A current-carrying wire is placed in the grooves of an insulating semicircular disc of radius R , as shown. The current enters at point A and leaves from point B . Determine the magnetic field at point D .

Step-by-step solution

Magnetic field due to wire AC , B AC = μ 0 I 4 π 2 R sin 30 cos 30 - cos 90 = 3 μ 0 I 8 π R Magnetic field due to wire BC , B BC = μ 0 I 4 π 2 R sin 60 cos 60 - cos 90 = μ 0 I 8 3 π R = 3 μ 0 I 24 π R B → net = B A - B B = 3 μ 0 I 8 π R 1 - 1 3 = 2 3 μ 0 I 2 4 π R = μ 0 I 4 3 π R