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} C m

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"xxdl`

`=pxx"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 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.