Electrostatic Potential and Capacitance · Question 40

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