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_(1)-r_(2))/(r_(1)r_(2)))`

Answer

C

Explanation

The magnetic induction due to both semicicular parts will be in the same direction perpendicular to the paper inwards.
`:. B=B_(1)+B_(2)=(mu_(0)i)/(4r_(1))+(mu_(0)i)/(4r_(2))=(mu_(0)i)/4((r_(1)+r_(2))/(r_(1)r_(2))) ox`