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 10^{5 }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 }Cm

Rate of increase of electric field per unit length,

`"dE"/"dl" = 10^-5 "NC"^-1`

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

F = qE

`"F" = "q""dE"/"dl" xx "dl"`

= `"p" xx "dE"/"dl"`

= −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 the electric field. Hence, the angle between the electric field and the dipole moment is 180°.

Torque (τ) is given by the relation,

τ = pE sin 180°

= 0

Therefore, the torque experienced by the system is zero.