A point charge `q` is located at the centre fo a thin ring of radius `R` with uniformly distributed charge `-q`, find the magnitude of the electric field strength vectro at the point lying on the axis of the ring at a distance `x` from its centre, if `x gt gt R`.

Options

A. `(QR^(2))/(8pi epsilon_(0)x^(4))`
B. `(3QR^(2))/(8 pi epsilon_(0)x^(4))`
C. `(5QR^(2))/(8pi epsilon_(0)x^(4))`
D. `(7QR^(2))/(8pi epsilon_(0)x^(4))`

Answer

B

Explanation

Electric field due to uniformly charged Ring at it's axis (at distance x) =`(-KQx)/((R^(2)+x^(2))^(3//2))`
and Electric field due to point charge `=(KQ)/(x^(2))`
So net electric field `=(KQ)/(x^(2))+(-KQx)/((R^(2)+x^(2))^(3//2))=(KQ[(R^(2)+x^(2))^(3//2)-x^(3)])/(x^(2)[R^(2)+x^(2)]^(3//2))`
When Rlt lt x=`(KQ[1+(3R^(2))/(2x^(2))-1])/(x^(2)[1])=(3KQR^(2))/(2x^(4))=-(3QR^(2))/(8piepsilon_(0)x^(4))`