes with the vertical is: $(take\,g=10m/{{s}^{2}})$ [JEE Main 8-4-2019 Morning]

A)
${{\tan }^{-1}}(5.0)$

B)
${{\tan }^{-1}}(2.0)$

C)
${{\tan }^{-1}}(0.5)$

D)
${{\tan }^{-1}}(0.2)$

• question_answer128) Voltage rating of a parallel plate capacitor is 500V. Its dielectric can withstand a maximum electric field of ${{10}^{6}}$ V/m. The plate area is ${{10}^{-4}}{{m}^{2}}.$What is the dielectric constant is the capacitance is 15 pF? (given ${{\in }_{0}}=8.86\times {{10}^{-12}}{{C}^{2}}/N{{m}^{2}}$) [JEE Main 8-4-2019 Morning]

A)
3.8

B)
4.5

C)
6.2

D)
8.5

• question_answer129) A solid conducting sphere, having a charge Q, is surrounded by an uncharged conducting hollow spherical shell. Let the potential difference between the surface of the solid sphere and that of the outer surface of the hollow shell be V. If the shell is now given a charge of -4 Q, the new potential difference between the same two surfaces is:      [JEE Main 8-4-2019 Morning]

A)
V

B)
2V

C)
-2V

D)
4V

• question_answer130) An electric dipole is formed by two equal and opposite charges q with separation d. The charges have same mass m. It is kept in a uniform electric field E. If it is slightly rotated from its equilibrium orientation, then its angular frequency $\omega$is :- [JEE Main 8-4-2019 Afternoon]

A)
$\sqrt{\frac{qE}{2md}}$

B)
$\sqrt{\frac{qE}{md}}$

C)
$\sqrt{\frac{2qE}{md}}$

D)
$\sqrt{\frac{qE}{md}}$

• question_answer131)  A positive point charge is released from rest at a distance${{r}_{0}}$from a positive line charge with uniform density. The speed (v) of the point charge, as a function of instantaneous distance r from line charge, is proportional to :- [JEE Main 8-4-2019 Afternoon]

A)
$\text{v}\propto {{\text{e}}^{+r/{{r}_{0}}}}$

B)
$\text{v}\propto \ell n\left( \frac{r}{{{r}_{0}}} \right)$

C)
$\text{v}\propto \left( \frac{r}{{{r}_{0}}} \right)$

D)
$\text{v}\propto \sqrt{\ell n\left( \frac{r}{{{r}_{0}}} \right)}$

• question_answer132) The electric field in a region is given by $\overrightarrow{E}=\left( Ax+B \right)\hat{i},$ where E is in $N{{C}^{-1}}$ and x is in metres. The values of constants are A = 20 SI unit and B = 10 SI unit. If the potential at x = 1 is ${{V}_{1}}$and that at x = -5 is ${{V}_{2}}$, then ${{V}_{1}}-{{V}_{2}}$ is :- [JEE Main 8-4-2019 Afternoon]

A)
- 48 V

B)
- 520 V

C)
180 V

D)
320 V

• question_answer133) A parallel plate capacitor has$1\mu F$ capacitance. One of its two plates is given$+2\mu C$charge and the other plate, $+4\mu C$ charge. The potential difference developed across the capacitor is:- [JEE Main 8-4-2019 Afternoon]

A)
5V

B)
2V

C)
3V

D)
1V

• question_answer134)  A system of three charges are placed as shown in the figure : If $D>>d,$the potential energy of the system is best given by:         [JEE Main 9-4-2019 Morning]

A)
$\frac{1}{4\pi {{\varepsilon }_{0}}}\left[ -\frac{{{q}^{2}}}{d}-\frac{qQd}{2{{D}^{2}}} \right]$

B)
$\frac{1}{4\pi {{\varepsilon }_{0}}}\left[ +\frac{{{q}^{2}}}{d}+\frac{qQd}{{{D}^{2}}} \right]$

C)
$\frac{1}{4\pi {{\varepsilon }_{0}}}\left[ -\frac{{{q}^{2}}}{d}+\frac{2qQd}{{{D}^{2}}} \right]$

D)
$\frac{1}{4\pi {{\varepsilon }_{0}}}\left[ -\frac{{{q}^{2}}}{d}-\frac{qQd}{{{D}^{2}}} \right]$

