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-z 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

The loop mentioned in the question must look like one shown in the figure.

Magnetic field at the centre due to semicircular loop lying in x-y plane,
`B_(xy)=(1)/(2)((mu_(0) f)/(2R))` negative z direction
Similarly field due to loop in x-z plane, `B_(max) = (1)/(2)((mu_(0) f)/(2R))` in negative y direction
Magnetic of resultant magnetic field
`B=sqrt(B_(xy)^(2)+B_(xz)^(2))=sqrt(((mu_(0)i)/(4R))^(2)=((mu_(0)i)/(4R))^(2))`
`=(mu_(0)i)/(4R)sqrt(2)-(mu_(0)f)/(2sqrt(2R))`.