Electrostatic Potential and Capacitance · Question 49

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