Consider a rectangular loop of wire of length a and height b sitting in the plan

Question

Consider a rectangular loop of wire of length a and height b sitting in the plane of the page. A current I goes through the loop in a clockwise fashion.

f) Find the net force on the loop of wire.
[Hint: Find the force on each of the four straight sides of the loop!]

g)  Will there be a net torque? If so, which way will the loop start to rotate?

Consider a rectangular loop of wire of length a and height b sitting in the plane of the page. A current I goes through the loop in a clockwise fashion. Find the net force on the loop of wire. [Hint: Find the force on each of the four straight sides of the loop!] Will there be a net torque? If so, which way will the loop start to rotate?

Explanation / Answer

Force on two sides of length a is equal to zero, since angle between L and B vector = 0 degree

Force on sides with length b = |F| = i(|L||B|sin 90) = i*b*B

Direction of forces:

On right side with length b = Outside the plane of paper ( and perpendicular to plane of paper)

On left side with length b = Inside the plane of paper ( and perpendicular to plane of paper)

Net force on loop = 0+0+ i*b*B - i*b*B =0

Torque = F*r

Net torque = i*b*B*a/2 + i*b*B*a/2 = i*b*B*a

Loop will rotate in anti clockwise direction

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