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 ${10}^5$ $N{C}^{-1}$ 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 is given as

$p=qdl$

which is given to be ${10}^{-7}cm$

Rate of increase of electric field with respect to length is

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

Force is related to the above quantity as

$F=qdl\frac{dE}{dl}$

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

negative sign indicates that the direction is opposite to the magnetic field i.e. negative z-direction.

The angle between Electric field and dipole moment is ${180}^o$

Torque is thus given as

$pEsin{180}^o$

$=0$