A rectangular loop of wire with sides H = 33 cm and W = 66 cm carries current I

Question

A rectangular loop of wire with sides H = 33 cm and W = 66 cm carries current I2 = 0.157 A. An infinite straight wire, located a distance L = 37 cm from segment ad of the loop as shown, carries current I1 = 0.613 A in the positive y-direction.

1)

What is Fad,x, the x-component of the force exerted by the infinite wire on segment ad of the loop?

2)

What is Fbc,x, the x-component of the force exerted by the infinite wire on segment bc of the loop?.

3)

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

4)

Another infinite straight wire, aligned with the y-axis is now added at a distance 2L = 74 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?

a)along the positive y-direction

b)along the negative y-direction

5)

What is the magnitude of I3?

Explanation / Answer

1) Fad,x = mue*I1*I2*H/(2*pi*L)

= 4*pi*10^-7*0.613*0.157*0.33/(2*pi*0.37)

= 1.72*10^-8 N (towards +x axis)

2) Fbc,x = mue*I1*I2*H/(2*pi*(L+W))

= 4*pi*10^-7*0.613*0.157*0.33/(2*pi*(0.37+0.66))

= -6.2*10^-9 N(towards -x axis)

3) Fnety = 0. (because force on upper and lower segments are equal and act in opposite direction)

4) b)along the negative y-direction

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