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

### done NEET PYQ - Electrostatics and Capacitance Total Questions - 82

• question_answer1) A point Q lies on die perpendicular bisector of an electrical dipole of dipole moment p. If the distance of Q from the dipole is r (much larger than the size of the dipole) then electric field at Q is proportional to:               [AIPMT 1998]

A)
${{p}^{-1}}$ and ${{r}^{2}}$

B)
$p$ and ${{r}^{-2}}$

C)
${{p}^{2}}$ and ${{r}^{-3}}$

D)
$p$ and ${{r}^{-3}}$

• question_answer2) A particle of mass m and charge q is placed at rest in a uniform electric field E and then released. The kinetic energy attained by the particle after moving a distance y is :               [AIPMT 1998]

A)
$qE{{y}^{2}}$

B)
$q{{E}^{2}}y$

C)
$qEy$

D)
${{q}^{2}}Ey$

• question_answer3) A hollow insulated conducting sphere is given a positive charge of $10\,\mu C$. What will be the electric field at the centre of the sphere if its radius is 2 m? [AIPMT 1998]

A)
Zero

B)
$5\,\mu \,C{{m}^{-2}}$

C)
$20\,\mu \,C{{m}^{-2}}$

D)
$8\,\mu \,C{{m}^{-2}}$

• question_answer4) When air is replaced by a dielectric medium of constant K, the maximum force of attraction between two charges, separated by a distance: [AIPMT 1999]

A)
decreases K times

B)
increase K times

C)
remains unchanged

D)
becomes $\frac{1}{{{K}^{2}}}$times

• question_answer5) In bringing an electron towards another electron, the electrostatic potential energy of the system: [AIPMT 1999]

A)
decreases

B)
increases

C)
remains same

D)
becomes zero

• question_answer6) A parallel plate condenser with oil (dielectric constant 2) between the plates has capacitance C. If oil is removed, the capacitance of capacitor becomes:                             [AIPMT 1999]

A)
$\sqrt{2}\,C$

B)
2 C

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

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

• question_answer7)  The effective capacitance between points x and y of figure shown is:            [AIPMT 1999]

A)
$6\,\mu F$

B)
$12\,\mu F$

C)
$18\,\mu F$

D)
$24\,\mu F$

• question_answer8) When a proton is accelerated through 1V its kinetic energy will be:                [AIPMT 1999]

A)
1540 eV

B)
13.6 eV

C)
1 eV

D)
zero

• question_answer9) A capacitor is charged by connecting a battery across its plates. It stores energy U. Now the battery is disconnected and another identical capacitor is connected across it, then the energy stored by both capacitors of the system will be:                                             [AIPMT 2000]

A)
U

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

C)
2U

D)
$\frac{3}{2}U$

• question_answer10) A charged wire is bent in the form of a semi-circular arc of radius a. If charge per unit length is $\lambda$  coulomb/metre, the electric field at the centre O is:

A)
$\frac{\lambda }{2\pi {{a}^{2}}{{\varepsilon }_{0}}}$

B)
$\frac{\lambda }{4{{\pi }^{2}}{{\varepsilon }_{0}}a}$

C)
$\frac{\lambda }{2{{\pi }^{2}}{{\varepsilon }_{0}}a}$

D)
zero

• question_answer11) A man goes at the top of a smooth inclined plane. He releases a bag to fall freely and he himself slides on inclined plane to reach the bottom. If ${{v}_{1}}$ and ${{v}_{2}}$ are the velocities of the man and bag respectively, then: [AIPMT 2000]

A)
${{v}_{1}}>{{v}_{2}}$

B)
${{v}_{1}}<{{v}_{2}}$

C)
${{v}_{1}}={{v}_{2}}$

D)
${{v}_{1}}$ and ${{v}_{2}}$ cannot be compared

• question_answer12) The reactance of a capacitor of capacitance C is X. If both the frequency and capacitance be doubled, then new reactance will be: [AIPMT 2001]

A)
X

B)
2X

C)
4X

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

• question_answer13) In a parallel plate capacitor, the distance between the plates is d and potential difference across plates is V. Energy stored per unit volume between the plates of capacitor is:        [AIPMT 2001]

A)
$\frac{{{Q}^{2}}}{2{{V}^{2}}}$

B)
$\frac{1}{2}{{\varepsilon }_{0}}\frac{{{V}^{2}}}{{{d}^{2}}}$

C)
$\frac{1}{2}\frac{{{V}^{2}}}{{{\varepsilon }_{0}}{{d}^{2}}}$

D)
$\frac{1}{2}{{\varepsilon }_{0}}\frac{{{V}^{2}}}{{{d}^{2}}}$

• question_answer14) A charge $q\mu C$ is placed at the centre of a cube of a side 0.1 m, then the electric flux diverging from each face of the cube is:                    [AIPMT 2001]

