JEE Main & Advanced Physics Electrostatics & Capacitance Question Bank

done Self Evaluation Test - Electrostatic Potential and Capacitance Total Questions - 100

• question_answer1)
  Charge +q and -q are placed at points A and B respectively which are a distance 2L apart, C is the midpoint between A and B.  The work done in moving a charge +Q along the semicircle CRD is
  A)
  \[\frac{qQ}{2\pi {{\varepsilon }_{0}}L}\] done clear
  B)
  \[\frac{qQ}{3\pi {{\varepsilon }_{0}}L}\] done clear
  C)
  \[-\frac{qQ}{6\pi {{\varepsilon }_{0}}L}\] done clear
  D)
  \[\frac{qQ}{4\pi {{\varepsilon }_{0}}L}\] done clear
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• question_answer2)
  Four identical particles each of mass m and charge q are kept at the four comers of a square of length L. The final velocity of these particles after setting them free will be
  A)
  \[{{\left[ \frac{K{{q}^{2}}}{mL}\left( 5.4 \right) \right]}^{1/2}}\] done clear
  B)
  \[{{\left[ \frac{K{{q}^{2}}}{mL}\left( 1.35 \right) \right]}^{1/2}}\] done clear
  C)
  \[{{\left[ \frac{K{{q}^{2}}}{mL}\left( 2.7 \right) \right]}^{1/2}}\] done clear
  D)
  None of these done clear
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• question_answer3)
  There is an infinite straight chain of alternating charges q and -q. The distance between the two neighboring charges is equal to a. Find the interaction energy of any charge with all the other charges.
  A)
  \[-\frac{2{{q}^{2}}}{4\pi {{\varepsilon }_{0}}a}\] done clear
  B)
  \[\frac{2{{q}^{2}}{{\log }_{e}}2}{4\pi {{\varepsilon }_{0}}a}\] done clear
  C)
  \[-\frac{2{{q}^{2}}{{\log }_{e}}2}{4\pi {{\varepsilon }_{0}}a}\] done clear
  D)
  Zero done clear
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• question_answer4)
  Three identical particles, each possessing the mass m and charge +q, are placed at the corners of an equilateral triangle with side \[{{r}_{0}}.\] The particles are simultaneously set free and start flying apart symmetrically due to Coulomb?s repulsion foces. The work performed by Coulomb?s forces acting on to a very large distance is \[(\text{where }k=1/4\pi {{\varepsilon }_{0}}.)\]
  A)
  \[\frac{3k{{q}^{2}}}{{{r}_{0}}}\] done clear
  B)
  \[\frac{k{{q}^{2}}}{{{r}_{0}}}\] done clear
  C)
  \[\frac{3k{{q}^{2}}}{2{{r}_{0}}}\] done clear
  D)
  \[\frac{k{{q}^{2}}}{2{{r}_{0}}}\] done clear
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• question_answer5)
  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 \[\frac{{{q}_{3}}}{4\pi \,{{\in }_{0}}}\,k,\] where k is
  A)
  \[8{{q}_{1}}\]  done clear
  B)
  \[6{{q}_{1}}\] done clear
  C)
  \[8{{q}_{2}}\] done clear
  D)
  \[6{{q}_{2}}\] done clear
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• question_answer6)
  When air in a capacitor is replaced by medium of dielectric constant K, the capacity
  A)
  decrease K times done clear
  B)
         increases K times done clear
  C)
  increases \[{{K}^{2}}\]times      done clear
  D)
  remains constant done clear
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• question_answer7)
  The work done in placing a charge of \[8\times {{10}^{-18}}\]coulomb on a condenser of capacity 100 microfarad is
  A)
  \[3.1\times {{10}^{-26}}joule\] done clear
  B)
         \[4\times {{10}^{-10}}joule\] done clear
  C)
  \[3.2\times {{10}^{-32}}joule\]  done clear
  D)
  \[16\times {{10}^{-32}}joule\] done clear
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• question_answer8)
  Consider the situation shown in the figure. The capacitor A has a charge q on it whereas vB is uncharged. The charge appearing on the capacitor B a long time after the switch is closed is
  A)
  zero                               done clear
  B)
  \[q/2\] done clear
  C)
  \[q\]                  done clear
  D)
         \[2q\] done clear
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• question_answer9)
  A parallel plate capacitor is located horizontally such that one of the plates is submerged in a liquid while the other is above the liquid surface. When plates are  charged the level of liquid
  A)
  rises done clear
  B)
  falls done clear
  C)
  remains unchanged done clear
  D)
  may rise or fall depending on the of charge amount done clear
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• question_answer10)
  What is the effective capacitance between points X and Y?
  A)
  \[8\mu F\] done clear
  B)
  \[9\mu F\] done clear
  C)
  \[10\mu F\] done clear
  D)
  \[12\mu F\] done clear
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• question_answer11)
  A hollow metal sphere of radius 5 cm is charged such that the potential on its surface is 10 V. The potential at a distance of 2 cm from the center of the sphere is
  A)
  zero       done clear
  B)
  10 V done clear
  C)
  4 V       done clear
  D)
  10/3 V done clear
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• question_answer12)
  A unit charge moves on an equipotential surface from a point A to point B, then
  A)
  \[{{V}_{A}}-{{V}_{B}}=+\,ve\]           done clear
  B)
  \[{{V}_{A}}-{{V}_{B}}=0\] done clear
  C)
  \[{{V}_{A}}-{{V}_{B}}=-\,ve\] done clear
  D)
  it is stationary done clear
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• question_answer13)
  A cube of a metal is given a positive charge Q. For this system, which of the following statements is true?
  A)
  Electric potential at the surface of the cube done clear
  B)
  Electric potential within the cube is zero done clear
  C)
  Electric field is normal to the surface of the cube done clear
  D)
  Electric field varies within the cube done clear
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• question_answer14)
  In moving from A to B along an electric field line, the work done by the electric field on an electron is \[6.4\times {{10}^{-19}}J.\] If \[{{\phi }_{1}}\] and \[{{\phi }_{2}}\]are equipotential surfaces, then the potential difference \[{{V}_{C}}-{{V}_{A}}\] is  
  A)
  -4V       done clear
  B)
  4V   done clear
  C)
  zero       done clear
  D)
  6.4V done clear
  View Solution play_arrow

