A square conducting loop of side length L carries a current I.The magnetic field at the centre of the loop is

Options

A. independent of L
B. proportional L
C. inversely proportional to L
D. linearly proportional to L

Answer

C

Explanation

(c) Magnetic field at the centre due to either arm
`B_1=(mu_0)/(4pi)xxI/(L//2)[sin45^@+sin45^@]`
`(mu_0)/(4pi)xx(2sqrt2l)/L`
Field at centre due to the four arms of the square
`B=4B_1=4xx(mu_0)/(4pi)xx(2sqrt2l)/L`
i.e.,`Bprop 1/L`