The figure shows a wire frame in xy-plane carrying current `I`. The magnetic field at the point `O` is

Options

A. `(mu_0)/8[1/a-1/b]hatk`
B. `(mu_0I)/8[1/b-1/a]hatk`
C. `(mu_0I)/4[1/a-1/b/]hatk`
D. `(mu_0I)/4[1/b-1/a]hatk`

Answer

A

Explanation

Arc of radius a(`1/4`th of circle) produces magnetic field in `hatk` direction field i `-hatk` direction.
`:.B=1/4((mu_0I)/(2a))hatk+1/4((mu_0I)/(2a))(-hatk)`
`=(mu_0I).8(1/a-1/b)hatk`