# Force on a rectangular loop

1. The problem statement, all variables and given/known data
Let d = 0.048m, L = 0.15m, r = 0.10m in the following diagram. Assume that the current I1 = 80.0A and I2 = 40.0A. Find the net force on the rectangle of wire and the direction it points, and state the direction of the emf if the current I1 is increasing in the direction of the arrow.

2. Relevant equations

3. The attempt at a solution
I have that the force is given by F = BIl. In this case, B would come from the field created by the current I1. So, we would get that the force will be (let force 1 be for the closest part of the loop and force 2 for the farthest part of the loop):

F1 = $\frac{μI2I1l}{2πd}$ ≈ -2×10-3N
F2 = $\frac{μI2I1l}{2π(d+r)}$ ≈ 6.49×10-3N

Then, the net force would be Fnet = -1.35×10-3N, pointing downwards. However, I get a mistake. Why is this the case? I’m thinking that my procedure is right until now, as there will be no force felt by the loop wires perpendicular to the long wire. I tried to perhaps calculate an induced current, but I can’t do so as I don’t have a resistance.

For the second part, the current would be induced to even out the flux change, so the induced B field should point down, leading to an opposite direction of the induced current as stated in the diagram. This is because the flux of the long wire would be increasing upwards in the plane of the wire.

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