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

Answer

A

Explanation

Due to semi-circular loop in `x-y` plane
`B_(1)=(mu_(0)i)/(4R)` along `Z`-axis.
Due semi-circular loop in `x-z` plane
`B_(2)=(mu_(0)i)/(4R)` along `Y`-axis
`B_(1)` is `bot^(ar)` to `B_(2)`
`B_(R)=sqrt(B_(1)^(2)+B_(2)^(2))=sqrt(2). (mu_(0)i)/(4R)=(mu_(0)i)/(2sqrt(2)R)`