• question_answer15)
  A non-conducting ring of radius 0.5 m carries a total charge of \[1.11\times {{10}^{-10}}C\]distributed non-uniformly on its circumference producing an electric field E everywhere in space. The value of the integral \[\int\limits_{\ell =\infty }^{\ell =0}{-E.dl}\] (\[\ell =0\]being center of the ring) in volts is
  A)
  +2 done clear
  B)
  -1    done clear
  C)
  -2 done clear
  D)
  zero done clear
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• question_answer16)
  Two equally charged spheres of radii a and b are connected together. What will be the ratio of electric field intensity on their surfaces?
  A)
  \[\frac{a}{b}\] done clear
  B)
  \[\frac{{{a}^{2}}}{{{b}^{2}}}\] done clear
  C)
  \[\frac{b}{a}\] done clear
  D)
  \[\frac{{{b}^{2}}}{{{a}^{2}}}\] done clear
  View Solution play_arrow

• question_answer17)
  If the electrostatic potential were given by \[\phi ={{\phi }_{0}}({{x}^{2}}+{{y}^{2}}+{{z}^{2}}),\]where is constant, then the charge density giving rise to the above potential would be.
  A)
  0 done clear
  B)
  \[-6{{\phi }_{0}}{{\varepsilon }_{0}}\] done clear
  C)
  \[-2{{\phi }_{0}}{{\varepsilon }_{0}}\] done clear
  D)
  \[-\frac{6{{\phi }_{0}}}{{{\varepsilon }_{0}}}\] done clear
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• question_answer18)
  A, B and C are three points in a uniform electric field. The electric potential is            
  A)
              maximum B done clear
  B)
              maximum C done clear
  C)
              same at all the three points A, B and C done clear
  D)
              maximum A done clear
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• question_answer19)
  An electric charge \[{{10}^{-3}}\mu C\] is placed at the origin (0, 0) of X-Y co-ordinate system. Two points A and B are situated at \[(\sqrt{2},\sqrt{2})\] and (2, 0) respectively. The potential difference between the points A and B will be [in volt]
  A)
  4.5        done clear
  B)
  9 done clear
  C)
  zero done clear
  D)
  2 done clear
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• question_answer20)
  Which of the following figure shows the correct equipotential surfaces of a system of two positive charges?
  A)
  done clear
  B)
  done clear
  C)
  done clear
  D)
  done clear
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• question_answer21)
  Equipotential surfaces are shown in figure. Then the electric field strength will be
  A)
  \[100\text{ }V{{m}^{-1}}\] along X-axis done clear
  B)
  \[100\text{ }V{{m}^{-1}}\] along Y-axis done clear
  C)
  \[200\text{ }V{{m}^{-1}}\]at an angle \[120{}^\circ \]with X-axis done clear
  D)
  \[50\text{ }V{{m}^{-1}}\] at an angle \[120{}^\circ \] with X-axis done clear
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• question_answer22)
  Two concepts spheres of radii R and r have similar charges with equal surface charge densities \[\left( \sigma  \right).\] what is the electric potential at their common center?
  A)
  \[\sigma /{{\varepsilon }_{0}}\] done clear
  B)
  \[\frac{\sigma }{{{\varepsilon }_{0}}}\left( R-r \right)\] done clear
  C)
  \[\frac{\sigma }{{{\varepsilon }_{0}}}\left( R+r \right)\] done clear
  D)
  None of these done clear
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• question_answer23)
  From a point charge, there is a fixed point A. At A, there is an electric field of 500 V/m and potential difference of 3000 V. Distance between point charge and A will be?
  A)
  6 m       done clear
  B)
  12 m done clear
  C)
  16 m done clear
  D)
  24 m done clear
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• question_answer24)
  Two metal pieces having a potential difference of 800 V are 0.02 m apart horizontally. A particle of mass \[1.96\times {{10}^{-15}}kg\] is suspended in equilibrium between the plates. If e is the elementary charge, then charge on the particle is
  A)
  8 done clear
  B)
  6 done clear
  C)
  0.1 done clear
  D)
  3 done clear
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• question_answer25)
  A point charge of magnitude \[+1\mu C\] is fixed at (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 center of the sphere is:
  A)
  \[1.8\times {{10}^{5}}V\text{ and }-5.625\times {{10}^{6}}V/m\] done clear
  B)
  0 V and 0 V/m done clear
  C)
  \[2.25\times {{10}^{5}}V\text{ and }-5.625\times {{10}^{6}}V/m\] done clear
  D)
  \[2.25\times {{10}^{5}}V\text{ and 0 V/m}\] done clear
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• question_answer26)
  A plastic disc is charged on one side with a uniform surface charge density \[\sigma \]and then three quadrant of the disk are removed. The remaining quadrant is shown in figure, with V=0 at infinity, the potential due to the remaining quadrant point P is
  A)
