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 the dipole be along z-direction (Figure)

`:.` Dipole moment, `p_(z) = - 10^(-7) C. m`
`( delE)/( delz) = 10^(5)N . C^(-1) .m^(-1)`
`:.` Net force `= p_(x) ( delE)/( delx) + p_(y) ( delE)/( dely ) + p_(z) ( del E )/( delz) ` `= 0+0-10^(-7) xx 10^(5) N = - 10^(-2) N `
Torque `= p E sin theta = p E sin 180^(@) = 0 `