In the figure shown there are two semicircles of radii `r_(1)` and `r_(2)` in which a current `i` is flowing. The magnetic induction at the centre `O` will be

Options

A. `(mu_(0) i)/( r) (r_(1) + r_(2))`
B. `(mu_(0) i)/(4) (r_(1) - r_(2))`
C. `(mu_(0) i)/(4) ((r_(1) + r_(2))/(r_(1) r_(2)))`
D. `(mu_(0) i)/(4) ((r_(2) - r_(1))/(r_(1) r_(2)))`

Answer

C

Explanation

`B_(1)` due to big semicircle , `B_(1) = (mu_(0) i)/( 4 r_(1)) otimes`
`B_(2)` due to small semicircle , `B_(2) = (mu_(0) i)/(4r_(2)) otimes` Total B = `(mu_(0) i)/(4) [ (1)/(r_(2)) + (1)/(r_(1)) ] otimes = (mu_(0) i)/(4) [ (r_(1) + r_(2))/(r_(1) r_(2))] otimes `