A)
$\frac{q\times {{10}^{-6}}}{24{{\varepsilon }_{0}}}$

B)
$\frac{q\times {{10}^{-4}}}{{{\varepsilon }_{0}}}$

C)
$\frac{q\times {{10}^{-6}}}{6{{\varepsilon }_{0}}}$

D)
$\frac{q\times {{10}^{-4}}}{12{{\varepsilon }_{0}}}$

• question_answer15) Torque acting on electric dipole of dipole moment $\vec{p}$ placed in uniform electric field $\vec{E}$ is:         [AIPMT 2001]

A)
$\vec{p}\times \vec{E}$

B)
$\vec{p}\,.\,\vec{E}$

C)
$\vec{p}\times \vec{E}\times \vec{p}$

D)
$\frac{\vec{E}\,.\,\vec{p}}{{{p}^{2}}}$

• question_answer16) Some charge is being given to a conductor then its potential is:                               [AIPMT 2002]

A)
maximum at surface

B)
maximum at centre

C)
same throughout the conductor

D)
maximum somewhere between surface and centre

• question_answer17) A capacitor of capacity ${{C}_{1}}$ is charged upto potential V volt and then connected in parallel to an uncharged capacitor of capacity ${{C}_{2}}$. The final potential difference across each capacitor will be: [AIPMT 2002]

A)
$\frac{{{C}_{2}}V}{{{C}_{1}}+{{C}_{2}}}$

B)
$\frac{{{C}_{1}}V}{{{C}_{1}}+{{C}_{2}}}$

C)
$\left( 1+\frac{{{C}_{2}}}{{{C}_{1}}} \right)V$

D)
$\left( 1-\frac{{{C}_{2}}}{{{C}_{1}}} \right)V$

• question_answer18) Identical charges $(-q)$ are placed at each corners of a cube of side b, then the electrostatic potential energy of charge $(+q)$ placed at the centre of the cube will be:

A)
$-\frac{4\sqrt{2}{{q}^{2}}}{\pi {{\varepsilon }_{0}}}$

B)
$\frac{8\sqrt{2}{{q}^{2}}}{\pi {{\varepsilon }_{0}}b}$

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

D)
$\frac{8\sqrt{2}{{q}^{2}}}{4\pi {{\varepsilon }_{0}}b}$

• question_answer19) An electron is moving round the nucleus of a hydrogen atom in a circular orbit of radius r. The coulomb force $\vec{F}$ between the two is: [AIPMT 2003]

A)
$k\frac{{{e}^{2}}}{{{r}^{3}}}\vec{r}$

B)
$-k\,\frac{{{e}^{2}}}{{{r}^{3}}}\vec{r}$

C)
$k\frac{{{e}^{2}}}{{{r}^{2}}}\hat{r}$

D)
$-k\frac{{{e}^{2}}}{{{r}^{3}}}\hat{r}$

• question_answer20) A charge q is located at the centre of a cube. The electric flux through any face is:   [AIPMT 2003]

A)
$\frac{\pi q}{6(4\pi {{\varepsilon }_{0}})}$

B)
$\frac{q}{6(4\pi {{\varepsilon }_{0}})}$

C)
$\frac{2\pi q}{6(4\pi {{\varepsilon }_{0}})}$

D)
$\frac{4\pi q}{6(4\pi {{\varepsilon }_{0}})}$

• question_answer21) Three capacitors each of capacity $4\,\mu F$ are to be connected in such a way that the effective capacitance is $6\,\mu F$. This can be done by: [AIPMT 2003]

A)
connecting two in series and one in parallel

B)
connecting two in parallel and one in series

C)
connecting all of diem in series

D)
connecting all of them in parallel

• question_answer22) An electric dipole has the magnitude of its charge as q and its dipole moment is p. It is placed in a uniform electric field E. If its dipole moment is along the direction of the field, the force on it and its potential energy are respectively: [AIPMT (S) 2004]

A)
$2qE$ and minimum.