  \[\frac{\sigma }{2{{\in }_{0}}}\left[ {{\left( {{r}^{2}}+{{R}^{2}} \right)}^{1/2}}-r \right]\]       done clear
  B)
  \[\frac{\sigma }{2{{\in }_{0}}}\left[ R-r \right]\] done clear
  C)
  \[\frac{\sigma }{8{{\in }_{0}}}\left[ {{\left( {{r}^{2}}+{{R}^{2}} \right)}^{1/2}}-r \right]\]       done clear
  D)
  none of these done clear
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• question_answer27)
  A conducting sphere of radius R is given a charge Q. The electric potential and the electric field at the center of the sphere respectively are:
  A)
  \[0\text{ and }\frac{Q}{4\pi \varepsilon {{  }_{0}}{{R}^{2}}}\]           done clear
  B)
  \[\frac{Q}{4\pi \varepsilon {{  }_{0}}R}\text{ and 0}\] done clear
  C)
  \[\frac{Q}{4\pi \varepsilon {{  }_{0}}R}\text{ and }\frac{Q}{4\pi \varepsilon {{  }_{0}}{{R}^{2}}}\text{ }\] done clear
  D)
  Both are 0 done clear
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• question_answer28)
  A conducting disc of radius R rotating about its axis with an angular velocity \[\omega \]. Then the potential difference between the center of the disk and its edge is (no magnetic field is present)
  A)
  zero                   done clear
  B)
         \[\frac{{{m}_{e}}{{\omega }^{2}}{{R}^{2}}}{2e}\] done clear
  C)
  \[\frac{{{m}_{e}}{{\omega }^{2}}{{R}^{3}}}{2e}\]   done clear
  D)
         \[\frac{e{{m}_{e}}\omega {{R}^{2}}}{2}\] done clear
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• question_answer29)
  Four points a, b, c and d are set at equal distance The electrostatic potential \[{{V}_{a}},{{V}_{b}},{{V}_{c}}\text{ and }{{V}_{d}}\]would  satisfy the following relation:
  A)
  \[{{V}_{a}}>{{V}_{b}}>{{V}_{c}}>{{V}_{d}}\] done clear
  B)
  \[{{V}_{a}}>{{V}_{b}}={{V}_{d}}>{{V}_{c}}\] done clear
  C)
  \[{{V}_{a}}>{{V}_{c}}={{V}_{b}}={{V}_{d}}\] done clear
  D)
  \[{{V}_{b}}={{V}_{d}}>{{V}_{a}}>{{V}_{c}}\] done clear
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• question_answer30)
  The potential at the point x (measured in\[\mu m\]) due to some charges situated on the x-axis is given by \[V(x)=20({{x}^{2}}-4)\] volt. The electric field E at \[x=4\mu m\]
  A)
  \[\left( 10/9 \right)\text{ }volt/\mu m\]and in the +ve x direction done clear
  B)
  \[\left( 5/3 \right)\text{ }volt/\mu m\]and in the -ve x direction done clear
  C)
  \[\left( 5/3 \right)\text{ }volt/\mu m\] and in the +ve x direction done clear
  D)
  \[\left( 10/9 \right)\text{ }volt/\mu m\]and in the -ve x direction done clear
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• question_answer31)
  The expression \[E=-\frac{dv}{dr}\]implies, that electric field is in that direction in which
  A)
  increase in potential is steepest.   done clear
  B)
  decrease in potential is steepest. done clear
  C)
  change is potential is minimum. done clear
  D)
  none of these done clear
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• question_answer32)
  In a hollow spherical shell, potential (V) changes with respect to distance (s) from center as
  A)
  done clear
  B)
  done clear
  C)
  done clear
  D)
  done clear
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• question_answer33)
  The 1000 small droplets of water each of radius r and charge Q, make a big drop of spherical shape. The potential of big drop is how many times the potential of one small droplet?
  A)
  1 done clear
  B)
  10    done clear
  C)
  100 done clear
  D)
  1000 done clear
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• question_answer34)
  The electric potential at a point (x, y) in the \[x\text{ }\text{ }y\] plane is given by \[V=-kxy.\] The field intensity at a distance r from the origin varies as
  A)
  \[{{r}^{2}}\] done clear
  B)
  \[r\] done clear
  C)
  \[\frac{1}{r}\] done clear
  D)
  \[\frac{1}{{{r}^{2}}}\] done clear
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• question_answer35)
  Four charges \[{{q}_{1}}=2\times {{10}^{-8}}C,\] \[{{q}_{2}}=-2\times {{10}^{-8}}C,\]\[{{q}_{3}}=-3\times {{10}^{-8}}C\], \[{{q}_{3}}=6\times {{10}^{-8}}C\]are placed at four corners of a square of side \[\sqrt{2}\] m. What is hollow spheres of radii r and R (R > r) such that the common center of the square?
  A)
  270 V done clear
  B)
  300 V done clear
  C)
  Zero      done clear
  D)
  100 V done clear
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• question_answer36)
  A charge Q is distributed over two concentric hollow spheres of radii r and R(R>r) such that the surface densities are equal. The potential at the common center is \[\frac{1}{4\pi {{\varepsilon }_{0}}}\]times-
  A)
  \[Q\left[ \frac{r+R}{{{r}^{2}}+{{R}^{2}}} \right]\]                  done clear
  B)
  \[\frac{Q}{2}\left[ \frac{r+R}{{{r}^{2}}+{{R}^{2}}} \right]\] done clear
  C)
  \[2Q\left[ \frac{r+R}{{{r}^{2}}+{{R}^{2}}} \right]\]    done clear
  D)
  zero done clear
  View Solution play_arrow

