In a certain region of space, electric field is along the z-direction throughout.
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 the force and torque experienced by a system having a total dipole moment equal to 10−7 Cm in the negative z-direction?

Solution:

Dipole moment of the system, p = q × dl = −10−7 C m

Rate of increase of electric field per unit length,

$\frac{d E}{d l}=10^{+5} \mathrm{~N} \mathrm{C}^{-1}$

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

F = qE

$F=q \frac{d E}{d l} \times d l$

$=p \times \frac{d E}{d l}$

= −10−7 × 10−5

= −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 sin180°

= 0

Therefore, the torque experienced by the system is zero.