A rectangular loop of wire with sides H = 27 cm and W = 50 cm carries current I

Question

A rectangular loop of wire with sides H = 27 cm and W = 50 cm carries current I2 = 0.359 A. An infinite straight wire, located a distance L = 22 cm from segment ad of the loop as shown, carries current I1 = 0.584 A in the positive y-direction.

1)

What is Fnet,y, the y-component of the net force exerted by the infinite wire on the loop?

Another infinite straight wire, aligned with the y-axis is now added at a distance 2L = 44 cm from segment bc of the loop as shown. A current, I3, flows in this wire. The loop now experiences a net force of zero.

2) What is the direction of I3?

Explanation / Answer

1)

Fnet,y = 0

since the wire apply force on the loop along X-direction

2)

wire with current I1 push the loop towards right. hence to have the net force on the loop zero , the wire having current I3 on right must push the loop towards right with the same magnitude of force as by wire on left .

To push the loop towards left , the current I3 must be in downward direction

3)

force by I1 = force by I3

2 I1 I2 (1/L - 1/(L + W)) = 2 I3 I2 (1/(2L) - 1/(2L + W))

(0.584)(1/0.22 - 1/(0.22 + 0.50)) = I3 (1/(2(0.22)) - 1/(2(0.22) + 0.50))

I3 = 1.52 A

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