B)
$qE$ and $pE$

C)
zero and minimum

D)
$qE$ and maximum

• question_answer23) A bullet of mass 2g is having a charge of $2\,\mu C$. Through what potential difference must it be accelerated, starting from rest, to acquire a speed of 10 m/s?               [AIPMT (S) 2004]

A)
5 kV

B)
50 kV

C)
5 V

D)
50 V

• question_answer24)  A network of four capacitors of capacity equal to ${{C}_{1}}=C,\text{ }{{C}_{2}}=2C,\text{ }{{C}_{3}}=3C$ and ${{C}_{4}}=4C$ are connected to a battery as shown in the figure The ratio of the charges on ${{C}_{2}}$ an ${{C}_{4}}$ is: [AIPMT (S) 2005]

A)
$\frac{22}{3}$

B)
$\frac{3}{22}$

C)
$\frac{7}{4}$

D)
$\frac{4}{7}$

• question_answer25) As per this diagram a point charge +q is placed at the origin O. Work done in taking another point chargeQ  from the point A [co-ordinates $(0,\,\,a)$] to another points [co-ordinates $(a,\text{ }0)$] along the straight path AB is:                  [AIPMT (S) 2005]

A)
zero

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

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

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

• question_answer26)  As a result of change in the magnetic flux linked to the closed loop shown in the figure, an emf V volt is induced in the loop. The work done (joules) in taking a charge Q coulomb once along the loop is: [AIPMT (S) 2005]

A)
QV

B)
zero

C)
2 QV

D)
QV/2

• question_answer27)  Two charges ${{q}_{1}}$ and ${{q}_{2}}$ are placed 30 cm apart as shown in the figure. A third charge ${{q}_{3}}$ is moved along the arc of a circle of radius 40 cm from C to D. The change in the potential energy of the system is $\frac{{{q}_{3}}}{4\pi {{\varepsilon }_{0}}}\,k,$ where k is:                                               [AIPMT (S) 2005]

A)
$8\,{{q}_{2}}$

B)
$8\,{{q}_{1}}$

C)
$6\,{{q}_{2}}$

D)
$6\,{{q}_{1}}$

• question_answer28) An electric dipole of moment $\vec{p}$ is lying along a uniform electric field $\vec{E}$. The work done in rotating the dipole by ${{90}^{o}}$ is. [AIPMT (S) 2006]

A)
$\sqrt{2}\,pE$

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

C)
$2\text{ }pE$

D)
pE

• question_answer29) A parallel plate air capacitor is charged to a potential difference of V volts. After disconnecting the charging battery the distance between the plates of the capacitor is increased using an insulating handle. As a result the potential difference between the plates:  [AIPMT (S) 2006]

A)
decreases

B)
does not change

C)
becomes zero

D)
increases

• question_answer30)  A square surface of side L m is in the plane of the paper. A uniform electric field $\vec{E}$ (V/m), also in the plane of the paper, is limited only to the lower half of the square surface, (see figure). The electric flux in SI units associated with the surface is: [AIPMT (S) 2006]

A)
$E{{L}^{2}}/(2{{\varepsilon }_{0}})$

B)
$E{{L}^{2}}/2$

C)
zero

D)
$E{{L}^{2}}$

• question_answer31) Three point charges $+q,-2q$ and $+q$ are placed at points $(x=0,y=a,z=0),$ $(x=0,y=0,z=0)$ and $(x=a,y=0,z=0),$ respectively. The magnitude and direction of the electric dipole moment vector of this charge assembly are: [AIPMT (S) 2007]

A)
$\sqrt{2}\,qa$ along $+y$ direction

B)
$\sqrt{2}\,qa$ along the line joining points $(x=0,y=0,z=0)$         and       $(x=a,y=a,z=0)$

C)
$qa$ along the line joining points $(x=0,y=0,z=0)$           and       $(x=a,y=a,z=0)$

D)
$\sqrt{2}\,qa$ along $+x$ direction

• question_answer32)  Two condensers, one of capacity C and the other of capacity $\frac{C}{2},$ are connected to a V volt battery, as shown. The work done in charging fully both the condensers is:                    [AIPMT (S) 2007]

A)
$2\,C{{V}^{2}}$

B)
$\frac{1}{4}\,C{{V}^{2}}$

C)
$\frac{3}{4}\,C{{V}^{2}}$

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

• question_answer33)  A hollow cylinder has a charge q coulomb within it. If $\phi$ is the electric flux in unit of voltmeter associated with the curved surface B, the  flux linked with the plane surface A in unit of voltmeter will be :     [AIPMT (S) 2007]