• question_answer37)
  Three concentric charged metallic spherical shells A, B and C have radii a, b and c; change densities \[\sigma ,-\sigma \] and \[\sigma \] and potentials \[{{V}_{A}},{{V}_{B}}\] and \[{{V}_{C}}\] respectively. Then which of the following relations is correct?
  A)
  \[{{V}_{A}}=\left( a+b+c \right)\frac{\sigma }{{{\varepsilon }_{0}}}\]   done clear
  B)
  \[{{V}_{B}}=\left( \frac{{{a}^{2}}}{b}-b+c \right)\frac{\sigma }{{{\varepsilon }_{0}}}\] done clear
  C)
  \[{{V}_{C}}=\left( \frac{{{a}^{2}}+{{b}^{2}}}{b}+c \right)\frac{\sigma }{{{\varepsilon }_{0}}}\] done clear
  D)
  \[{{V}_{A}}={{V}_{B}}={{V}_{C}}=\left( a+b+c \right)\frac{\sigma }{{{\varepsilon }_{0}}}\] done clear
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• question_answer38)
  An electron having charge e and mass m starts from the lower plate of two metallic plates separated by a distance d. If the potential difference between the plates is V, the time taken by the electron to reach the upper plate is given charge on C is           
  A)
  \[\sqrt{\frac{2m{{d}^{2}}}{eV}}\] done clear
  B)
  \[\sqrt{\frac{m{{d}^{2}}}{eV}}\] done clear
  C)
  \[\sqrt{\frac{m{{d}^{2}}}{2eV}}\] done clear
  D)
  \[\frac{2m{{d}^{2}}}{eV}\] done clear
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• question_answer39)
  There is a uniform electrostatic filed in a region. The potential at various points on a small sphere centered at P, in the region, is found to vary between in the limits 589.0 V to 589.8 V. What is the potential at a point on the sphere whose radius vector makes an angle of \[60{}^\circ \]with the direction of the field?
  A)
  589.5 V done clear
  B)
  589.2 V done clear
  C)
  589.4 V done clear
  D)
  589.6 V done clear
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• question_answer40)
  A charge of 3 coulomb moving in uniform electric field experiences a force of 3000 newton. The potential difference between the two points situated in a field at a distance of 1 cm from each other will be:
  A)
  100       done clear
  B)
  5000 done clear
  C)
  10 done clear
  D)
  50 done clear
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• question_answer41)
  Three identical metallic uncharged spheres A, B and C each of radius a, are kept at the corners of an equilateral triangle of side d(d>>a) as shown in Fig. The fourth sphere (of radius a), which has a charge q, touches A and is then removed to a position far away. B is earthed and then the earth connection is removed. C is then earthed. The charge on C is
  A)
  \[\frac{qa}{2d}\left( \frac{2d-a}{2d} \right)\] done clear
  B)
  \[\frac{qa}{2d}\left( \frac{2d-a}{d} \right)\] done clear
  C)
  \[-\frac{qa}{2d}\left( \frac{d-a}{d} \right)\] done clear
  D)
  \[-\frac{2qa}{d}\left( \frac{d-a}{2d} \right)\] done clear
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• question_answer42)
  Three charges -q, +q and +q are situated in X-Y plane at points (0, -a), (0, 0) and (0, a) respectively. The potential at a point distant r (r>a) in a direction making an angle \[\theta \]from Y-axis will be
  A)
  \[\frac{Kq}{r}\left( 1-\frac{2a\cos \theta }{r} \right)\] done clear
  B)
  \[\frac{2kq\cos \theta }{{{r}^{2}}}\] done clear
  C)
  \[\frac{Kq}{r}\] done clear
  D)
  \[\frac{Kq}{r}\left( 1+\frac{2a\cos \theta }{r} \right)\] done clear
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• question_answer43)
  In a region, the potential is represented by \[V\left( x,y,z \right)=6x-8xy-8y+6yz,\] where V is in volts and x, y, z are in meters. The electric force experienced by change of 2 coulomb situate at point (1, 1, 1) is:
  A)
  \[6\sqrt{5}N\] done clear
  B)
  \[30N\] done clear
  C)
  \[24N\] done clear
  D)
  \[4\sqrt{3}N\] done clear
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• question_answer44)
  Figure shows a system of three concentric metal shells A, B and C with radii a, 2a and 3a respectively. Shell B is earthed and shell C is given a charge Q. Now if shell C is connected to shell, A then the final charge on the shell B, is equal to
  A)
  -4Q/3 done clear
  B)
  -8Q/11 done clear
  C)
  -5Q/3 done clear
  D)
  -3Q/7 done clear
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• question_answer45)
  A charge +q fixed at each of the points \[x={{x}_{0}},x=3{{x}_{0}},x=5{{x}_{0}}....\] up to \[\infty \] on X-axis and charge -q is fixed on each of the points \[x=2{{x}_{0}},x=4{{x}_{0}},....\] up to \[\infty \]. Here \[{{x}_{0}}\] is a positive constant. Take the potential at a point due to a charge Q at a distance r form it to be \[\frac{Q}{4\pi {{\varepsilon }_{0}}r},\] then the potential at the origin due to above system of charges will be:
  A)
  zero       done clear
  B)
  infinite done clear
  C)
  \[\frac{q}{8\,\pi \,{{\varepsilon }_{0}}{{x}_{0}}\,{{\log }_{e}}\,2}\] done clear
  D)
  \[\frac{q\,{{\log }_{e}}\,2}{4\,\pi \,{{\varepsilon }_{0}}{{x}_{0}}}\] done clear
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• question_answer46)
  Two small identical metal balls of radius r are at a distance a from each other and are charged, one with a potential V, and the other with a potential. The charges on the balls are:
  A)
  \[{{q}_{1}}={{V}_{1}}a,{{q}_{2}}={{V}_{2}}a\] done clear
  B)
  \[{{q}_{1}}={{V}_{1}}r,{{q}_{2}}={{V}_{2}}r\] done clear
  C)
  \[{{q}_{1}}=\left( \frac{{{V}_{1}}+{{V}_{2}}}{2} \right)a,{{q}_{2}}=\left( \frac{{{V}_{1}}+{{V}_{2}}}{2} \right)r\] done clear
  D)
  \[{{q}_{1}}=-\frac{r}{a}\left( r{{V}_{2}}-a{{V}_{1}} \right)a,{{q}_{2}}=-\frac{r}{a}\left( r{{V}_{1}}-a{{V}_{2}} \right)\] done clear
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• question_answer47)
  A sphere of radius 2R has a uniform charge density \[\rho .\] The difference in the electric potential at \[r=R\], \[r=0\]from the center is
  A)
  \[\frac{-\rho {{R}^{2}}}{{{\in }_{0}}}\] done clear
  B)
  \[\frac{-2\rho {{R}^{2}}}{{{\in }_{0}}}\] done clear
  C)
  \[\frac{\rho {{R}^{2}}}{3{{\in }_{0}}}\] done clear
  D)
  \[\frac{-\rho {{R}^{2}}}{6{{\in }_{0}}}\,\] done clear
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• question_answer48)
  The electric field intensity at all points in space is given by \[\vec{E}=\sqrt{3}\hat{i}-\hat{j}\text{ volt/meter}\text{.}\] The nature of equipotential lines in xy-plane is given by
  A)
  done clear
  B)
  done clear
  C)
       done clear
  D)
  done clear
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• question_answer49)
  The electric potential at a point (x, y, z) is given by \[V=-{{x}^{2}}y-x{{z}^{3}}+4.\] The electric field E at that point is
  A)
  \[\vec{E}=\hat{i}2xy+\hat{j}({{x}^{2}}+{{y}^{2}})+\hat{k}(3xz-{{y}^{2}})\] done clear
  B)
  \[\vec{E}=\hat{i}{{z}^{3}}+\hat{j}xyz+\hat{k}{{z}^{2}}\] done clear
  C)
  \[\vec{E}=\hat{i}(2xy-{{z}^{3}})+\hat{j}x{{y}^{2}}+\hat{k}3{{z}^{2}}x\] done clear
  D)
  \[\vec{E}=\hat{i}(2xy+{{z}^{3}})+\hat{j}{{x}^{2}}+\hat{k}3x{{z}^{2}}\] done clear
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• question_answer50)
  An infinite non-conducting sheet has a surface charge density \[\sigma =0.1\mu C/{{m}^{2}}\]on one side. How far apart are equipotential surfaces whose potential differ by 50 volt?
  A)
  \[8.8mm\] done clear
  B)
  \[8.8cm\] done clear
  C)
  \[8.8\text{ }\mu rn\] done clear
  D)
  \[8.8pm\] done clear
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• question_answer51)
  Two concentric conducting spherical shells of radii \[{{a}_{1}}\]and \[{{a}_{2}}\]\[({{a}_{2}}>{{a}_{1}})\] are charged to potentials \[{{\phi }_{1}}\] and \[{{\phi }_{2}}\], respectively. Find the charge on the inner shell.
  A)
  \[{{q}_{1}}=4\pi {{\varepsilon }_{0}}\left( \frac{{{\phi }_{1}}-{{\phi }_{2}}}{{{a}_{2}}-{{a}_{1}}} \right){{a}_{1}}{{a}_{2}}\]       done clear
  B)
  \[{{q}_{1}}=4\pi {{\varepsilon }_{0}}\left( \frac{{{\phi }_{1}}+{{\phi }_{2}}}{{{a}_{2}}+{{a}_{1}}} \right){{a}_{1}}{{a}_{2}}\] done clear
  C)
  \[{{q}_{1}}=4\pi {{\varepsilon }_{0}}\left( \frac{{{\phi }_{1}}-{{\phi }_{2}}}{{{a}_{2}}+{{a}_{1}}} \right){{a}_{1}}{{a}_{2}}\] done clear
  D)
  \[{{q}_{1}}=4\pi {{\varepsilon }_{0}}\left( \frac{{{\phi }_{1}}+{{\phi }_{2}}}{{{a}_{2}}-{{a}_{1}}} \right){{a}_{1}}{{a}_{2}}\] done clear
  View Solution play_arrow

