Electrostatic Potential and Capacitance

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). In the light of the above statements, choose the most appropriate answer from the options given below :

1. Both (A) and (R) are correct but (R) is not the correct explanation of (A)
2. (A) is correct but (R) is not correct
3. Both (A) and (R) are correct and (R) is the correct explanation of (A)
4. (A) is not correct but (R) is correct

A parallel plate capacitor has charge 5 10-6 C. A dielectric slab is inserted between the plates and almost fills the space between the plates. If the induced charge on one face of the slab is 4 10-6 C then the dielectric constant of the slab is .

Four capacitors each of capacitance 16 are connected as shown in the figure. The capacitance between points A and B is : (in ). [figure]

Three parallel plate capacitors C1, C2 and C3 each of capacitance 5 are connected as shown in figure. The effective capacitance between points A and B, when the space between the parallel plates of C1 capacitor is filled with a dielectric medium having dielectric constant of 4, is : [figure]

1. 9
2. 30
3. 7.5
4. 22.5

A parallel plate capacitor is filled equally (half) with two dielectrics of dielectric constants 1 and 2, as shown in figures. The distance between the plates is d and area of each plate is A. If capacitance in first configuration and second configuration are C1 and C2 respectively, then C1C2 is: First Configuration [figure] Second Configuration [figure]

1. 0( 1 + 2)2
2. 1 22( 1 + 2)2
3. 4 1 2( 1 + 2)2
4. 1 2 1 + 2

The electrostatic potential on the surface of uniformly charged spherical shell of radius R = 10 cm is 120 V. The potential at the centre of shell, at a distance r = 5 cm from centre, and at a distance r = 15 cm from the centre of the shell respectively, are:

1. 0 V, 120 V, 40 V
2. 120 V, 120 V, 80 V
3. 40 V, 40 V, 80 V
4. 0 V, 0 V, 80 V

Using a battery, a 100 pF capacitor is charged to 60 V and then the battery is removed. After that, a second uncharged capacitor is connected to the first capacitor in parallel. If the final voltage across the second capacitor is 20 V, its capacitance is: (in pF)

1. 600
2. 100
3. 400
4. 200

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). In the light of the above statements, choose the most appropriate answer from the options given below :

1. Both (A) and (R) are correct and (R) is the correct explanation of (A)
2. Both (A) and (R) are correct but (R) is not the correct explanation of (A)
3. (A) is not correct but (R) is correct
4. (A) is correct but (R) is not correct

Two large plane parallel conducting plates are kept 10 cm apart as shown in figure. The potential difference between them is V. The potential difference between the points A and B (shown in the figure) is : [figure]

1. 1 V
2. 14 V
3. 34 V
4. 25 V

A capacitor, C1=6 is charged to a potential difference of V0=5 V using a 5V battery. The battery is removed and another capacitor, C2=12 is inserted in place of the battery. When the switch 'S' is closed, the charge flows between the capacitors for some time until equilibrium condition is reached. What are the charges (q1 and q2) on the capacitors C1 and C2 when equilibrium condition is reached. [figure]

1. q1=10 , q2=20
2. q1=15 , q2=30
3. q1=20 , q2=10
4. q1=30 , q2=15

Three infinitely long wires with linear charge density are placed along the x-axis, y-axis and z-axis respectively. Which of the following denotes an equipotential surface?

1. (x2 + y2)(y2 + z2)(z2 + x2) = constant
2. xyz = constant
3. xy + yz + zx = constant
4. (x + y)(y + z)(z + x) = constant

Two capacitors C1 and C2 are connected in parallel to a battery. Charge-time graph is shown below for the two capacitors. The energy stored with them are U1 and U2, respectively. Which of the given statements is true? [figure]

1. C2 > C1, U2 > U1
2. C1 > C2, U1 > U2
3. C2 > C1, U2 < U1
4. C1 > C2, U1 < U2

A particle of mass 'm' and charge 'q' is fastened to one end 'A' of a massless string having equilibrium length l, whose other end is fixed at point 'O'. The whole system is placed on a frictionless horizontal plane and is initially at rest. If uniform electric field is switched on along the direction as shown in figure, then the speed of the particle when it crosses the x-axis is [figure]

1. qEl2m
2. qEl4m
3. qElm
4. 2qElm

A parallel plate capacitor of capacitance 1 μF is charged to a potential difference of 20 V. The distance between plates is 1 μm. The energy density between plates of capacitor is :

1. 1.8 103 J/m3
2. 2 102 J/m3
3. 2 10-4 J/m3
4. 1.8 105 J/m3

An electric dipole of dipole moment 6 10-6 C m is placed in uniform electric field of magnitude 106 V/m. Initially, the dipole moment is parallel to electric field. The work that needs to be done on the dipole to make its dipole moment opposite to the field, will be J.

Consider a parallel plate capacitor of area A (of each plate) and separation 'd' between the plates. If E is the electric field and 0 is the permittivity of free space between the plates, then potential energy stored in the capacitor is

1. 0E2Ad
2. 34 0E2Ad
3. 14 0E2Ad
4. 12 0E2Ad

A parallel plate capacitor was made with two rectangular plates, each with a length of l=3 cm and breadth of b=1 cm. The distance between the plates is 3 . Out of the following, which are the ways to increase the capacitance by a factor of 10 ? Choose the correct answer from the options given below:

1. C only
2. A only
3. B and D only
4. C and E only

[figure] In the first configuration (1) as shown in the figure, four identical charges (q0) are kept at the corners A, B, C and D of square of side length 'a'. In the second configuration (2), the same charges are shifted to mid points G, E, H and F, of the square. If K= 14 0, the difference between the potential energies of configuration (2) and (1) is given by :

1. Kq02a (4-2 2 )
2. Kq02a (4 2-2 )
3. Kq02a (3- 2 )
4. Kq02a (3 2-2 )

Two point charges -4 and 4 , constituting an electric dipole, are placed at (-9,0,0) cm and (9,0,0) cm in a uniform electric field of strength 104 N C-1. The work done on the dipole in rotating it from the equilibrium through 180 is :

1. 18.4 mJ
2. 12.4 mJ
3. 16.4 mJ
4. 14.4 mJ

Two charges 7 and -4 are placed at (-7 cm,0,0) and (7 cm,0,0) respectively. Given, 0=8.85 10-12 C2 N-1 m-2, the electrostatic potential energy of the charge configuration is :

1. -2.0 J
2. -1.5 J
3. -1.2 J
4. -1.8 J

A parallel-plate capacitor of capacitance 40 is connected to a 100 V power supply. Now the intermediate space between the plates is filled with a dielectric material of dielectric constant K=2. Due to the introduction of dielectric material, the extra charge and the change in the electrostatic energy in the capacitor, respectively, are

1. 8 mC and 2.0 J
2. 4 mC and 0.2 J
3. 2 mC and 0.2 J
4. 2 mC and 0.4 J

For a short dipole placed at origin O , the dipole moment P is along x-axis, as shown in the figure. If the electric potential and electric field at A are V0 and E0, respectively, then the correct combination of the electric potential and electric field, respectively, at point B on the y-axis is given by [figure]

1. V02 and E016
2. zero and E08
3. V0 and E04
4. zero and E016