In the diagram shown below, a very long straight wire has current I_1 going upwa

Question

In the diagram shown below, a very long straight wire has current I_1 going upwards. On the right side of the straight wire is a rectangular loop of wire with current I_2 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, pie, I_2, c, and a. Also please include the direction of the force.

Explanation / Answer

Force = iL X B

Force on left side of loop F1 = I2 L (uoI1/2 pi c) leftward

Force on right side of loop F2 = - I2 L [uoI1/(2 pi (c+a))] leftward

Net force = F1 + F2 = I2 L (uoI1/(2 pi c)) - I2 L [uoI1/(2 pi (c+a))]   = [ uoI1I2 L /2 pi] (1/c- 1/(c+a))

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