Electrostatic Potential and Capacitance · Question 41

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