A current loop consists of two identical semicircular parts each of radius 2 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

Step-by-step solution

The magnetic field at the center of a semicircular loop of radius r carrying current I is given by B = ₀ I 4r . In this problem, the radius of each semicircular part is 2R . Therefore, the magnitude of the magnetic field due to each semicircular part at the common center is B₁ = B₂ = ₀ I 4(2R) = ₀ I 8R . The first semicircular part lies in the x-y plane. By the right-hand rule, its magnetic field vector is directed along the z -axis, so B ₁ = ₀ I 8R k . The second semicircular part lies in the x-z plane. By the rig