## Answers

the answer start like this-Dipole in an external field

Consider a permanent dipole of dipole moment 'p' in a uniform external field E, which implies that p does not depend E nor it is induced due to E.

The force on q is qE and on -q is -qE and net force on dipole is zero. However, the charges are separated so the force act on different points, giving rise to a torque (twisting force) on the dipole. When net force is zero, torque is independent of the origin. Its magnitude equals the magnitude of each force multiplied by perpendicular distance between the two antiparallel forces. That is,

Magnitude of torque (t) = qE x 2a sinq

In vector notationare assumed to be in the plane of the paper.

From the above, it is found that an electric dipole placed in uniform electric field experiences a torque which align the dipole parallel to the direction of the electric field.

Forces on a dipole in a non - uniform electric field

When electric field is not uniform, the net force will be non-zero, there will also be torque on the system.

When p is parallel or antiparallel to E, the net torque is zero, but there is a force on the dipole E which is not uniform. It is seen that when p is parallel to E, dipole has a net force in the direction of increasing field and when p is antiparallel to E, the net force on dipole is in the direction of decreasing field.

Force depends on the orientation of dipole moment with respect to the external field.