A)
$\frac{1}{2}\left( \frac{q}{{{\varepsilon }_{0}}}-\phi \right)$

B)
$\frac{q}{2\,{{\varepsilon }_{0}}}$

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

D)
$\frac{q}{{{\varepsilon }_{0}}}-\phi$

• question_answer34)  Charges $+q$ and $-q$ are placed at points A and B respectively which are a distance 2 L apart, C is the midpoint between A and S. The work done in moving a charge +Q along the semicircle CRD is:[AIPMT (S) 2007]

A)
$\frac{qQ}{4\pi {{\varepsilon }_{0}}L}$

B)
$\frac{qQ}{2\pi {{\varepsilon }_{0}}L}$

C)
$\frac{qQ}{6\pi {{\varepsilon }_{0}}L}$

D)
$-\frac{qQ}{6\pi {{\varepsilon }_{0}}L}$

• question_answer35) The electric potential at a point in free space due to a charge Q coulomb is $Q\times {{10}^{11}}V$. The electric field at that point is  [AIPMPT (S) 2008]

A)
$4\pi {{\varepsilon }_{0}}Q\times {{10}^{22}}V/m$

B)
$12\pi {{\varepsilon }_{0}}Q\times {{10}^{20}}V/m$

C)
$4\pi {{\varepsilon }_{0}}Q\times {{10}^{20}}V/m$

D)
$12\pi {{\varepsilon }_{0}}Q\times {{10}^{22}}V/m$

• question_answer36) The energy required to charge a parallel plate condenser of plate separation a and plate area of cross-section A such that the uniform electric field between the plates is E, is   [AIPMPT (S) 2008]

A)
$\frac{1}{2}{{\varepsilon }_{0}}{{E}^{2}}/Ad$

B)
${{\varepsilon }_{0}}{{E}^{2}}/Ad$

C)
${{\varepsilon }_{0}}{{E}^{2}}Ad$

D)
$\frac{1}{2}{{\varepsilon }_{0}}{{E}^{2}}Ad$

• question_answer37) Three concentric spherical shells have radii a, b and $c(a<b<c)$ and have surface charge densities   $\sigma ,\,-\sigma$ and $\sigma$ respectively.   If ${{V}_{A}},\,{{V}_{B}}$ and ${{V}_{C}}$ denote the potentials of the three shells, then for $C=a+b,$ we have [AIPMT (S) 2009]

A)
${{V}_{A}}={{V}_{C}}\ne {{V}_{B}}$

B)
${{V}_{C}}={{V}_{B}}\ne {{V}_{A}}$

C)
${{V}_{C}}\ne {{V}_{B}}\ne {{V}_{A}}$

D)
${{V}_{C}}={{V}_{B}}={{V}_{A}}$

• question_answer38) A student measures the terminal potential difference (V) of a cell (of emf s and internal resistance r) as a function of the current (I) flowing through it. The slope and intercept of the graph between V and I, then respectively, equal      [AIPMT (S) 2009]

A)
$\varepsilon$ and $-r$

B)
$-r$ and $\varepsilon$

C)
$r$ and $-\,\varepsilon$

D)
$-\,\varepsilon$ and $r$

• question_answer39) Three capacitors each of capacitance C and of breakdown voltage V are joined in series. The [Capacitance and breakdown voltage of the combination will be    [AIPMT (S) 2009]

A)
$\frac{C}{3},\,\frac{V}{3}$

B)
$3C,\,\,\frac{V}{3}$

C)
$\frac{C}{3},\,3V$

D)
$3C,\,3V$

• question_answer40) The electric potential at a point $(x,\text{ }y,\text{ }z)$ is given by $V=-{{x}^{2}}\,y-x{{z}^{3}}+4$ The electric field $\vec{E}$ at that point is [AIPMT (S) 2009]

A)
$\vec{E}=\hat{i}\,(2xy+{{z}^{3}})+\hat{j}\,{{x}^{2}}+\hat{k}\,3x{{z}^{2}}$

B)
$\vec{E}=\hat{i}\,2xy+\hat{j}({{x}^{2}}+{{y}^{2}})+\hat{k}\,(3xz-{{y}^{2}})$

C)
$\vec{E}=\hat{i}\,{{z}^{3}}+\hat{j}\,xyz+\hat{k}\,{{z}^{2}}$

D)
$\vec{E}\,=\,\hat{i}\,(2xy-{{z}^{3}})+\hat{j}\,x{{y}^{2}}+\hat{k}\,3{{z}^{2}}x$

• question_answer41) The mean free path of electrons in a metal is $4\times {{10}^{-8}}\,m$. The electric field which can give on an average 2 eV energy to an electron in the metal will be in unit of $V{{m}^{-1}}$               [AIPMT (S) 2009]

