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 meter. 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 ?

Explanation

As shown in the figure, consider a point dipole (very tiny) with length dz, as shown in the figure. Its electric dipole moment is,
`vecp =(-vecdz)q`
`therefore p = (dz)q`………..(1)
Resultant electric force exerted on above dipole by given electric field which is along + Z axis and increases with a rate `(dvecE)/(dz)` along + Z axis (as per the statement) is,
`vecF = vecF_(+) + vecF_(-)`
`=qvecE + (-q)(vecE + dvecE)`
`=-qdvecE`
`=-q (dvecE)/(dz) dz`
`therefore vecF = -p (dvecE)/(dz)`............(2)
(From equation (1)) Here, negative sign indicates that above force is along - Z axis. Taking magnitude,
`F = p(dE)/(dz)`
`=(10^(-7)) (10^(5))`
`therefore F = 10^(-2) N` (Along -Z axis) Now, torque exerted on above dipole by the applied electric field is,
`tau = pEsin theta`
`=pEsin 180^(@) (therefore vecp || -vecE)`
`therefore tau =0`