• question_answer52)
  The potential energy of a system of two charges is negative when
  A)
  both the charges are positive   done clear
  B)
  both the charges are negative done clear
  C)
  one charge is positive and other is negative done clear
  D)
  both the charges are separated by infinite  distance done clear
  View Solution play_arrow

• question_answer53)
  In the electric field of a point charge q, a certain charge is carried from point A to B, C, D and E. Then the work done is
  A)
  least along the path AB done clear
  B)
  least along the path AD done clear
  C)
  zero along all the paths AB, AC, AD and AE done clear
  D)
  least along AE done clear
  View Solution play_arrow

• question_answer54)
  Figure shows a system of three positive charges placed at the verticals of and equilateral triangle. To decrease the potential energy of the system,
  A)
  a positive charge should be placed at centroid. done clear
  B)
  a negative charge should be placed at centroid. done clear
  C)
  distance between the charges should be decreased. done clear
  D)
  it should be rotated by an angle of \[\frac{\pi }{2}\] radian. done clear
  View Solution play_arrow

• question_answer55)
  Two conducting spheres of radii \[{{R}_{1}}\] and \[{{R}_{2}}\]having charges \[{{Q}_{1}}\] and \[{{Q}_{2}}\]respectively are connected to each other. There is
  A)
  no change in the energy of the system done clear
  B)
  an increase in the energy of the system done clear
  C)
  always a decrease in the energy of the system done clear
  D)
  a decrease in the energy of the system unless \[{{Q}_{1}}{{R}_{2}}={{Q}_{2}}{{R}_{1}}\] done clear
  View Solution play_arrow

• question_answer56)
  A and B are two points in an electric field. If the work done in carrying 4.0C of electric charge from work done in moving 100 electrons from P to Q
  A)
  zero       done clear
  B)
  2.0 V done clear
  C)
  4.0 V done clear
  D)
  16.0 V done clear
  View Solution play_arrow

• question_answer57)
  Two points P and Q are maintained at the potentials of 10 V and -4 V, respectively. The work done in moving 100 electrons from P to Q is:
  A)
  \[9.60\times {{10}^{-17}}J\] done clear
  B)
  \[-2.24\times {{10}^{-16}}J\] done clear
  C)
  \[2.24\times {{10}^{-16}}J\] done clear
  D)
  \[-9.60\times {{10}^{-17}}J\,\] done clear
  View Solution play_arrow

• question_answer58)
  A ball of mass 1 g carrying a change \[{{10}^{-8}}C\]moves from a point A at potential 600 V to a point B at zero potential. The change in its K.E.
  A)
  \[-6\times {{10}^{-6}}erg\] done clear
  B)
  \[-6\times {{10}^{-6}}J\] done clear
  C)
  \[6\times {{10}^{-6}}J\] done clear
  D)
  \[6\times {{10}^{-6}}erg\] done clear
  View Solution play_arrow

• question_answer59)
  As per the diagram, a point charge +q is placed at the origin O. Work done in taking another point charge-Q from the point A [coordinates (0, a)] to another point B [coordinates (a, 0)] along the straight path AB is:
  A)
  zero       done clear
  B)
  \[\left( \frac{-qQ}{4\pi {{\varepsilon }_{0}}}\frac{1}{{{a}^{2}}} \right)\sqrt{2}a\] done clear
  C)
  \[\left( \frac{-qQ}{4\pi {{\varepsilon }_{0}}}\frac{1}{{{a}^{2}}} \right).\frac{a}{\sqrt{2}}\] done clear
  D)
  \[\left( \frac{qQ}{4\pi {{\varepsilon }_{0}}}\frac{1}{{{a}^{2}}} \right).\sqrt{2}a\] done clear
  View Solution play_arrow

• question_answer60)
  Positive and negative point charges of equal magnitude are kept at (0, 0, \[\frac{a}{2}\]) and [0, 0, \[-\frac{a}{2}\] ] respectively. The work done by the electric field when another positive point charge is moved from (-a, 0, 0) to (0, a, 0) is
  A)
  positive   done clear
  B)
                     negative   done clear
  C)
  zero done clear
  D)
  depends on the path connecting the initial and final positions done clear
  View Solution play_arrow

• question_answer61)
  Four identical charges are placed at the four charge is moved along A-axis. The variation of potential energy (U) along X axis is correctly represented by   
  A)
  done clear
  B)
  done clear
  C)
  done clear
  D)
  done clear
  View Solution play_arrow

