# electrostatic potential and capacitance neet questions || electrostatic potential and capacitance jee questions

*Dear students numericals of electrostatic potential and capacitance neet questions and electrostatic potential and capacitance jee questions aiims important questions have been collected at one place to get you all prepared for your neet, aiims ,jee main, advance exams as well as cbse board exams and other board exams. Visit my nawendu classes youtube channel for more help.*

**Answer- 2/3m from 4 $\mu $C**

**JIPMER 1998**

Answer- 8 x ${{10}^{6}}$ V

3. 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 (√2, √2) and (2, 0) respectively. The potential difference between the points A and B will be

AIEEE 2007

Answer- Zero

4. Four electric charges +q, +q,-q and -q are placed at the corners of a square of side 2 L (see figure). The electric potential at point A, mid-way between the two charges +q and +q is

CBSE AIPMT 2011

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

5. Four point charges-Q,-q, 2q and 2Q are placed, one at each corner of the square. The relation between Q and q for which the potential at the centre of the square is zero, is

CBSE AIPMT 2012

Answer- Q= -q

6. A, B and C are three points in a uniform electric field. The electric potential is

NEET 2013

Answer- maximum at B

7. A hollow metal sphere of radius 10 cm is charged such that the potential on its surface is 80 V. The potential at the center of the sphere is

CBSE AIPMT 1994

Answer- 80V

8. 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

CBSE AIPMT 2014

Answer- $\frac{Q}{4\pi {{\varepsilon }_{0}}R}$ and zero

9. The electric potential at a point in free space due to a charge Q coulomb is Qx${{10}^{11}}$ V. The electric field at that paint is

CBSE AIPMT 2008

**Answer- $4\pi {{\varepsilon }_{0}}Q$ x${{10}^{22}}$ V/m**

10. A cube of side b has a charge q at each of its vertices. Determine the potential and electric field due to this charge array at the center of the cube.

Answer- Potential = $V=\frac{4q}{\sqrt{3}\pi {{\varepsilon }_{0}}b}$ , Electric field= 0

11. Two concentric spheres of radii R and r have similar charges with equal surface charge densities ($\sigma $). What is the electric potential at their common center ?

CBSE AIPMT 1991

**Answer- $\frac{\sigma }{{{\varepsilon }_{0}}}(R+r)$**

12. 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 [coordinates (0,a)] to another point B [Coordinates (a, 0)] along the straight Path AB is .

13. charges + q and -q are placed at points A and B respectively Which are a distance 2L apart, C Is the mid-point between A and B . The work done in moving a charge +Q along the semicircle CRD is

CBSE AIPMT 2007, AIIMS 2017

Answer- 2.24 x${{10}^{-16}}$ J

15. A ball of mass 1 g and charge ${{10}^{-8}}$ C moves from a point A where potential is 600 V to the point B Where potential is zero. Velocity of the ball at the point B is 20 cm/s. The velocity of the ball at the point A will be

AIIMS 2009

Answer- 16.7cm/s

16. A proton is about 1840 times heavier than an electron. When it is accelerated by a potential difference of 1 kV, its kinetic energy will be

**AIIMS 2003**

Answer- 1KeV

17. Two spheres A and B of radius a and b respectively are at the same potential. The ratio the surface charge density of A and B is

Answer- b/a

18. An infinite thin plane sheet of charge density ${{10}^{-8}}$${{m}^{-2}}$ is held in air.

How far apart are two equipotential surfaces, whose p.d. is 5 volt ?

C.B.S.E. 2003

Answer- 8.85 x ${{10}^{-3}}$ m

19.Two point charges A and B of value + 15 $\mu $C and + 9 $\mu $C are kept 18 cm

apart in air. Calculate the work done when charge B is moved by 3 cm

towards A.

20. There are four point charges +q, -q, +q and -q are placed at the corners A, B, C, and D respectively of a square of side a. The potential energy of the system is $\frac{1}{4\pi {{\varepsilon }_{0}}}$ times

AIIMS 2013

Answer- r/4

22. 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

CBSE AIPMT 2005

Answer- 8${{q}_{2}}$

23. An electric dipole of moment p is lying along a uniform electric field E. The work done in rotating the dipole by 90° is

CBSE AIPMT 2006

Answer- pE

24. Capacitance of a spherical conductor with radius 1 m is

AIEEE 2002

Answer- 1.1 x ${{10}^{-10}}$ F

25. A spherical drop of capacitance 1$\mu $F is broken into eight drops of equal radius . Then, the capacitance of each small drop is

AIIMS 2012

Answer- 1/2 $\mu $F

26. In a parallel plate capacitor with air between the plates, each plate has an area of 6 × ${{10}^{-3}}$ ${{m}^{2}}$ and the distance between the plates is 3 mm. Calculate the capacitance of the capacitor.

