In the figure below, the current in the long, straight wire is and the wire lies

Question

In the figure below, the current in the long, straight wire is

and the wire lies in the plane of the rectangular loop, which carries a current

The dimensions in the figure are

and

Find the magnitude and direction of the net force exerted on the loop by the magnetic field created by the wire.

In the figure below, the current in the long, straight wire is I1 = 3.20 A and the wire lies in the plane of the rectangular loop, which carries a current I2 = 10.0 A. The dimensions in the figure are c = 0.100 m, a = 0.150 m, and = 0.420 m. Find the magnitude and direction of the net force exerted on the loop by the magnetic field created by the wire

Explanation / Answer

Use F = IL x B, where I = Ib, L = 0.25 m, and B = ??Ia/2?r

So the wire induces a B field that point inward into the screen, and this induces a net force on the square loop only for the part of the square loop that is parallel to the long straight wire. The part of the square loop that is perpendicular to the long wire has ZERO net force acting on it.

So for the part of the square loop that's closer to the wire, r = 0.1 m.

B = (4? x 10^-7)(5) / 2?(0.1) = 1 x 10^-5 T

For the part of teh square loop that's further away from the wire, r = 0.35 m

B = (4? x 10^-7)(5) / 2?(0.35) = 2.86 x 10^-6 T

Now the net force acting on the square loo is:

F = (2.4)(0.25)(10^-5 - 2.86x10^-6) = 4.29 x 10^-6 N

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