Two infinitely long wires each carrying current I along the same direction are made into the geometry as shown in the figure. The magnetic field at the point P is

Step-by-step solution

( B )₀=( B )_ wire AB +( B )_ BC Arc + B _ CD wire +( B )_ PQ wire + B _ QR ( Arc ) + B _ RS wire B _ PQ = B _ RS =0 B _ BC =- B _ QR ( B )_ wire AB = B _ CD B _ net =( B )_ wire AB +( B )_ wire CD ₀ I 4 r + ₀ I 4 r B _ net = ₀ I 2 r