In Fig. infinite conducting rings each having current i in the direciton shown are placed concentrically in the same plane as shown in the figure. The radii of rings are `r,2r,2^2r,2^3r,......,(oo)`. The magnetic field at the centre of rings 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)`