(a) If this capacitor is connected to a 100 V supply, what is the charge on each plate of the capacitor?

(b) Explain what would happen if 3 mm thick mica sheet (of dielectric constant = 6) were inserted between the plates, (1) while the voltage supply remained connected.

(2) after the supply was disconnected.

Answer- (a)18 pF, 1.8 × ${{10}^{-9}}$ C

(b)(1)V = 100 V, C = 108 pF, Q = 1.08 × ${{10}^{-8}}$ C

(2)Q = 1.8 × ${{10}^{-9}}$ C, C = 108 pF, V = 16.6 V

27. A parallel plate condenser with oil (dielectric constant 2) between the plates has capacitance C. If oil is removed, the capacitance of capacitor becomes

CBSE AIPMT 1999

Answer- C / 2

28. A parallel plate capacitor with air between the plates has capacitance of 9pF. The separation between its plates is ‘d’ the space between the plates is now filed with two dielectrics. One of the dielectric has dielectric constant k1 = 3 and thickness d/3 while the other one has dielectric constant k2 = 6 and thickness 2d/3. Capacitance of capacitor is now

AIEEE 2008

Answer- 40.5 pF

29. The capacitance of a parallel plate condenser is 10 $\mu $ F, when the distance between its plates is 8 cm. If the distance between plates is reduced to 4 cm then the capacity of this parallel plate condenser will be

Answer- 20 $\mu $ F

30. A parallel plate capacitor with air between the plates has a capacitance of 8 pF (1pF = ${{10}^{-12}}$ F). What will be 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 6?

Answer- 96 pF

31. 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

32.The work done in placing a charge of 8 x ${{10}^{-18}}$ coulomb on a condenser of

capacity 100 $\mu $ F is

AIEEE 2003

Answer- 32 x ${{10}^{-32}}$ J

33. If the potential of a capacitor having capacity 6 $\mu $ F is increased from 10 V to 20 V, then increase in its energy will be

CBSE AIPMT 1995

Answer- 9 x ${{10}^{-4}}$J

34. If there are n capacitors in parallel connected to V volt source, then the energy stored is equal to

AIEEE 2002

Answer- $\frac{1}{2}nC{{V}^{2}}$

35. A 4$\mu $F capacitor is charged to 400 V and then its plates are joined through a resistance of 1 k$\Omega $ .The heat produced in the resistance is

Answer- 0.32 J

36. The energy required to charge a parallel plate condenser of plate separation d and plate area of cross-section A such that the uniform electric field between the plates E, is

CBSE AIPMT 2008

Answer- ${{\varepsilon }_{0}}{{E}^{2}}Ad$

37. 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(m2 ), the energy (joule) stored in the condenser is

CBSE AIPMT 2011

Answer- $\frac{1}{2}{{\varepsilon }_{0}}{{E}^{2}}Ad$

38. 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

CBSE AIPMT 2015

Answer- $\frac{C{{V}^{2}}}{2d}$

39. A parallel plate capacitor has an electric field of ${{10}^{5}}$ V/m between the plates. If the charge on the capacitor plates is 1$\mu $C, the force on each capacitor plate is

AIIMS 2017

Answer- 0.05N

40. A charged oil drop of mass 2.5 x ${{10}^{-7}}$ kg is in space between the two plates, each of area 2 x ${{10}^{-2}}$ ${{m}^{2}}$ of a parallel plate capacitor. When the upper plate has a charge of 5 x${{10}^{-7}}$ C and the lower plate has an equal negative charge, the oil remains stationary. The charge of the oil drop is (Take, g = 10m/${{s}^{2}}$)

AIIMS 2010

Answer- 8.85x${{10}^{-13}}$ C

41. A 600 pF capacitor is charged by a 200 V supply. It is then disconnected from the supply and is connected to another uncharged 600 pF capacitor. How much electrostatic energy is lost in the process?

Answer-6 × ${{10}^{-6}}$ J

42. 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

CBSE AIPMT 2000

Answer- U/2

43.Two capacitors C and C/2 are connected to a battery of V volts, as shown below .The work done in charging both the capacitors fully is

**CBSE AIPMT 2007 , AIIMS 2017**

44.The effective capacitance between points X and Y of figure shown is

CBSE AIPMT 1999

45. A capacitor of 2$\mu $F is charged as shown in the figure. When the switch S is turned to position 2, the percentage of its stored energy dissipated is

NEET 2016

Answer- 80%

46. A gang capacitor is formed by interlocking a number of plates as shown in figure. The distance between the consecutive plates is 0.885 cm and the overlapping area of the plates is 5 $c{{m}^{2}}$ . The capacity of the unit is

AIIMS 2011

Answer.- 4pF

47. Three plates of Common surface area A are connected as shown in figure.

The effective capacitance will be

AIIMS 2013

Answer-\[2A{{\varepsilon }_{0}}/d\]

48. In the circuit shown in the figure, the potential difference across the 4.5 $\mu $F capacitor is

AIIMS 2010

Answer- 8V

49. A network of four capacitors of ${{C}_{1}}$=C , ${{C}_{2}}$=2C , ${{C}_{3}}$=3C and ${{C}_{4}}$=4C are connected to a battery as shown in the figure.

