Electrostatic Potential and Capacitance · Question 35

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

In a region, the potential is represented by V(x, y, z) = 6x - 8xy - 8y + 6yz, where V is in volts and x, y, z are in metres. The electric force experienced by a charge of 2 coulomb situated at point (1, 1, 1) is

1. 6 5 N
2. 30 N
3. 24 N
4. 4 35 N

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

1. maximum at C
2. same at all the three points A, B and C
3. maximum at A
4. maximum at B

An electric dipole of dipole moment p is aligned parallel to a uniform electric field E. The energy required to rotate the dipole by 90 is

1. p2E
2. pE
3. infinity
4. pE2

A parallel plate capacitor has a uniform electric field E in the space between the plates. If the distance between the plates is d and area of each plate is A, the energy stored in the capacitor is

1. 12 0E2
2. E2Ad 0
3. 12 0E2Ad
4. 0EAd