A)
$8\times {{10}^{7}}$

B)
$5\times {{10}^{-11}}$

C)
$8\times {{10}^{-11}}$

D)
$5\times {{10}^{7}}$

• question_answer42) Two positive ions, each carrying a charge q, are separated by a distance d. If F is the force of repulsion between the ions, the number of electrons missing from each ion will be (e being the charge on an electron)   [AIPMT (S) 2010]

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

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

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

D)
$\frac{4\pi {{\varepsilon }_{0}}F{{d}^{2}}}{{{q}^{2}}}$

• question_answer43)  A square surface of side L metre in the plane of the paper is placed in a uniform electric field E (volt/m) acting along the same place at an angle $\theta$ with the horizontal side of the square as shown in figure. The electric flux linked to the surface in unit of $V-m$, is                [AIPMT (S) 2010]

A)
$E{{L}^{2}}$

B)
$E{{L}^{2}}\cos \,\theta$

C)
$E{{L}^{2}}\sin \,\theta$

D)
0

• question_answer44) A series combination of n1 capacitors, each of value ${{C}_{1}},$ is charged by a source of potential difference 4V. When another parallel combination of ${{n}_{2}}$ capacitors, each of value ${{C}_{2}},$ 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                      [AIPMT (S) 2010]

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

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

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

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

• question_answer45) Two parallel metal plates having charges $+Q$ and $-Q$ face each other at a certain distance between them. If the plates are now dipped in kerosene oil tank, the electric field between the plates will [AIPMT (M) 2010]

A)
become zero

B)
increase

C)
decrease

D)
remain same

• question_answer46) The electric field at a distance $\frac{3R}{2}$ from the centre of a charged conducting spherical shell of radius R is E. The electric field at a distance $\frac{R}{2}$ from the centre of the sphere is           [AIPMT (M) 2010]

A)
zero

B)
E

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

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

• question_answer47) The electric potential V at any point $(x,y,z),$ all in metres in space is given by $V=4{{x}^{2}}$ volt. The electric field at the point $(1,0,2)$ in volt/metre is [AIPMT (M) 2011]

A)
8 along positive .X-axis

B)
16 along negative X-axis

C)
16 along positive X-axis

D)
8 along negative X-axis

• question_answer48)  Three charges, each $+q,$ are placed at the comers of an isosceles triangle ABC of sides Be and AC, 2a. D and E are the mid points of Be and CA. The work done in taking a charge Q from D to E is [AIPMT (M) 2011]

A)
$\frac{eqQ}{8\pi {{\varepsilon }_{0}}a}$

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

C)
zero

D)
$\frac{3qQ}{4\pi {{\varepsilon }_{0}}a}$

• question_answer49) A parallel plate condenser has a uniform electric field E(V/m) in the space between the plates. If the distance between the plates is d(m) and area of each plate is $A({{m}^{2}})$ the energy (joule) stored in the condenser is [AIPMT (S) 2011]

A)
$\frac{1}{2}{{\varepsilon }_{0}}{{E}^{2}}$

B)
${{\varepsilon }_{0}}EAd$

C)
$\frac{1}{2}{{\varepsilon }_{0}}{{E}^{2}}Ad$

D)
${{E}^{2}}Ad/{{\varepsilon }_{0}}$

• question_answer50) A charge Q is enclosed by a Gaussian spherical surface of radius R. If the radius is doubled, then the outward electric flux will    [AIPMT (S) 2011]

A)
be reduced to half

B)
remain the same

C)
be doubled

D)
increase four time

• question_answer51)  Pour electric charges $+q,+q,-q$ and $-q$ are placed at the comers of a square of side 2L (see figure). The electric potential at point A, mid-way between the two charges $+q$ and $+q,$ is [AIPMT (S) 2011]

A)
$\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{2q}{L}\left( 1+\frac{1}{\sqrt{5}} \right)$

B)
$\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{2q}{L}\left( 1-\frac{1}{\sqrt{5}} \right)$

C)
zero

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

• question_answer52) A uniform electric field and a uniform magnetic field are acting along the same direction in a certain region. If an electron is projected in the region such that its velocity is pointed along the direction of fields, then the electron [AIPMT (S) 2011]

A)
speed will decrease

B)
speed will increase

C)
will turn towards left of direction of motion

D)
will turn towards right of direction a motion

• question_answer53) A parallel plate condenser has a uniform electric field E(V/m) in the space between the plates. If the distance between the plates is d(m) and area of each plate is $A({{m}^{2}})$ the energy (joule) stored in the condenser is [AIPMT (S) 2011]

