Magnetic field due to currentHard

Question

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

Options

A.
B.
C.
D.

Solution

         
The loop mentioned in the question must look like one as shown in the figure
Magentic field at the centre due to semicircular loop lying in x-y plane, Bx,y  = negative z direction.
Similarly field due to the loop in x-z plane, Bxz = in negative y direction.
∴     Magnitude of resultant magnetic field

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