• question_answer62)
  Each corner of a cube of side l has a negative charge, -q. The electrostatic potential energy of a charge q at the center of the cube is
  A)
  \[-\frac{4{{q}^{2}}}{\sqrt{2}\pi {{\varepsilon }_{0}}l}\] done clear
  B)
         \[\frac{\sqrt{3}{{q}^{2}}}{4\pi {{\varepsilon }_{0}}l}\] done clear
  C)
  \[\frac{4{{q}^{2}}}{\sqrt{2}\pi {{\varepsilon }_{0}}l}\] done clear
  D)
         \[-\frac{4{{q}^{2}}}{\sqrt{3}\pi {{\varepsilon }_{0}}l}\] done clear
  View Solution play_arrow

• question_answer63)
  Two identical thin rings each of radius R meters are coaxially placed at a distance R meters apart. If \[{{Q}_{1}}\]coulomb and \[{{Q}_{2}}\]coulomb are respectively the charges uniformly spread on the two rings, the work done in moving a charge q from the center of one ring to that of other is
  A)
  zero                   done clear
  B)
         \[\frac{q\left( {{Q}_{1}}-{{Q}_{2}} \right)\left( \sqrt{2}-1 \right)}{\sqrt{2}.4\pi {{\varepsilon }_{0}}R}\] done clear
  C)
  \[\frac{q\sqrt{2}\left( {{Q}_{1}}+{{Q}_{2}} \right)}{4\pi {{\varepsilon }_{0}}R}\]                                    done clear
  D)
  \[\frac{q\left( {{Q}_{1}}+{{Q}_{2}} \right)\left( \sqrt{2}+1 \right)}{\sqrt{2}.4\pi {{\varepsilon }_{0}}R}\] done clear
  View Solution play_arrow

• question_answer64)
  On decreasing the distance between the plates of a parallel plate capacitor, its capacitance
  A)
  remains unaffected done clear
  B)
  decreases done clear
  C)
  first increases then decreases. done clear
  D)
  increases done clear
  View Solution play_arrow

• question_answer65)
  If in parallel plate capacitor, which is connected to a battery, we fill dielectrics in whole space of its plates, then which of the following increases?
  A)
  Q and V            done clear
  B)
         V and E done clear
  C)
  E and C done clear
  D)
         Q and C done clear
  View Solution play_arrow

• question_answer66)
  Two vertical metallic plates carrying equal and opposite charges are kept parallel to each other like a parallel plate capacitor. A small spherical metallic ball is suspended by a long insulated thread such that it hangs freely in the center of the two metallic plates. The ball, which is uncharged, is taken slowly towards the positively charged plate and is made to touch and plate. Then the ball will
  A)
  stick to the positively charged plate   done clear
  B)
  come back to its original position and will remain there    done clear
  C)
  oscillate between the two plates touching each plate in turn   done clear
  D)
  oscillate between the two plates without touch them   done clear
  View Solution play_arrow

• question_answer67)
  Eight drops of mercury of equal radii possessing equal charges combine to form a big drop. Then the capacitance of bigger drop compared to each individual small drop is
  A)
  8 times done clear
  B)
  4 times done clear
  C)
  2 times done clear
  D)
  32 times done clear
  View Solution play_arrow

• question_answer68)
  A parallel plate condenser is filled with two dielectrics as shown. Area of each plate is \[A{{m}^{2}}\]and the separation is t m. The dielectric constants are \[{{k}_{1}}\] and \[{{k}_{2}}\] respectively. Its capacitance in farad will be
  A)
  \[\frac{{{\varepsilon }_{0}}A}{t}\left( {{k}_{1}}+{{k}_{2}} \right)\] done clear
  B)
  \[\frac{{{\varepsilon }_{0}}A}{t}.\frac{{{k}_{1}}+{{k}_{2}}}{2}\] done clear
  C)
  \[\frac{2{{\varepsilon }_{0}}A}{t}\left( {{k}_{1}}+{{k}_{2}} \right)\] done clear
  D)
  \[\frac{{{\varepsilon }_{0}}A}{t}.\frac{{{k}_{1}}-{{k}_{2}}}{2}\] done clear
  View Solution play_arrow

• question_answer69)
  The resultant capacity of n condensers of capacitances \[{{C}_{1}},{{C}_{2}}\ldots .{{C}_{n}}\]connected in parallel is
  A)
  \[{{C}_{p}}={{C}_{1}}+{{C}_{2}}+\ldots .+{{C}_{n}}\] done clear
  B)
  \[{{C}_{p}}={{C}_{1}}-{{C}_{2}}-\ldots .-{{C}_{n}}\] done clear
  C)
  \[\frac{1}{{{C}_{p}}}=\frac{1}{{{C}_{1}}}+\frac{1}{{{C}_{2}}}+\ldots .+\frac{1}{{{C}_{n}}}\] done clear
  D)
  \[\frac{1}{{{C}_{p}}}=\frac{1}{{{C}_{1}}}-\frac{1}{{{C}_{2}}}-\ldots .-\frac{1}{{{C}_{n}}}\] done clear
  View Solution play_arrow

• question_answer70)
  If earth is assumed to be a conducting sphere having radius \[R=6400km,\]it?s capacitance will be:
  A)
  \[711\mu F\] done clear
  B)
  \[218\mu F\] done clear
  C)
  \[16\mu F\] done clear
  D)
  \[8\mu F\] done clear
  View Solution play_arrow

• question_answer71)
  A capacitor has two circular plates whose radius are 8cm and distance between them is 1mm. When mica (dielectric constant = 6) is placed between the plates. The capacitance of this capacitor and the energy stored when it is given potential of 150 volt respectively are
  A)
  \[1.06\times {{10}^{-5}}F,1.2\times {{10}^{-9}}J\] done clear
  B)
  \[1.068\times {{10}^{-9}}F,1.2\times {{10}^{-5}}J\] done clear
  C)
  \[1.2\times {{10}^{-9}}F,1.068\times {{10}^{-5}}J\] done clear
  D)
  \[1.6\times {{10}^{-9}}F,1.068\times {{10}^{-5}}J\] done clear
  View Solution play_arrow

• question_answer72)
  Three condenser each of capacitance 2F are put in series. The resultant capacitance is 
  A)
  6 F        done clear
  B)
  3/2 F done clear
  C)
  2/3 F     done clear
  D)
  5 F done clear
  View Solution play_arrow

