Electrostatic Potential and Capacitance · Question 31

The electrostatic force between the metal plates of an isolated parallel plate capacitor C having a charge Q and area A, is

1. Independent of the distance between the plates
2. Linearly proportional to the distance between the plates
3. Proportional to the square root of the distance between the plates
4. Inversely proportional to the distance between the plates

A capacitor is charged by a battery. The battery is removed and another identical uncharged capacitor is connected in parallel. The total electrostatic energy of resulting system

1. decreases by a factor of 2
2. remains the same
3. increases by a factor of 2
4. increases by a factor of 4

The diagrams below show regions of equipotentials. [figure] A positive charge is moved from A to B in each diagram.

1. In all the four cases the work done is the same.
2. Minimum work is required to move q in figure (I).
3. Maximum work is required to move q in figure (II).
4. Maximum work is required to move q in figure (III)

A capacitor of 2 is charged as shown in the diagram. When the switch S is turned to position 2, the percentage of its stored energy dissipated is [figure]

1. 75%
2. 80%
3. 0%
4. 20%

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. 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 [figure]

1. k = k1 + k2 + k3 + 3k4
2. k = 23(k1 + k2 + k3) + 2k4
3. 2k = 3k1 + k2 + k3 + 1k4
4. 1k = 1k1 + 1k2 + 1k3 + 32k4

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

1. CV2d
2. C2V22d2
3. C2V22d
4. CV22d

If potential (in volts) in a region is expressed as V(x, y, z) = 6xy − y + 2yz, the electric field (in N/C) at point (1, 1, 0) is

1. - (2 i + 3 j + k )
2. - (6 i + 9 j + k )
3. - (3 i + 5 j + 3 k )
4. - (6 i + 5 j + 2 k )

A parallel plate air capacitor of capacitance C is connected to a cell of emf V and then disconnected from it. A dielectric slab of dielectric constant K, which can just fill the air gap of the capacitor, is now inserted in it. Which of the following is incorrect?

1. The change in energy stored is 12CV2 ( 1K-1 )
2. The charge on the capacitor is not conserved.
3. The potential difference between the plates decreases K times.
4. The energy stored in the capacitor decreases K times.

Two thin dielectric slabs of dielectric constants K1 and K2 (K1 < K2) are inserted between plates of a parallel plate capacitor, as shown in the figure. The variation of electric field E between the plates with distance d as measured from plate P is correctly shown by [figure]

1. [figure]
2. [figure]
3. [figure]
4. [figure]

A conducting sphere of radius R is given a charge Q. The electric potential and the electric field at the centre of the sphere respectively are

1. zero and Q4 0R2
2. Q4 0R and zero
3. Q4 0R and Q4 0R2
4. both are zero