Question

A loop of flexible conducting wire of length 0.5 m lies in a magnetic field of 1.0 T perpendicular to the plane of the loop. Show that when a current as shown in Fig. 1.112 is passed through the loop, it opens into a circle. Also calculate the tension developed in the wire if the current is 1.57 A.

Answer 1

The loop may be divided into a large number of small length elements. When a current I is passed through the loop placed in the magnetic field such that the plane of the loop is perpendicular to field, then force on each element is
`dvecF=IdveclxxvecB=IdlBsin90^@`
`=Idlb`

Perpendicular to current element `Ivecdl` as well as magnetic field `vecB`. Hence, the loop opens into a circle.
Consider an element of length dl of circle of radius r, making an angle `alpha` at centre. If T is the tension in the wire, then force toward centre
`2T sinalpha.2=IBdl`
`T=(IBdl)/alpha=IBr" "(:. alpha=dl/r)`
`=IB(l/(2pi))" "( :. l=2pir)`
`=1.57xx1xx(0.5/(2xx3.14))=0.125N`
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