• question_answer135) Four point charges $q,+q,+q$and -q are placed on y-axis at $y=2d,y=d,y=+d$ and $y=+2d,$respectively. The magnitude of the electric field E at a point on the x-axis at $x=D,$ with $D>>d,$will behave as :- [JEE Main 9-4-2019 Afternoon]

A)
$E\propto \frac{1}{D}$

B)
$E\propto \frac{1}{{{D}^{3}}}$

C)
$E\propto \frac{1}{{{D}^{2}}}$

D)
$E\propto \frac{1}{{{D}^{4}}}$

• question_answer136) The parallel combination of two air filled parallel plate capacitors of capacitance C and nC is connected to a battery of voltage, V. When the capacitors are fully charged, the battery is removed and after that a dielectric material of dielectric constant K is placed between the two plates of the first capacitor. The new potential difference of the combined system is :- [JEE Main 9-4-2019 Afternoon]

A)
$\frac{V}{K+n}$

B)
$V$

C)
$\frac{(n+1)V}{(K+n)}$

D)
$\frac{nV}{K+n}$

• question_answer137)  Figure shows charge (q) versus voltage (V) graph for series and parallel combination of two given capacitors. The capacitances are : [JEE Main 10-4-2019 Morning]

A)
$50\mu F\text{ }and\text{ }30\mu F$

B)
$20\mu F\text{ }and\text{ }30\mu F$

C)
$60\mu F\text{ }and\text{ }40\mu F$

D)
$40\mu F\text{ }and\text{ }10\mu F$

• question_answer138) A uniformly charged ring of radius 3a and total charge q is placed in xy-plane centred at origin. A point charge q is moving towards the ring along the z-axis and has speed u at z = 4a. The minimum value of u such that it crosses the origin is :      [JEE Main 10-4-2019 Morning]

A)
$\sqrt{\frac{2}{m}}{{\left( \frac{1}{15}\frac{{{q}^{2}}}{4\pi {{\varepsilon }_{0}}a} \right)}^{1/2}}$

B)
$\sqrt{\frac{2}{m}}{{\left( \frac{2}{15}\frac{{{q}^{2}}}{4\pi {{\varepsilon }_{0}}a} \right)}^{1/2}}$

C)
$\sqrt{\frac{2}{m}}{{\left( \frac{4}{15}\frac{{{q}^{2}}}{4\pi {{\varepsilon }_{0}}a} \right)}^{1/2}}$

D)
$\sqrt{\frac{2}{m}}{{\left( \frac{1}{5}\frac{{{q}^{2}}}{4\pi {{\varepsilon }_{0}}a} \right)}^{1/2}}$

• question_answer139)  A simple pendulum of length L is placed between the plates of a parallel plate capacitor having electric field E, as shown in figure. Its bob has mass m and charge q. The time period of the pendulum is given by : [JEE Main 10-4-2019 Afternoon]

A)
$2\pi \sqrt{\frac{L}{\sqrt{{{g}^{2}}+{{\left( \frac{qE}{m} \right)}^{2}}}}}$

B)
$2\pi \sqrt{\frac{L}{\sqrt{g+\left( \frac{qE}{m} \right)}}}$

C)
$2\pi \sqrt{\frac{L}{\left( g-\begin{matrix} qE \\ m \\ \end{matrix} \right)}}$

D)
$2\pi \sqrt{\frac{L}{\left( {{g}^{2}}-\begin{matrix} {{q}^{2}}{{E}^{2}} \\ {{m}^{2}} \\ \end{matrix} \right)}}$

• question_answer140) In free space, a particle A of charge $1\mu C$is held fixed at a point P. Another particle B of the same charge and mass $4\mu g$is kept at a distance of 1 mm from P. if B is released, then its velocity at a distance of 9 mm from P is : $\left[ \text{Take}\frac{1}{4\pi {{\varepsilon }_{0}}}=9\times {{10}^{9}}N{{m}^{2}}{{C}^{-2}} \right]$ [JEE Main 10-4-2019 Afternoon]

A)
$2.0\times {{10}^{3}}m/s$

B)
$3.0\times {{10}^{4}}m/s$

C)
$1.5\times {{10}^{2}}m/s$

D)
$1.0\,m/s$

• question_answer141)  Shown in the figure is a shell made of a conductor. It has inner radius a and outer radius b, and carries charge Q. At its centre is a dipole $\vec{p}$ as shown. In this case: [JEE Main Held on 12-4-2019 Morning]

A)
Electric field outside the shell is the same as that of a point charge at the centre of the shell.