• question_answer73)
  Two spherical conductors \[{{A}_{1}}\] and \[{{A}_{2}}\] of radii \[{{r}_{1}}\]and \[{{r}_{2}}\left( {{r}_{2}}>{{r}_{1}} \right)\] are placed concentrically in air.  \[{{A}_{1}}\]is given a charge +Q while \[{{A}_{2}}\] is earthed. Then the equivalent capacitance of the system is
  A)
  \[\frac{4\pi {{\in }_{0}}{{r}_{1}}{{r}_{2}}}{{{r}_{2}}-{{r}_{1}}}\] done clear
  B)
  \[4\pi r{{\in }_{0}}\left( {{r}_{1}}+{{r}_{2}} \right)\] done clear
  C)
  \[4\pi {{\in }_{0}}{{r}_{2}}\] done clear
  D)
  \[4\pi {{\in }_{0}}{{r}_{1}}\] done clear
  View Solution play_arrow

• question_answer74)
  The capacitor, whose capacitance is 6, 6 and\[3\mu F\]respectively are connected in series with 20 volt line. Find the charge on \[3\mu F\].
  A)
  \[30\mu C\] done clear
  B)
  \[60\mu F\] done clear
  C)
  \[15\mu F\] done clear
  D)
  \[90\mu F\] done clear
  View Solution play_arrow

• question_answer75)
  A parallel plate capacitor with air between the plates has a capacitance of 8 pF. Calculate the capacitance if the distance between the plates is reduced by half and the space between them is filled with a substance of dielectric constant. \[\left( {{\varepsilon }_{r}}=6 \right)\]
  A)
  72 pF done clear
  B)
  81 pF    done clear
  C)
  84 pF done clear
  D)
  96 PF done clear
  View Solution play_arrow

• question_answer76)
  A parallel plate air capacitor has a capacitance of \[100\mu F.\]The plates are at a distance d apart. If a slab of thickness t(t<d) and dielectric constant 5 is introduced between the parallel plates, then the capacitance will be 
  A)
  \[50\mu F\] done clear
  B)
  \[100\mu F\] done clear
  C)
  \[200\mu F\] done clear
  D)
  \[500\mu F\] done clear
  View Solution play_arrow

• question_answer77)
  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 \[\frac{1}{3}\]A, dialectic constant 2K and another with area \[\frac{2}{3}A\] and dielectric constant K. If the capacitance of this new capacitor is C then \[\frac{C}{{{C}_{0}}}\]is
  A)
  1                      done clear
  B)
         \[\frac{4}{3}\] done clear
  C)
  \[\frac{2}{3}\]              done clear
  D)
         \[\frac{1}{3}\] done clear
  View Solution play_arrow

• question_answer78)
  A parallel plate capacitor with air between the plates is charged to a potential difference of 500 V and then insulated. A plastic plate is inserted between the plates filling the whole gap. The potential difference between the plates now becomes 75V. The dielectric constant of plastic is
  A)
  10/3                  done clear
  B)
         5 done clear
  C)
  20/3                  done clear
  D)
         10 done clear
  View Solution play_arrow

• question_answer79)
  The effective capacitance of combination of equal capacitors between points A and B shown in figure is.
  A)
  \[C\]      done clear
  B)
  \[2C\] done clear
  C)
  \[3C\]    done clear
  D)
  \[\frac{C}{2}\] done clear
  View Solution play_arrow

• question_answer80)
  Three capacitors are connected in the arms of a triangle ABC as shown in figure 5 V is applied between A and B. The voltage between B and C is.
  A)
  2 V done clear
  B)
  1 V done clear
  C)
  3 V done clear
  D)
  1.5 V done clear
  View Solution play_arrow

• question_answer81)
  To obtain \[3\mu F\]capacity from three capacitors of \[2\mu F\]each, they will be arranged.
  A)
  all the three in series done clear
  B)
  all the three in parallel   done clear
  C)
  two capacitors in series and the third in parallel with the combination of first two done clear
  D)
  two capacitors in parallel and the third in series with the combination of first two done clear
  View Solution play_arrow

• question_answer82)
  The energy required to change a parallel plate condenser of plate separation d and plated area of cross-section A such that the uniform electric field between the plates is E, is
  A)
  \[{{\in }_{0}}{{E}^{2}}Ad\]                done clear
  B)
  \[\frac{1}{2}{{\in }_{0}}{{E}^{2}}Ad\] done clear
  C)
  \[\frac{1}{2}{{\in }_{0}}{{E}^{2}}/Ad\] done clear
  D)
         \[{{\varepsilon }_{0}}{{E}^{2}}/Ad\] done clear
  View Solution play_arrow

• question_answer83)
  In the circuit given below, the charge in \[\mu C\] , on the capacitor having capacitance \[5\mu F\]is
  A)
  4.5        done clear
  B)
  9 done clear
  C)
  7 done clear
  D)
  15 done clear
  View Solution play_arrow

• question_answer84)
  Capacitance (in F) of a spherical conductor with radius 1 m is
  A)
  \[1.1\times {{10}^{-10}}\] done clear
  B)
  \[{{10}^{6}}\] done clear
  C)
  \[9\times {{10}^{-9}}\] done clear
  D)
  \[{{10}^{-3}}\] done clear
  View Solution play_arrow

• question_answer85)
  The capacitance of a metallic sphere is \[1\mu F\], then it?s radius is nearly
  A)
  1.11 m done clear
  B)
  10 m done clear
  C)
  9 km     done clear
  D)
  1.11 cm done clear
  View Solution play_arrow

• question_answer86)
  A network of six identical capacitors, each of value C is made as shown in the figure. Equivalent capacitance between points A and B is
  A)
  C/4       done clear
  B)
  3C/4 done clear
  C)
  4C/3     done clear
  D)
  3C done clear
  View Solution play_arrow

• question_answer87)
  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 deference 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
  A)
  \[16\frac{{{n}_{2}}}{{{n}_{1}}}{{C}_{1}}\] done clear
  B)
  \[\frac{2{{C}_{1}}}{{{n}_{1}}{{n}_{2}}}\] done clear
  C)
  \[2\frac{{{n}_{1}}}{{{n}_{2}}}{{C}_{1}}\] done clear
  D)
         \[\frac{16{{C}_{1}}}{{{n}_{1}}{{n}_{2}}}\] done clear
  View Solution play_arrow

• question_answer88)
  Two capacitors of capacitances and are connected in series, assume that the equivalent capacitance of this arrangement is C, where
  A)
  \[C<{{C}_{1}}/2\] done clear
  B)
  \[{{C}_{1}}/2<C<{{C}_{2}}/2\] done clear
  C)
   \[{{C}_{1}}<C<{{C}_{2}}\] done clear
  D)
  \[{{C}_{2}}<C<2{{C}_{2}}\] done clear
  View Solution play_arrow

