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 ${10}^{5}N{C}^{-1}{m}^{-1}$ 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 ?

Answer 1

Dipole moment of the system, $p=q\times dl=-{10}^{-7}Cm$

Rate of increase of electric field per unit length,

$\frac{dE}{dl}={10}^{+5}N{C}^{-1}$

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

$F=qE$

$F=q\frac{dE}{dl}\times dl$

$=p\times \frac{dE}{dl}$

$={10}^{-7}\times {10}^{-5}$

$=-{10}^{-2}N$

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 ${180}^o$.

Torque (τ) is given by the relation,

$T=pEsin{180}^o=0$

Therefore, the torque experienced by the system is zero.