Three long straight and parallel wires carrying currents are arranged as shown The wire C which carries a current of 50 ~A is so placed that it experiences no force. The distance of wire C from wire A is

Step-by-step solution

The correct option is (C). Concept: Using Ampear's circuital law the magnetic field due to a current carrying wire at a distance r is given by, B= ₀ I 2 r where, I is the current through the wire. If the magnetic field due to the wire A cancels out the magnetic field due to the wire B at the wire C , then ₀ I_A 2 x = ₀ I_B 2 (15-x) (15-x) x = I_B I_A Therefore, for I _ B =10 ~A and I _ A =15 ~A , we get x =9 ~cm .