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)`
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

Consider an electric dipole with charge `-q` at A and charge `+q` at B, placed along Z-axis, such that its dipole moment is in negative z-direction, i.e. `p_(Z)=-10^(-7)` C-m, as shown in the figure.
The electric field is along
positive direction of Z-axis such that
`(dE)/(dZ)=10^(5)"NC"^(-1)m^(-1)`
Using `F=qdE`
`=qxx(dE)/(dZ)=(qxxdZ)xx(dE)/(dZ)`
`=p(dE)/(dZ)`
`:." "F=10^(-7)xx0^(5)=-10^(-2)N`
Thus, the force on the dipole is along negative direction of Z-axis.
As, `theta=180^(@)`
`:.` Torque on dipole,
`taupEsin 180^(@)=0`