A)
$\frac{1}{2}{{\varepsilon }_{0}}{{E}^{2}}$

B)
${{\varepsilon }_{0}}EAd$

C)
$\frac{1}{2}{{\varepsilon }_{0}}{{E}^{2}}Ad$

D)
${{E}^{2}}Ad/{{\varepsilon }_{0}}$

• question_answer54) A parallel plate capacitor has a uniform electric field E in the space between the plates. If the distance between the plates is d and area of each plate is A, the energy stored in the capacitor is [AIPMT (M) 2012]

A)
$\frac{1}{2}{{\varepsilon }_{0}}{{E}^{2}}$

B)
${{E}^{2}}Ad/{{\varepsilon }_{0}}$

C)
$\frac{1}{2}{{\varepsilon }_{0}}{{E}^{2}}Ad$

D)
${{\varepsilon }_{0}}EAd$

• question_answer55) A cell having an emf e and internal resistance r is connected across a variable external resistance R. As the resistance R is increased, the plot of potential difference V across R is given by [AIPMT (M) 2012]

A)

B)

C)

D)

• question_answer56) An electric dipole of moment p is placed in an electric field of intensity E. The dipole acquires a position such that the axis of the dipole makes an angle $\theta$ with the direction of the field. Assuming that the potential energy of the dipole to be zero when $\theta ={{90}^{0}},$ the torque and the potential energy of the dipole will respectively be [AIPMT (S) 2012]

A)
$pE\sin \theta ,\,-pE\cos \theta$

B)
$pE\sin \theta ,-2\,pE\cos \theta$

C)
$pE\sin \theta ,-2pE\cos \theta$

D)
$pE\cos \theta ,-pE\sin \theta$

• question_answer57) Four point charges $-Q,\,-q,\text{ }2q$ and $2Q$ are placed, one at each comer of the square. The relation between Q and q for which the potential at the centre of the square is zero, is [AIPMT(S) 2012]

A)
$Q=-q$

B)
$Q=-\frac{1}{q}$

C)
$Q=q$

D)
$Q=\frac{1}{q}$

• question_answer58) What is the through a cube of side a if a point charge of q is a one of its corner? [AIPMT (S) 2012]

A)
$\frac{2q}{{{\varepsilon }_{0}}}$

B)
$\frac{q}{8{{\varepsilon }_{0}}}$

C)
$\frac{q}{{{\varepsilon }_{0}}}$

D)
$\frac{q}{2{{\varepsilon }_{0}}}6{{a}^{2}}$

• question_answer59)  Two pith balls carrying equal charges are suspended from a common point by strings of equal length, the equilibrium separation between them is r. Now the strings are rigidly clamped at half the height. The equilibrium separation between the balls now become.    [NEET 2013]

A)
${{\left( \frac{1}{\sqrt{2}} \right)}^{2}}$

B)
$\left( \frac{r}{\sqrt[3]{2}} \right)$

C)
$\left( \frac{2r}{\sqrt{3}} \right)$

D)
$\left( \frac{2r}{3} \right)$

• question_answer60)  A, B and C are three points in a uniform electric field. The electric potential is        [NEET 2013]

A)
maximum at A

B)
maximum at B

C)
maximum at C

D)
same at all the three points A, B and C A

• question_answer61) In a region, the potential is represented by $V(x,\,y,\,z)=6x-8xy-8y+6yz,$ where V is in volts and x, y, z are in metres. The electric force experienced by a charge of 2 coulomb situated at point $(1,\text{ }1,\text{ }1)$ is           [NEET 2014]

A)
$6\sqrt{5}N$

B)
$30\,N$

C)
$24\,N$

D)
$4\sqrt{35}N$

• question_answer62)  Two thin dielectric slabs of dielectric constants ${{K}_{1}}$ and ${{K}_{2}}({{K}_{1}}<{{K}_{2}})$ are inserted between plates of a parallel plate capacitor, as shown in the figure. The variation of electric field E between the plates with distance d as measured from plate P is correctly shown by                [NEET 2014]

A)

B)

C)

D)

• question_answer63) A conducting sphere of radius R is given a charge Q. The electric potential and the electric field at the centre of the sphere respectively are   [NEET 2014]

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

B)
$\frac{Q}{4\pi {{\varepsilon }_{0}}R}$ and zero

C)
$\frac{Q}{4\pi {{\varepsilon }_{0}}R}$ and $\frac{Q}{4\pi {{\varepsilon }_{0}}{{R}^{2}}}$

