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)m^(-1)`. 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

Given `(dE)/(dz)=10^(5)NC^(-1)m^(-1)`
Then `F=qdE`, represent the force on the system
i.e. `F=q(dE)/(dz). dz`
i.e. `F=(q dZ)=(dE)/(dz)`, dipole moment `p=q dz`
or `F=(pdE)/(dz)`
i.e. `vecF=-vecp(dvecE)/(dz)`
`:.F=-10^(-7)xx10^(5)N`
i.e.` F=-10^(-2)N`
Force on the dipole is `-10^(-2)`N
now the angle between the dipole and the electric field is `180^(@)`
Torque `tau=pEsin theta`
i.e. `tau=-10^(-7)xx10^(-2)xxsin 180^(@)`
i.e. `tau=0`
Thus the torque on the dipole is zero.