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

Here, `p=10^(-7) Cm`
`(dE)/(dZ)=10^(5)NC^(-1)m^(-1)`
From fig.
`vec(F)=q vec(E )+(-q)(vec(E )+dvec(E ))-qdvec(E )`
`=-q[(dvec(E ))/(dZ)]dZ`
`-qdZ[(dvec(E ))/(dZ)]=-p(dvec(E ))/(dZ)`

(as q dZ=p=dipole moment)
Thus, `vec(F)` acts in a direction opposite to `d vec(E )//dZ`, i.e. along the negative z-direction. Further,
`F=|vec(F)|=p(dE)/(dZ)`
`=(10^(-7)Cm)(10^(-5)(N)/(Cm))=10^(-2)N`
Since `vec(p) darr uarr vecE, tau=0` (or `tau=pE sin theta=pE=sin 180^(@)=0)`.