D)
Both are zero

• question_answer64) A parallel plate air capacitor of capacitance C is connected to a cell of emf V and then disconnected from it. A dielectric slab of dielectric constant K, which can just fill the air gap of the capacitor is now inserted in it. Which of the following is incorrect?                     [NEET 2015]

A)
The potential difference between the plates decreases K times

B)
The energy stored in the capacitor decreases K times

C)
The change in energy stored is $\frac{1}{2}C{{V}^{2}}\left( \frac{1}{K}-1 \right)$

D)
The charge on the capacitor is not conserved

• question_answer65) The electric field in a certain region is acting radially outward and is given by $E=Ar.\text{ }A$. charge contained in a sphere of radius $'a'$ centred at the origin of the field' will be given by [NEET 2015]

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

B)
$A{{\varepsilon }_{0}}{{a}^{2}}$

C)
$A\pi {{\varepsilon }_{0}}A{{a}^{3}}$

D)
${{\varepsilon }_{0}}A{{a}^{3}}$

• question_answer66) If potential (in volts) in a region is expressed as$V(x,y,z)=6xy-y+2yz,$ the electric field (in N/C) at point $(1,1,0)$is           [NEET (Re) 2015]

A)
$-(3\hat{i}+5\hat{j}+3\hat{k})$

B)
$-(6\hat{i}+5\hat{j}+2\hat{k})$

C)
$-(2\hat{i}+3\hat{j}+\hat{k})$

D)
$-(6\hat{i}+9\hat{j}+\hat{k})$

• question_answer67) A parallel plate air capacitor has capacity C, distance of separation between plates is d and potential difference V is applied between the plates. Force of attraction between the plates of the parallel plate air capacitor is    [NEET (Re) 2015]

A)
$\frac{{{C}^{2}}{{V}^{2}}}{2d}$

B)
$\frac{C{{V}^{2}}}{2d}$

C)
$\frac{C{{V}^{2}}}{d}$

D)
$\frac{{{C}^{2}}{{V}^{2}}}{2{{d}^{2}}}$

• question_answer68)  A capacitor of $2\mu F$ is charged as shown in the diagram. When the switch S is turned to position 2, the percentage of its stored energy dissipated is:                                              [NEET - 2016]

A)
0%

B)
20%

C)
75%

D)
80%

• question_answer69) Two identical charged spheres suspended from a common point by two massless strings of lengths $l,$ are initially at a distance $d\,(d<<l)$ apart because of their mutual repulsion. The charges begin to leak from both the spheres at a constant rate. As a result, the spheres approach each other with a velocity v. Then v varies as a function of the distance x between the spheres, as: [NEET - 2016]

A)
$v\propto {{x}^{\frac{1}{2}}}$

B)
$v\propto x$

C)
$v\propto {{x}^{-\frac{1}{2}}}$

D)
$v\propto {{x}^{-1}}$

• question_answer70) A capacitor is charged by a battery. The battery is removed and another identical uncharged capacitor is connected in parallel. The total electrostatic energy of resulting system [NEET-2017]

A)
Increases by a factor of 2

B)
Increases by a factor of 4

C)
Decreases by a factor of 2

D)
Remains the same

• question_answer71) Suppose the charge of a proton and an electron differ slightly. One of them is $-\,e,$ the other is$(e+\Delta e)$. If the net of electrostatic force and gravitational force between two hydrogen atoms placed at a distance d (much greater than atomic size) apart is zero, then $\Delta e$ is of the order of [Given mass of hydrogen${{m}_{h}}=1.67\times {{10}^{-27}}kg$] [NEET-2017]

A)
${{10}^{-47}}C$

B)
${{10}^{-20}}C$

C)
${{10}^{-23}}C$

D)
${{10}^{-37}}C$

• question_answer72)  The diagrams below show regions of equipotentials.                         [NEET-2017] A positive charge is moved from A to B in each diagram.

