In the arrangement shown below, what is the magnitude of force experienced by 20 cm length of wire Z Distance between the wires X and Z is 9 cm and between X and Y is 6 cm .

Step-by-step solution

The magnetic field B at a distance r from a long straight wire carrying current I is given by B = ₀ I 2 r . The force per unit length between two parallel wires carrying currents I₁ and I₂ separated by distance r is f = ₀ I₁ I₂ 2 r . Let the wires be X, Y, Z with currents I_X = 45 A , I_Y = 15 A , and I_Z = 20 A . The distance between X and Z is r_ XZ = 9 cm = 0.09 m . The distance between Y and Z is r_ YZ = r_ XZ - r_ XY = 9 cm - 6 cm = 3 cm = 0.03 m . The magnetic field at wire Z due to wire X is B_X = ₀ I_X 2 r_