In a certain region of space, electric field is along the z-direction throughout. The magnitude of electric field is, however, not constant but increases uniformly along the positive z-direction, at the rate of 10⁵ NC⁻¹ per metre. What are the force and torque experienced by a system having a total dipole moment equal to 10⁻⁷ Cm in the negative z-direction ?

Dipole moment of the system, p=q x dl =10⁻⁷Cm

Rate of increase of electric field per unit length dE/dl =10⁵ NC^_1

Force (F) experienced by the system is given by the relation,

F = qE = q x (dE/dl) x dl = q x dl x (dE/dl) = p x (dE/dl)

= —1(10⁻⁷ x 10⁵ )= —10⁻² N

The force is -10^-2 N in the negative z-direction i.e., opposite to the direction of electric field. Hence, the angle between electric field and dipole moment is 180°.

Torque (τ) is given by the relation, τ = pE sinl80° = 0

Therefore, the torque experienced by the system is zero.