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 system having a total dipole moment equal to `10^(-7)`Cm in the negative z-direction?

Explanation

Dipole moment of the system `p=qxxdl=-10^(-7)Cm`
Rate of increase of electric field per unit length,
`(dE)/(dl)=10^(+5)NC^(-1)`
Force (F) experienced by the system is given by the relation
F=Qe
`F=a(dE)/(dl)xxdl`
`=pxx(dE)/(dl)`
`-10^(-7)xx10^(-5)`
`-10^(-2)N`
The force is `-10^(-2)N` in the negative z-direction i.e., opposite to the direction of electric field. Hence, the angle between electric field and dipole moment is `180^(@)`.
Torque (τ) is given by the relation,
`tau = pE sin180^(@)`.
=0
Therefore, the torque experienced by the system is zero.