Electrostatic Potential and Capacitance

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

A capacitor is made of a flat plate of area A and a second plate having a stair-like structure as shown in figure. If the area of each stair is A3 and the height is d, the capacitance of the arrangement is : [figure]

1. 11 0 A20 d
2. 13 0 A17 d
3. 18 0 A11 d
4. 11 0 A18 d

At the centre of a half ring of radius R = 10 cm and linear charge density 4 nC m-1, the potential is x V. The value of x is .