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)/(r) ((r_(1) + r_(2))/(r_(1) r_(2)))`
D. `(mu_(0) i)/(r) ((r_(2) - r_(1))/(r_(1) r_(2)))`

Answer

C

Explanation

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