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(2R))`
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 as shown in the figure

Magnetic field at the centre due to semicircular loop lying in x-y plane, `B_(xy) =1/2((mu_(0)i)/(2R))` negative z direction similarly field due to loop in x-z plane, `B_(xz)=1/2((mu_(0)i)/(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)i)/(2sqrt(2)R)`