• question_answer89)
  Four identical square plates of side a are arranged as shown. The equivalent capacity between A and C
  A)
  \[\frac{3{{\varepsilon }_{0}}{{a}^{2}}}{2d}\] done clear
  B)
  \[\frac{3{{\varepsilon }_{0}}{{a}^{2}}}{5d}\] done clear
  C)
  \[\frac{3{{\varepsilon }_{0}}{{a}^{2}}}{3d}\] done clear
  D)
  \[\frac{5{{\varepsilon }_{0}}{{a}^{2}}}{3d}\] done clear
  View Solution play_arrow

• question_answer90)
  Two parallel plate capacitors of capacitance C and 2C are connected in parallel and charged to a potential difference V. The battery is then disconnected, and the region between the plates of C is filled completely with a material of dielectric constant K. The common potential difference across the combination becomes
  A)
  \[\frac{2V}{K+2}\] done clear
  B)
  \[\frac{V}{K+2}\] done clear
  C)
  \[\frac{3V}{K+3}\] done clear
  D)
  \[\frac{3V}{K+2}\] done clear
  View Solution play_arrow

• question_answer91)
  Seven capacitors each of capacitance \[2\mu F\]are to be connected in a configuration to obtain an effective capacitance of \[\left( \frac{10}{11} \right)\mu F.\] Which of the combination (s) shown in figure will achieve the desired result?
  A)
  done clear
  B)
  done clear
  C)
  done clear
  D)
  done clear
  View Solution play_arrow

• question_answer92)
  In figure, there is a four way key at the middle. If key is shown from situation BD to AD, then how much charge will flow through point O?
  A)
  \[24\mu C\] done clear
  B)
  \[36\mu C\] done clear
  C)
  \[72\mu C\] done clear
  D)
  \[12\mu C\] done clear
  View Solution play_arrow

• question_answer93)
              An uncharged parallel plate capacitor having a dielectric of dielectric constant K is connected to a similar air cored parallel plate capacitor charged to a potential \[{{V}_{0}}.\] The two share the charge, and the common potential becomes V. The dielectric constant K is
  A)
  \[\frac{{{V}_{0}}}{V}-1\] done clear
  B)
  \[\frac{{{V}_{0}}}{V}+1\] done clear
  C)
  \[\frac{V}{{{V}_{0}}}-1\] done clear
  D)
  \[\frac{V}{{{V}_{0}}}+1\] done clear
  View Solution play_arrow

• question_answer94)
  A capacitor of capacity \[{{C}_{1}}\] is charged up to V volt and then connected to an uncharged capacitor of capacity \[{{C}_{2}}.\] Then final potential difference across each will be
  A)
  \[\frac{{{C}_{2}}V}{{{C}_{1}}+{{C}_{2}}}\] done clear
  B)
  \[\left( 1+\frac{{{C}_{2}}}{{{C}_{1}}} \right)V\] done clear
  C)
  \[\frac{{{C}_{1}}V}{{{C}_{1}}+{{C}_{2}}}\,\] done clear
  D)
  \[\,\left( 1-\frac{{{C}_{2}}}{{{C}_{1}}} \right)V\] done clear
  View Solution play_arrow

• question_answer95)
  A parallel plate capacitor of area ?A? plate separation ?d? is filled with two dielectrics as shown. What is the capacitance of the arrangement?
  A)
  \[\frac{3K{{\varepsilon }_{0}}A}{4d}\] done clear
  B)
  \[\frac{4K{{\varepsilon }_{0}}A}{4d}\] done clear
  C)
  \[\frac{\left( K+1 \right){{\varepsilon }_{0}}A}{2d}\] done clear
  D)
  \[\frac{K\left( K+3 \right){{\varepsilon }_{0}}A}{2\left( K+1 \right)d}\] done clear
  View Solution play_arrow

• question_answer96)
  In the circuit shown, the effective capacitano between points X and Y is 
  A)
  \[3.33\mu F\] done clear
  B)
  \[1\mu F\] done clear
  C)
  \[0.44\mu F\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• 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.
  A)
  3 done clear
  B)
  4     done clear
  C)
  5 done clear
  D)
  6 done clear
  View Solution play_arrow

• question_answer98)
  For the configuration of media permittivities \[{{\varepsilon }_{0}},\varepsilon \] and \[{{\varepsilon }_{0}}\]between parallel plated each of area A, as shown in Fig. the equivalent capacitance
  A)
  \[{{\varepsilon }_{0}}A/d\] done clear
  B)
  \[\varepsilon {{\varepsilon }_{0}}A/d\] done clear
  C)
  \[\frac{\varepsilon {{\varepsilon }_{0}}A}{d\left( \varepsilon +{{\varepsilon }_{0}} \right)}\] done clear
  D)
  \[\frac{\varepsilon {{\varepsilon }_{0}}A}{\left( 2\varepsilon +{{\varepsilon }_{0}} \right)d}\] done clear
  View Solution play_arrow

• question_answer99)
  In a Van de Graff generator, a spherical metal shell is to be \[15\times {{10}^{6}}V\] electrode. The dielectric strength of the gas surrounding the electrode is \[15\times {{10}^{-7}}V{{m}^{-1}}.\] The minimum radius of the spherical shell required is
  A)
  1m done clear
  B)
  2m   done clear
  C)
  1.5m done clear
  D)
  3m done clear
  View Solution play_arrow

• question_answer100)
  A unit positive point charge of mass m is projected with a velocity V inside the tunnel as tunnel as shown.  The tunnel has been made inside a uniformly charged nonconducting sphere (charge density\[\rho \]). The minimum velocity with which the point charge should be projected such that it can reach the opposite end of the tunnel is equal to    
  A)
  \[{{[\rho {{R}^{2}}/4m{{\varepsilon }_{0}}]}^{1/2}}\] done clear
  B)
              \[{{[\rho {{R}^{2}}/24m{{\varepsilon }_{0}}]}^{1/2}}\] done clear
  C)
              \[{{[\rho {{R}^{2}}/6m{{\varepsilon }_{0}}]}^{1/2}}\] done clear
  D)
              zero because the initial and the final points are        at some potential              done clear
  View Solution play_arrow