Electrostatic Potential and Capacitance

In a certain region of space with volume 0.2 m3, the electric potential is found to be 5 V throughout. The magnitude of electric field in this region is :

1. 0.5 N/C
2. 1 N/C
3. 5 N/C
4. zero

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

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

Two metallic spheres of radii 1 cm and 3 cm are given charges of -1 10-2 C and 5 10-2 C, respectively. If these are connected by a conducting wire, the final charge on the bigger sphere is

1. 2 10-2 C
2. 3 10-2 C
3. 4 10-2 C
4. 1 10-2 C

An electric dipole of moment p is placed in an electric field of intensity E. The dipole acquires a position such that the axis of the dipole makes an angle with the direction of the field. Assuming the potential energy of the dipole to be zero when = 90 , the torque and the potential energy of the dipole will respectively be

1. pE , -pE
2. pE , -2pE
3. pE , 2pE
4. pE , -pE

Four point charges -Q, -q, 2q and 2Q are placed, one at each corner of the square. The relation between Q and q for which the potential at the centre of the square is zero is

1. Q = -q
2. Q = - 1q
3. Q = q
4. Q = 1q

Three charges, each +q, are placed at the corners of an isosceles triangle ABC of sides BC and AC, 2a. D and E are the mid points of BC and CA. The work done in taking a charge Q from D to E is [figure]

1. 3qQ4 0 a
2. 3qQ8 0 a
3. qQ4 0 a
4. zero

The electric potential V at any point (x, y, z), all in metres in space is given by V = 4x2 volt. The electric field at the point (1, 0, 2) in volt/metre, is

1. 8 along negative X-axis
2. 8 along positive X-axis
3. 16 along negative X-axis
4. 16 along positive X-axis

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

Four electric charges +q, +q, −q and −q are placed at the corners of a square of side 2L (see figure). The electric potential at point A, midway between the two charges +q and +q, is [figure]

1. 14 0 2qL (1 + 5 )
2. 14 0 2qL (1 + 1 5 )
3. 14 0 2qL (1 - 1 5 )
4. zero

Two parallel metal plates having charges +Q and -Q face each other at a certain distance between them. If the plates are now dipped in kerosene oil tank, the electric field between the plates will

1. become zero
2. increase
3. decrease
4. remain same

A series combination of n1 capacitors, each of value C1, is charged by a source of potential difference 4V. When another parallel combination of n2 capacitors, each of value C2, is charged by a source of potential difference V, it has the same (total) energy stored in it as the first combination has. The value of C2, in terms of C1, is then

1. 2C1n1 n2
2. 16 n2n1C1
3. 2 n2n1C1
4. 16C1n1 n2

Three concentric spherical shells have radii a, b and c (a < b < c) and have surface charge densities , - and respectively. If VA, VB and VC denote the potentials of the three shells, then, for c = a + b, we have

1. VC = VB VA
2. VC VB VA
3. VC = VB = VA
4. VC = VA VB

Three capacitors each of capacitance C and of breakdown voltage V are joined in series. The capacitance and breakdown voltages of the combination will be

1. 3C, V3
2. C3, 3V
3. 3C, 3V
4. C3, V3

The electric potential at a point (x, y, z) is given by V = -x2y - xz3 + 4 The electric field at that point is

1. E = i 2xy + j (x2 + y2) + k (3xz - y2)
2. E = i z3 + j xyz + k z2
3. E = i (2xy - z3) + j xy2 + k 3z2x
4. E = i (2xy + z3) + j x2 + k 3xz2

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

The electric potential at a point in free space due to charge Q coulomb is Q 1011 volts. The electric field at that point is

1. 4 0 Q 1020 volt/m
2. 12 0 Q 1022 volt/m
3. 4 0 Q 1022 volt/m
4. 12 0 Q 1020 volt/m

Charges +q and -q are placed at points A and B respectively which are a distance 2L apart, C is the midpoint between A and B. The work done in moving a charge +Q along the semicircle CRD is [figure]

1. qQ2 0L
2. qQ6 0L
3. - qQ6 0L
4. qQ4 0L