A rectangular loop of wire with sides H = 37 cm and W = 77 cm carries current I

Question

A rectangular loop of wire with sides H = 37 cm and W = 77 cm carries current I2 = 0.273 A. An infinite straight wire, located a distance L = 33 cm from segment ad of the loop as shown, carries current I1 = 0.532 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?N

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2)

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

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3)

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

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4)

Another infinite straight wire, aligned with the y-axis is now added at a distance 2L = 66 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

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5)

What is the magnitude of I3?

A

Explanation / Answer

a) Fad,x= ( 0.532)( 0.273 A.) ( 4pi x 10^-7)( 0.37)/ ( 2 pi x 0.33) = 0.325 x 10^-7 N

b) Fbc , x = ( 0.532)( 0.273 A.) ( 4pi x 10^-7)( 0.37)/ (2 pi x 1.1) = 0.0977 x 10^-7 N

c) Fnet y = 0 N ( due to symmetry as currents are moving in opposite direction in rectangular loop)

d) along negative y direction because frorce from I1 is along +y axis , so the force from i3 must be along -Y axois fro net force to be 0.

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