Current I is following through a toroidal solenoid of radius r, length l and area A. If the number of turns of toroidal solenoid is N, then energy stored in the toroidal solenoid is …..

Options

A. `1/2 (mu_0N^2 A I^2)/(pir)`
B. `1/8 (mu_0 N^2 A I^2)/(pir)`
C. `1/6 (mu_0 N^2 AI^2)/(pir)`
D. `1/4 (mu_0N^2A I^2)/(pir)`

Answer

D

Explanation

Energy stored in inductor `U=1/2 LI^2` Put `L=(mu_0N^2A)/l` in `U=1/2xxL(mu_0N^2AI^2)/l`
But for toroid `l=2pir`
`therefore U=1/2xx(mu_0N^2 AI^2)/(2pir)`
`therefore U=1/4 xx (mu_0N^2AI^2)/(pir)`