A long wire carries a current I 1 upward, and a rectangular loop of height h and

Question

A long wire carries a current I1 upward, and a rectangular loop of height h and width w carries a current I2 clockwise (see figure below). The loop is a distance d away from the long wire. The long wire and the rectangular loop are in the same plane.

Find the magnitude and direction of the net magnetic force exerted by the long wire on the rectangular loop. (Use the following as necessary: 0, I1, I2, h, w and d.)

Briefly explain your work, including a diagram

|F| =

Explanation / Answer

Magnetic Force/length due to two Current carrying wire is given by, F = (uo*I1*I2)/(2**r)
Where r is the distance btw wire,

In our case, For the upper and lower side of the loop wire, the Force would balnce each other out, So Net Force will be due to Left and Right side.

Now,
Force on the Left side
FL =  (o*I1*I2*h)/(2**d) , Towards Left.

Force on the Right side
FR =  (o*I1*I2*h)/(2**(d+w)) , Towards Right.

Net Force, Fnet = FL - FR
Fnet = (o*I1*I2*h)/(2**d) - (o*I1*I2*h)/(2**(d+w))
Fnet = (o*I1*I2*h)/(2*) * [1/d - 1/(d+w)]

Direction :- Towards Left.

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