A)
Maximum work is required to move q in figure [b]

B)
Maximum work is required to move q in figure [c]

C)
In all the four cases the work done is the same

D)
Minimum work is required to move q in figure [a]

• question_answer73) An electron falls from rest through a vertical distance h in a uniform and vertically upward directed electric field E. The direction of electric field is now reversed, keeping its magnitude the same. A proton is allowed to fall from rest in it through the same vertical distance h. The time of fall of the electron, in comparison to the time of fall of the proton is                [NEET - 2018]

A)
10 times greater

B)
5 times greater

C)
Smaller

D)
Equal

• question_answer74) The electrostatic force between the metal plates of an isolated parallel plate capacitor C having a charge Q and area A, is                      [NEET - 2018]

A)
Proportional to the square root of the distance between the plates

B)
Linearly proportional to the distance between the plates

C)
Independent of the distance between the plates

D)
Inversely proportional to the distance between the plates

• question_answer75) A toy car with charge q moves on a frictionless horizontal plane surface under the influence of a uniform electric field$\overrightarrow{\text{E}}$. Due to the force q$\overrightarrow{\text{E}}$, its velocity increases from 0 to 6 m/s in one second duration. At that instant the direction of the field is reversed. The car continues to move for two more seconds under the influence of this field. The average velocity and the average speed of the toy car between 0 to 3 seconds are respectively      [NEET - 2018]

A)
1 m/s, 3.5 m/s

B)
1 m/s, 3 m/s

C)
2 m/s, 4 m/s

D)
1.5 m/s, 3 m/s

• question_answer76) A hollow metal sphere of radius R is uniformly charged. The electric field due to the sphere at a distance r from the centre:           [NEET 2019]

A)
Zero as r increases for r < R, increases as r increases for r > R

B)
Decreases as r increases for r < R and for r > R

C)
Increases as r increases for r < R and for r > R

D)
Zero as r increases for r < R, decreases as r increases for r > R

• question_answer77) Two parallel infinite line charges with linear charge densities +λ C/m and λ C/m are placed at a distance of 2R in free space. What is the electric field mid-way between the two line charges?                                 [NEET 2019]

A)
$\frac{\lambda }{\pi {{\in }_{0}}R}N/C$

B)
$\frac{\lambda }{2\pi {{\in }_{0}}R}N/C$

C)
Zero

D)
$\frac{2\lambda }{\pi {{\in }_{0}}R}N/C$

• question_answer78) Two point charges A and B, having charges +Q and Q respectively, are placed at certain distance apart and force acting between them is F. If 25 % charge of A is transferred to B, then force between the charges becomes-                   [NEET 2019]

A)
$\frac{16F}{9}$

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

C)
F

D)
$\frac{9F}{16}$

• question_answer79) In a certain region of space with volume$0.2\text{ }{{m}^{3}}$, the electric potential is found to be 5V throughout. The magnitude of electric field in this region is: [NEET 2020]

A)
0.5 N/C

B)
1 N/C

C)
5 N/C

D)
zero

• question_answer80) A short electric dipole has a dipole moment of $16\times {{10}^{9\text{ }}}C\text{ }m$. The electric potential due to the dipole at a point at a distance of 0.6 m from the centre of the dipole, situated on a line making an angle of $60{}^\circ$ with the dipole axis is: $\left( \frac{1}{4\pi {{\in }_{0}}}=9\times {{10}^{9}}N\,{{m}^{2}}/{{C}^{2}} \right)$          [NEET 2020]

A)
200 V

B)
400 V

C)
zero

D)
50 V

• question_answer81) The capacitance of a parallel plate capacitor with air as medium is $6\mu F$. With the introduction of a dielectric medium, the capacitance becomes$30\mu F$. The permittivity of the medium is: $({{\in }_{0}}=8.85\times {{10}^{12}}{{C}^{2}}\text{ }{{N}^{1}}{{m}^{2}})$    [NEET 2020]

A)
$1.77\times {{10}^{12}}{{C}^{2}}{{N}^{1}}{{m}^{2}}$

B)
$0.44\times {{10}^{10}}{{C}^{2}}{{N}^{1}}{{m}^{2}}$

C)
$5.00\text{ }{{C}^{2}}{{N}^{1}}{{m}^{2}}$

D)
$0.44\times {{10}^{13}}{{C}^{2}}{{N}^{1}}{{m}^{2}}$

• question_answer82) A spherical conductor of radius 10 cm has a charge of $3.2\times {{10}^{7}}C$distributed uniformly. What is the magnitude of electric field at a point 15 cm from the centre of the sphere?          [NEET 2020] $\left( \frac{1}{4\pi {{\in }_{0}}}=9\times {{10}^{9}}N{{m}^{2}}/{{C}^{2}} \right)$

A)
$1.28\times {{10}^{5}}\,N/C$

B)
$1.28\times {{10}^{6}}\,N/C$

C)
$1.28\times {{10}^{7}}\,N/C$

D)
$1.28\times {{10}^{4}}\,N/C$