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_0i)/(sqrt2R)`
B. `(mu_0i)/(2sqrt2R)`
C. `(mu_0i)/(2R)`
D. `(mu_0i)/(4R)`

Answer

B

Explanation

Magnetic fields due to the two parts at their common centre are respectively ,
`B_y=(mu_0i)/(4R) and B_Z =(mu_0i)/(4R)`
Resultant field `=sqrt(B_y^2+B_Z^2)`
`=sqrt(((mu_0i)/(4R))^2+((mu_0i)/(4R)))^2`
`=sqrt2.(mu_0i)/(4R) =(mu_0i)/(2sqrt2R)`