B)
Surface charge density on the inner surface of the shell is zero everywhere.

C)
Surface charge density on the inner surface is uniform and equal to $\frac{(Q/2)}{4\pi {{a}^{2}}}.$

D)
Surface charge density on the outer surface depends on $\left| {\vec{p}} \right|$

• question_answer142)  Two identical parallel plate capacitors, of capacitance C each, have plates of area A, separated by a distance d. The space between the plates of the two capacitors, is filled with three dielectrics, of equal thickness and dielectric constants ${{K}_{1}},{{K}_{2}}$and ${{K}_{3}}.$The first capacitor is filled as shown in fig. I, and the second one is filled as shown in fig. II. If these two modified capacitors are charged by the same potential V, the ratio of the energy stored in the two, would be (${{E}_{1}}$refers to capacitor (I) and ${{E}_{2}}$to capacitor (II)): [JEE Main Held on 12-4-2019 Morning]

A)
$\frac{{{E}_{1}}}{{{E}_{2}}}=\frac{9{{K}_{1}}{{K}_{2}}{{K}_{3}}}{({{K}_{1}}+{{K}_{2}}+{{K}_{2}})({{K}_{2}}{{K}_{3}}+{{K}_{3}}{{K}_{1}}+{{K}_{1}}{{K}_{2}})}$

B)
$\frac{{{E}_{1}}}{{{E}_{2}}}=\frac{{{K}_{1}}{{K}_{2}}{{K}_{3}}}{({{K}_{1}}+{{K}_{2}}+{{K}_{2}})({{K}_{2}}{{K}_{3}}+{{K}_{3}}{{K}_{1}}+{{K}_{1}}{{K}_{2}})}$

C)
$\frac{{{E}_{1}}}{{{E}_{2}}}=\frac{({{K}_{1}}+{{K}_{2}}+{{K}_{2}})({{K}_{2}}{{K}_{3}}+{{K}_{3}}{{K}_{1}}+{{K}_{1}}{{K}_{2}})}{{{K}_{1}}{{K}_{2}}{{K}_{3}}}$

D)
$\frac{{{E}_{1}}}{{{E}_{2}}}=\frac{({{K}_{1}}+{{K}_{2}}+{{K}_{2}})({{K}_{2}}{{K}_{3}}+{{K}_{3}}{{K}_{1}}+{{K}_{1}}{{K}_{2}})}{9{{K}_{1}}{{K}_{2}}{{K}_{3}}}$

• question_answer143) A point dipole $\vec{p}=-{{p}_{0}}\hat{x}$is kept at the origin. The potential and electric field due to this dipole on the y-axis at a distance d are, respectively: [JEE Main Held on 12-4-2019 Morning] (Take V = 0 at infinity):

A)
$\frac{|\vec{p}|}{4\pi {{\varepsilon }_{0}}{{d}^{2}}},\frac{-\vec{p}}{4\pi {{\varepsilon }_{0}}{{d}^{3}}}$

B)
$0,\frac{{\vec{p}}}{4\pi {{\varepsilon }_{0}}{{d}^{3}}}$

C)
$\frac{|\vec{p}|}{4\pi {{\varepsilon }_{0}}{{d}^{3}}},\frac{{\vec{p}}}{4\pi {{\varepsilon }_{0}}{{d}^{3}}}$

D)
$0,\frac{-\vec{p}}{4\pi {{\varepsilon }_{0}}{{d}^{3}}}$

• question_answer144) A thin ring of 10 cm radius carries a uniformly distributed charge. The ring rotates at a constant angular speed of $40\pi \,rad\,{{s}^{-1}}$about its axis, perpendicular to its plane. If the magnetic field at its centre is $3.8\times {{10}^{9}}T,$then the charge carried by the ring is close to $({{\mu }_{0}}=4\pi \times {{10}^{7}}\text{ }N/{{A}^{2}})$ : [JEE Main Held on 12-4-2019 Morning]

