A rectangular loop of wire with sides H = 36 cm and W = 78 cm carries current I

Question

A rectangular loop of wire with sides H = 36 cm and W = 78 cm carries current I2= 0.304 A. An infinite straight wire, located a distance L = 24 cm from segment ad of the loop as shown, carries current I1= 0.552 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?

Another infinite straight wire, aligned with the y-axis is now added at a distance 2L = .48 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.

4)What is the direction of I3? along the positive y-direction, along the negative y-direction

Explanation / Answer

H = 0.36 m
W = 0.78 m
L = 0.24m
i1 = 0.552 A
i2 = 0.304 A

1) Fad = mue*i1*i2*H/(2*pi*L) = 5.034*10^-8 N(towards +x axis)

2) Fbc = mue*i1*i2*H/(2*pi*(L+W)) = 1.1845*10^-8 N(towards - x axis)

Force on loop due to i1, F1 = Fad - Fbc = 3.8495*10^-8 N(towards +x axis)

3) Fnet,y = 0( because on upper and lower sections magnetic force acts in the opposite direction)

4) along the negative y direction


5)

1) Fad = mue*i3*i2*H/(2*pi*(2L+W)) = i3*1.737*10^-8 N(towards +x axis)

2) Fbc = mue*i3*i2*H/(2*pi*2L) = i3*5.718*10^-8 N(towards - x axis)

Force on loop due to i3, F3 = Fad - Fbc = -i3*3.981*10^-8 N(towards -x axis)


when net force is zero

F1 = F2

3.8495*10^-8 = i3*3.981*10^-8

i3 = 3.8495*10^-8/(3.981*10^-8) = 0.967 A

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