A rectangular loop of wire with sides H = 26 cm and W = 54 cm carries current I_

Question

A rectangular loop of wire with sides H = 26 cm and W = 54 cm carries current I_2 = 0.267 A. An infinite straight wire, located a distance L = 38 cm from segment ad of the loop as shown, carries current I_1 = 0.679 A in the positive y-direction. What is F_ad, X, the x-component of the force exerted by the infinite wire on segment ad of the loop? What is F_bC, X, the x-component of the force exerted by the infinite wire on segment be of the loop?. What is F_net, 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 = 76 cm from segment be of the loop as shown. A current, I_3, flows in this wire. The loop now experiences a net force of zero. What is the direction of I_3? along the positive y-direction along the negative y-direction What is the magnitude of I_3?

Explanation / Answer

1) Fad = iLB

= i2*H*uo i1/[2piL]

= 0.267*0.679*0.26*2e-7/0.38

= 2.48*10^-8 N

2)Fbc = iLB

= i2*H*uo i1/[2pi(L+W)]

= 0.267*0.679*0.26*2e-7/0.92

= 1.02*10^-8 N

3) Fnet = Fad-Fbc

= 1.46*10^-8 N

4) Along the negative, because both i1 and i3 must cause repulsive force on loop

5) 1.46E-8= [0.267*0.26*2e-7/0.76 -  0.267*0.26*2e-7/1.30] i3

i3 = 1.46e-8/ [0.267*0.26*2e-7/0.76 -  0.267*0.26*2e-7/1.30]

= 1.924 A

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