A)
$2\times {{10}^{-6}}C$

B)
$3\times {{10}^{-5}}C$

C)
$4\times {{10}^{-5}}C$

D)
$7\times {{10}^{-6}}C$

• question_answer145) Let a total charge 2Q be distributed in a sphere of radius R, with the charge density given by $\rho (r)=kr,$where r is the distance from the centre. Two charges A and B, of -Q each, are placed on diametrically opposite points, at equal distance, a, from the centre. If A and B do not experience any force, then: [JEE Main 12-4-2019 Afternoon]

A)
$a=\frac{3R}{{{2}^{{}^{1}/{}_{4}}}}$

B)
$a=R/\sqrt{3}$

C)
$a={{8}^{-1/4}}R$

D)
$a={{2}^{-1/4}}R$

• question_answer146)  A parallel plate capacitor has plates of area A separated by distance d between them. It is filled with a dielectric which has a dielectric constant that varies as $k(x)=K(1+\alpha x)$ where x is the distance measured from one of the plates. If $(\alpha d)<<1$, the total capacitance of the system is best given by the expression [JEE MAIN Held on 07-01-2020 Morning]

A)
$\frac{AK{{\varepsilon }_{0}}}{d}(1+\alpha d)$

B)
$\frac{A{{\varepsilon }_{0}}K}{d}\left( 1+\frac{{{\alpha }^{2}}{{d}^{2}}}{2} \right)$

C)
$\frac{AK{{\varepsilon }_{0}}}{d}\left( 1+\frac{\alpha d}{2} \right)$

D)
$\frac{A{{\varepsilon }_{0}}K}{d}\left( 1+{{\left( \frac{\alpha d}{2} \right)}^{2}} \right)$

• question_answer147)  Two infinite planes each with uniform surface charge density $+\sigma$ are kept in such a way that the angle between them is $30{}^\circ$. The electric field in the region shown between them is given by [JEE MAIN Held on 07-01-2020 Morning]

A)
$\frac{\sigma }{2{{\varepsilon }_{0}}}\left[ \left( 1+\sqrt{3} \right)\hat{y}+\frac{{\hat{x}}}{2} \right]$

B)
$\frac{\sigma }{2{{\varepsilon }_{0}}}\left[ \left( 1+\sqrt{3} \right)\hat{y}-\frac{{\hat{x}}}{2} \right]$

C)
$\frac{\sigma }{2{{\varepsilon }_{0}}}\left[ \left( 1-\frac{\sqrt{3}}{2} \right)\hat{y}-\frac{{\hat{x}}}{2} \right]$

D)
$\frac{\sigma }{{{\varepsilon }_{0}}}\left[ \left( 1+\frac{\sqrt{3}}{2} \right)\hat{y}+\frac{{\hat{x}}}{2} \right]$

• question_answer148) A 60 pF capacitor is fully charged by a 20 V supply. It is then disconnected from the supply and is connected to another uncharged 60 pF capacitor in parallel. The electrostatic energy that is lost in this process by the time the charge is redistributed between them is (in nJ) _________. [JEE MAIN Held on 07-01-2020 Evening]

• question_answer149) Effective capacitance of parallel combination of two capacitors ${{C}_{1}}$and ${{C}_{2}}$is$10\mu F$. When these capacitors are individually connected to a voltage source of 1 V, the energy stored in the capacitor ${{C}_{2}}$is 4 times that of${{C}_{1}}$. If these capacitors are connected in series, their effective capacitance will be : [JEE MAIN Held On 08-01-2020 Morning]

A)
1.6 $\mu F$

B)
3.2 $\mu F$

C)
4.2 $\mu F$

D)
8.4 $\mu F$

• question_answer150)  Three charged particles A, B and C wit charges -4q, 2q and -2q are present on the circumference of a circle of radius d. The charged particles A, C and centre O of the circle formed an equilateral triangle as shown in figure. Electric field at O along x-direction is [JEE MAIN Held On 08-01-2020 Morning]