The ratio of the charges on ${{C}_{2}}$ and ${{C}_{3}}$ is

AIIMS 2009

Answer- 3/22

50. A series combination of ${{n}_{1}}$ 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 term of ${{C}_{1}}$ is then

CBSE AIPMT 2010

Answer- $\frac{16{{C}_{1}}}{{{n}_{1}}{{n}_{2}}}$

51. A 40 $\mu $F capacitor in a defibrillator is charged to 3000 V. The energy stored in the capacitor is sent through the patient during a pulse of duration 2 ms. The power delivered to the patient is

** ** AIIMS
2004

Answer- 90KW

52. Two material having the dielectric constants K1 and K2 are filled between two Parallel plates of a capacitor. Where area of each plate is A and the distance between the plates is d.

Answer- $\frac{A{{\varepsilon }_{0}}({{K}_{1}}+{{K}_{2}})}{2d}$

53. Minimum number of 80$\mu $F and 250 V capacitors are used to make a combination of 16$\mu $F and 1000 V are

AIIMS 1996

Answer- 32

**# Assertion and Reason**

54. Assertion-Net electric field inside a conductor is 0

Reason-Charge is present on the surface of conductor.

AIIMS 2018

Answer-a

55. Assertion- The lighting conductor at the top of high building has sharp pointed ends

Reason-The surface density of charge at sharp points is very high resulting in setting up of electric wind.

AIIMS 2005

Answer-a

56. Assertion- A metallic shield in form of a hollow shell may be built to block an electric field.

Reason -In a hollow spherical shield, the electric field inside it is zero at every point. AIIMS 2001

Answer-a

57. (a) Two materials having the dielectric constants k1 and k2 are filled between two parallel plates of a capacitor .Where area of each plate is A. and the distance between the plates is d.

The capacity of the capacitor is

AIIMS 2001

Answer- $\frac{A{{\varepsilon }_{0}}({{k}_{1}}+{{k}_{2}})}{2d}$

58. A parallel-plate capacitor of area A, plate separation d and capacitance C is filled with four dielectric materials having dielectric Constants k1 ,k2 ,k3 and k4 as shown in the figure below. If a single dielectric material is to be used to have the same capacitance C in this capacitor, then its dielectric constant k is given by

NEET 2016

Answer- $\frac{2}{3}[\frac{{{k}_{1}}{{k}_{4}}}{{{k}_{1}}+{{k}_{4}}}+\frac{{{k}_{2}}{{k}_{4}}}{{{k}_{2}}+{{k}_{4}}}+\frac{{{k}_{3}}{{k}_{4}}}{{{k}_{3}}+{{k}_{4}}}]$

59. Electric field inside a parallel plate capacitor is 100 V/m and dielectric constant inside it is 5.5. Then, the value of polarization is

** ** AIIMS 2018

Answer- 450

60. 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

IIT Main 2019. 10 April ll

Answer- 20000 m/s

61. The electric field in a region is given by E=(Ax+B)$\widehat{i}$ where E is in N/C and x is in meters. The values of constants are A = 20 SI unit and B = 10 SI unit. If the potential at x = 1 is V1 and that at x = - 5 is V2, then V1 -V2 is

IIT Main2019, 8 April II

Answer- 180V

62. 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 IIT Main 2019, 11 Jan I

Answer- $\frac{-\sqrt{2q}}{\sqrt{2}+1}$

63. Assume that an electric field E= 30 ${{x}^{2}}\widehat{i}$ exists in space. Them the potential difference VA - V0 , where V0 is the potential at the origin and VA the potential at x = 2 m is

** ** IIT 2014 Main

Answer- -80J

64. An alpha particle of energy 5 MeV is scattered through 180° by a fixed uranium nucleus. The distance of closest approach is of the order of

IIT 1981, 2M

Answer- ${{10}^{-12}}$ cm

65. A point charge q moves from a point P to a point S along the path PQRS in a uniform electric field $\overrightarrow{E}$ along positive direction of x-axis. Calculate work done in this process, when co-ordinates of P, Q, R, S are (a, b, 0),(2a, 0, 0), (a, -b, 0) and (0, 0, 0) respectively.

I.I.T.

Answer- -q E a

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