A current loop consists of two identical semicircular parts each of radius R, one lying in the x-y plane and the other in x-y plane. If the current in the loop is i, the resultant magnetic field due to two semicircular parts at their common centre is

Options

A. `(mu_(0) i)/(2 sqrt2 R)`
B. `(mu_(0) i)/(2R)`
C. `(mu_(0) i)/(4R)`
D. `(mu_(0) i)/(sqrt2 R)`

Answer

A

Explanation

`B_(1) = B_(2) = (1)/(2) (mu_(0) I)/(2R)`
`therefore B_("net") = sqrt(B_(1)^(2) + B_(2)^(2)) = (mu_(0) I)/(2sqrt2 R)`