A)
$\frac{\sqrt{3}q}{\pi {{\varepsilon }_{0}}{{d}^{2}}}$

B)
$\frac{3\sqrt{3}q}{4\pi {{\varepsilon }_{0}}{{d}^{2}}}$

C)
$\frac{\sqrt{3}q}{4\pi {{\varepsilon }_{0}}{{d}^{2}}}$

D)
$\frac{2\sqrt{3}q}{\pi {{\varepsilon }_{0}}{{d}^{2}}}$

• question_answer151) In finding the electric field using Gauss law the Formula $\left| {\vec{E}} \right|=\frac{{{q}_{enc}}}{{{\varepsilon }_{0}}\left| A \right|}$ is applicable. In the formula${{\varepsilon }_{0}}$ is permittivity of free space, A is the area of Gaussian surface and ${{q}_{enc}}$is charge enclosed by the Gaussian surface. This equation can be used in which of the following situation? [JEE MAIN Held On 08-01-2020 Morning]

A)
Only when the Gaussian surface is an equipotential surface and $\left| {\vec{E}} \right|$ is constant on The surface.

B)
Only when$\left| {\vec{E}} \right|=$ constant on the surface.

C)
Only when the Gaussian surface is a equipotential surface.

D)
For any choice of Gaussian surface.

• question_answer152) A particle of mass m and charge q is released from rest in a uniform electric field. If there is no other force on the particle, the dependence of its speed v on the distance x travelled by it is correctly given by (graphs are schematic and not drawn to scale)  [JEE MAIN Held on 08-01-2020 Evening]

A)

B)

C)

D)

• question_answer153)  A capacitor is made of two square plates each of side a making a very small angle $\alpha$ between them, as shown in figure. The capacitance will be close to [JEE MAIN Held on 08-01-2020 Evening]

A)
$\frac{{{\varepsilon }_{0}}{{a}^{2}}}{d}\left( 1-\frac{3\alpha a}{2d} \right)$

B)
$\frac{{{\varepsilon }_{0}}{{a}^{2}}}{d}\left( 1-\frac{\alpha a}{2d} \right)$

C)
$\frac{{{\varepsilon }_{0}}{{a}^{2}}}{d}\left( 1+\frac{\alpha a}{d} \right)$

D)
$\frac{{{\varepsilon }_{0}}{{a}^{2}}}{d}\left( 1-\frac{\alpha a}{4d} \right)$

• question_answer154) Consider two charged metallic spheres ${{S}_{1}}$ and ${{S}_{2}}$ of radii ${{R}_{1}}$ and${{R}_{2}}$, respectively. The electric fields ${{E}_{1}}$ (on ${{S}_{1}}$) and ${{E}_{2}}$ (on ${{S}_{2}}$) on their surfaces are such that ${{E}_{1}}$/${{E}_{2}}$ = ${{R}_{1}}$/${{R}_{2}}$. Then the ratio ${{V}_{1}}$(on ${{S}_{1}}$)/${{V}_{2}}$(on ${{S}_{2}}$) of the electrostatic potentials on each sphere is [JEE MAIN Held on 08-01-2020 Evening]

A)
${{\left( {{R}_{1}}\text{/}{{R}_{2}} \right)}^{2}}$

B)
$\left( {{R}_{2}}\text{/}{{R}_{1}} \right)$

C)
${{\left( \frac{{{R}_{1}}}{{{R}_{2}}} \right)}^{3}}$

D)
${{R}_{1}}/{{R}_{2}}$

• question_answer155)  Consider a sphere of radius R which carries a uniform charge density$\rho$. If a sphere of radius $\frac{R}{2}$is carved out of it, as shown, the ratio $\frac{\left| {{{\vec{E}}}_{A}} \right|}{\left| {{{\vec{E}}}_{B}} \right|}$ of magnitude of electric field ${{\vec{E}}_{A}}$ and ${{\vec{E}}_{B}}$respectively, at points A and B due to the remaining portion is: [JEE MAIN Held on 09-01-2020 Morning]

A)
$\frac{18}{34}$

B)
$\frac{18}{54}$

C)
$\frac{21}{34}$

D)
$\frac{17}{54}$

• question_answer156)  An electric field $\vec{E}=4\text{x}\hat{i}-({{y}^{2}}+1)\hat{j}\,\,N/C$ passes through the box shown in figure. The flux of the electric field through surfaces ABCD and BCGF are marked as ${{\phi }_{l}}$ and ${{\phi }_{ll}}$ respectively. The difference between $({{\phi }_{l}}-{{\phi }_{ll}})$ is (in$N{{m}^{2}}/C$) ______. [JEE MAIN Held on 09-01-2020 Evening]