Thank you A rectangular loop of wire with sides H = 21 cm and W = 58 cm carries

Question

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A rectangular loop of wire with sides H = 21 cm and W = 58 cm carries current I2 = 0.393 A. An infinite straight wire, located a distance L = 30 cm from segment ad of the loop as shown, carries current It = 0.754 A in the positive y-direction. What is Fad,x, the x-component of the force exerted by the infinite wire on segment ad of the loop? What is Fbc,x, the x-component of the force exerted by the infinite wire on segment ad of the loop?. 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 = 60 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. What is the direction of I3? along the positive y-direction along the negative y-direction. What is the magnitude of I3?

Explanation / Answer

1) Fadx = B*I2*H = u0*I1*I2*H/(2*pi*L) = 4*pi*10^-7*0.754*0.393*0.21/(2*pi*0.3)

Fadx =41.48508e?9 N towards right



2) B = u0*I1/(2*pi*(L+W))

Fbcx = B*I2*H = u0*I1*I2*H/(2*pi*(L+W)) = 4*pi*10^-7*0.754*0.393*0.21/(2*pi*0.88)

Fbc x = 14.142640909e?9 N towards left

3) Fnet = u0*I1*I2*H/(2*pi*L)-u0*I1*I2*H/(2*pi*(L+W))
Fnet = 27.342439091e?9 N

4) Fnet due to second wire = u0*I1*I3*H/(2*pi*L2)-u0*I1*I2*H/(2*pi*(L2+W))

Fnet1 = -Fnet2

I1*((1/L1)-(1/L1+W)) = =I3*((1/L2)-(1/L@+W))
I3 = -2.022 A

along -y direction
5) I3 = 2.022A

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