A uniform circular wire loop of radius R is bent along its diameter so that the two semicircular halves lie in mutually perpendicular planes. A steady total current I enters the loop at one end of the common diameter and leaves at the other end. The magnitude of the net magnetic field at the centre of the bent loop is:

Step-by-step solution

Since the wire loop is uniform, the two semicircular halves have equal resistance. When the total current I enters at one end of the diameter, it divides equally into the two parallel branches. Current in each semicircle = I 2 . The magnetic field at the centre due to a semicircle carrying current i is B = ₀ i 4R . For the first semicircle: B₁ = ₀ (I/2) 4R = ₀ I 8R This field is directed perpendicular to the plane of the first semicircle. For the second semicircle: B₂ = ₀ (I/2) 4R = ₀ I 8R This field is directed pe