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# A thin flexible wire of length L is connected to two adjacent fixed points and the wire carries a current I in the clockwise direction. When the system is put in a uniform magnetic field with a strength of B going into the plane of the paper, the wire takes the shape of a circle. The tension in the wire is?

Arun
25763 Points
2 years ago
Dear student

you have not attached an image.

but I remember that similiar question has been asked in IIT in 2010 or 2011.

So I am answering it from that context.

Considering an elemental length dL of the wire, the magnetic force F acting on the element is given by

idLB = iRdθB, as is clear from the figure.

The tension developed in the wire is resolved into rectangular components T sin(dθ/2) and Tcos(dθ/2) as indicated in the figure.

The magnetic force is related to the tension T as

iRdθB = 2T sin(dθ/2)

Since  is a very small angle, sin(dθ/2) ≈ dθ/2

Therefore, the above equation gives T = iRB

But R = L /

Therefore, T = iBL /