Electrostatic Potential and Capacitance

As per the diagram a point charge +q is placed at the origin O. Work done in taking another point charge −Q from the point A [coordinates (0, a)] to another point B [coordinates (a, 0)] along the straight path AB is [figure]

1. zero
2. ( qQ4 0 1a2 ) 2a
3. ( -qQ4 0 1a2 ) 2a
4. ( qQ4 0 1a2 ) a 2

Two charges q1 and q2 are placed 30 cm apart, as shown in the figure. A third charge q3 is moved along the arc of a circle of radius 40 cm from C to D. The change in the potential energy of the system is q34 0k, where k is [figure]

1. 8q1
2. 6q1
3. 8q2
4. 6q2

A bullet of mass 2 g is having a charge of 2 C. Through what potential difference must it be accelerated, starting from rest, to acquire a speed of 10 m/s ?

1. 5 kV
2. 50 kV
3. 5 V
4. 50 V

An electric dipole has the magnitude of its charge as q and its dipole moment is p. It is placed in a uniform electric field E. If its dipole moment is along the direction of the field, the force on it and its potential energy are respectively

1. 2q.E and minimum
2. q.E and p.E
3. zero and minimum
4. q.E and maximum

Three capacitors each of capacity 4 are to be connected in such a way that the effective capacitance is 6 . This can be done by

1. connecting all of them in series
2. connecting them in parallel
3. connecting two in series and one in parallel
4. connecting two in parallel and one in series

Identical charges (-q) are placed at each corner of a cube of side b then electrostatic potential energy of charge (+q) which is placed at centre of cube will be

1. -4 2q2 0 b
2. -8 2q2 0 b
3. -4q2 3 0 b
4. 8 2q24 0 b

Some charge is being given to a conductor. Then its potential is

1. maximum at surface
2. maximum at centre
3. remains same throughout the conductor
4. maximum somewhere between surface and centre.

A capacitor of capacity C1 charged up to V volt and then connected to an uncharged capacitor of capacity C2. The final potential difference across each will be

1. C1VC1+C2
2. C2VC1+C2
3. (1- C2C1 )V
4. (1+ C2C1 )V

Energy per unit volume for a capacitor having area A and separation d kept at potential difference V is given by

1. 12 0 V2d2
2. 12 0 V2d2
3. 12CV2
4. Q22C

A capacitor is charged with a battery and energy stored is U. After disconnecting battery another capacitor of same capacity is connected in parallel to the first capacitor. Then energy stored in each capacitor is

1. U/2
2. U/4
3. 4U
4. 2U