Question

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 force and torque experienced by a system having a total dipole moment equal to 10^-7 Cm in the negative z- direction.

Answer 1

Dipole moment of the system, p = q × dl = −10⁻⁷ C m
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 xdE/dlxdl =qxdlxdE/dl=pxdE/dl

= -10^-7x10⁵

-10^-2N

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 sin180° = 0
Therefore, the torque experienced by the system is zero.