Question

An electric dipole is placed at a distance x from centre O on the axis of a charged ring of R and charge Q uniformly distributed over it.

(a) Find the net force acting on the dipole.
(b) What is the work done in rotating the dipole through `180^@`?

Answer 1

Correct Answer - A::B::C
a. `E=(kQx)/(R^2+x^2)^(3//2)`
`(dE)/(dx)=kQ[((R^2+x^2)^(3//2)-x.3/2(R^2+x^2)^(1//2)(2x))/((R^2+x^2)^3)]`
or `(dE)/(dx)=kQ[(R^2+x^2-3x^2)/((R^2+x^2)^(5//2))]`
or `dE=Q/(4piepsilon_0)[(R^2-2x^2)/((R^2+x^2)^(5//2))]dx`
`:.|/_E|=Q/(4piepsilon_0)[(R^2-2x^2)/((R^2+x^2)^(5//2))]/_x`
Her `/_x=2a`
`:. F=|q/_E|=(Qqa)/(2piepsilon_0)[(R-2x^2)/((R^2+x^2)^(5//2))]`
b. `W=U_f-U_i`
`=-pEcos180^@+pEcos0^@=2pE`
`2(q)(2a)[1/(4piepsilon_0 (Qx)/((R^2+x^2)^(3//2)))]`
`=(aqQx)/(piepsilon(R^2+x^2)^(3//2)`