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 the two semicircular parts at their common centre is

The correct option is µ₀i2√2R
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, Bxy = 1/2(µ₀i√2R) negative z direction
Similarly field due to loop in x-z plane, Bxz = 1/2(µ₀i√2R) in negative y direction.
∴Magnitude of resultant magnetic field, B = √Bxy² + Bxz² = √(µ₀i/4R)² + (µ₀i/4R)² = µ₀i/4R√2 = µ₀i2√2R