Electrostatic Potential and Capacitance

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 .

Two charged conducting spheres of radii a and b are connected to each other by a conducting wire. The ratio of charges of the two spheres respectively is:

1. ab
2. ba
3. ab
4. ab

A capacitor has air as dielectric medium and two conducting plates of area 12 cm2 and they are 0.6 cm apart. When a slab of dielectric having area 12 cm2 and 0.6 cm thickness is inserted between the plates, one of the conducting plates has to be moved by 0.2 cm to keep the capacitance same as in previous case. The dielectric constant of the slab is : (Given 0 = 8.834 10-12 F/m)

1. 1.50
2. 0.66
3. 1.33
4. 1

A capacitor of 10 capacitance whose plates are separated by 10 mm through air and each plate has area 4 cm2 is now filled equally with two dielectric media of K1 = 2, K2 = 3 respectively as shown in figure. If new force between the plates is 8 N. The supply voltage is V. [figure]

Three capacitors of capacitances 25 , 30 and 45 are connected in parallel to a supply of 100 V. Energy stored in the above combination is E. When these capacitors are connected in series to the same supply, the stored energy is 9xE. The value of x is .