In a certain region of space, electric field is along the z-direction throughout. The magnitude of the 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)` C. m in the negative z-direction.

Explanation

Let `Deltaz` be the length of the electric dipole kept along Z-axis. Let the electric field change by amount `DeltaE` when we move `Deltaz` along Z-axis . The net force on the dipole can be written as follows :
`F=q(E+DeltaE)-qE=qDeltaE=q(Deltaz)xx(DeltaE)/(Deltaz)`
`rArr F=p(dE)/(dz)`
`rArr F=p (dE)/(dz) =(10^(-7))(10^5)=10^(-2)` N
According to the direction of the electric dipole moment, the electric field intensity is more at the location of the negative charge. Therefore, the negative charge will experience a greater force along the negative Z-axis. And the net force on the electric dipole will be along the negative Z-direction.
The forces on positive and negative ends of the electric dipole are along the same line and therefore net torque will be zero.