Electrostatic Potential and Capacitance

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

Two condensers, one of capacity C and other of capacity C/2 are connected to a V-volt battery, as shown in the figure. The work done in charging fully both the condensers is [figure]

1. 14CV2
2. 34CV2
3. 12CV2
4. 2CV2

A parallel plate air capacitor is charged to a potential difference of V volts. After disconnecting the charging battery the distance between the plates of the capacitor is increased using an insulating handle. As a result the potential difference between the plates

1. increases
2. decreases
3. does not change
4. becomes zero

An electric dipole of moment p is lying along a uniform electric field E. The work done in rotating the dipole by 90 is

1. pE
2. 2pE
3. pE/2
4. 2pE