In a certain region of space, electric field is along the Z-direction throught. 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)` per metre. Whay are the force and torque experienced by a system having a total dipolemoment equal to `10^(7)` Cm in the negative Z-direction?

Explanation

The electric field increases in positive Z-direction.
`(dE)/(dZ)=10^(5) N//C-m`
The direction of dipolement is in the negative Z-direction
So the negative charge q is placed at A and positive charge q is placed at B as the direction of dipole moment is from negative charge to positive charge.
`P_(Z)=-10^(-7) C-m`
The negative sign shows its direction in negative Z-axis. According to the basic definition of electric field, F = qdE Now, multiplying and dividing by dz,
`F=q (dE)/(dz). dz=q.dz (dE)/(dz)`
qdz = dipolemoment `p_(z)`, as the length of the dipole is dz.
`:. F=P_(z). (dE)/(dz)=-10^(-7) xx10^(5) =-10^(-2) N`
Torque, `tau =PE sin theta` (`:' theta =180^(@)` angle between P and E)
`tau=PE sin 180^(@)=0`
Thus the force is `-10^(-2)N` and the torque is 0.