Two insulated current-carrying wires (wire 1 and wire 2) are bound together with

Question

Two insulated current-carrying wires (wire 1 and wire 2) are bound together with wire ties to form a two-wire unit. The wires are 2.85 m long and are stretched out horizontally parallel to each other. Wire 1 carries a current of I1 = 8.00 A and the other wire carries a current I2 in the opposite direction. The two-wire unit is placed in a uniform magnetic field of magnitude 0.400 T such that the angle between the direction of I1 and the magnetic field is 71.5°. While we don't know the current in wire 2, we do know that it is smaller than the current in wire 1. If the magnitude of the net force experienced by the two-wire unit is 3.50 N, determine the current in wire 2.

Explanation / Answer

if the currents are inopposite directions then they will repel each other

Given that Fnet = F1-F2 = 3.5 N

F1 = i*l*B*sin(theta) = 8*2.85*0.4*sin(71.5) = 8.65 N

F2 = i*l*B*sin(theta) = i*2.85*0.4*sin(71.5) = 1.08*i

8.65-(1.08*i) = 3.5

current in wire 2 is i = 4.76 A

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