In figure, infinite conducting ring each having current i in the direction shown are places concentricallly in the same plane . The radius of ring are `r, 2r, 2^(2)r, 2^(3)r….oo` . The magnetic field at the centre of ring will be

Options

A. zero
B. `(mu_i)/r`
C. `(mu_i)/(2r)`
D. `(mu_i)/(3r)`

Answer

B

Explanation

(d) `B=(mu_0i)/(2r)-(mu_0i)/(2(2r))+(mu_0i)/(2(2^2r))+......(oo)`
`B=(mu_0i)/(2r)[1-1/2+1/(2^2)-1/(2^3)+.....(oo)]`
`B=(mu_0i)/(2r)[1/(1-(-1/2))]=(mu_0i)/(3r)`