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Question

A wire bent as shown in figure carries a current i and is placed in a uniform field of magnetic induction B that emerges out from the plane of the figure.The magnetic force acting on the wire is:



A
2BIR
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B
4BIR
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C
BIR
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D
52BIR
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Solution

The correct option is B 4BIR
The given wire is composed of two straight sections and one semi-circular section.

The effective length vector L of wire is shown below:


|L|=R+2R+R=4R
Since, the angle between L&B is 90, using relation for magnetic force:

F=iLBsinθ

F=i(4R)Bsin90

F=4BIR

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