Please show all work. In the diagram shown below, a very long straight wire has

Question

Please show all work.

In the diagram shown below, a very long straight wire has current Ii going upwards. On the right side of the straight wire is a rectangular loop of wire with current b going clockwise as shown. The longer side of the loop has a length of L. The shorter side of the loop has a length of a. The distance between the long wire and the left side of the loop is c. Calculate the net force of long straight wire on the rectangular loop. The answer will be in terms of I_1, L, mu_0, pi, I_2, c, and a. Also please include the direction of the force.

Explanation / Answer

integral B.dl = uo*i1

B = uo*i1/2pi*r

field goes into the page inside the rectangular loop .

By the right-hand rule, all the forces on the loop are perpendicular to the wire pointing away from the center of the rectangle. The two forces on the wires of length are the same size but opposite in direction, so they cancel

F1 = uo*i1*i2*L/2pi*c

F2 = -uo*i1*i2*L/2pi*(c+a)

F = uo*i1*i2*L*a/[2pi*c*(c+a)]

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