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Question

A wire carrying current I, bent in the form of a quarter circle, is held at rest on a smooth table with two threads as shown. A uniform magnetic field exists in the region directed into the plane, select the correct alternatives.


A
Net force on wire is zero
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B
Net magnetic force on wire is BIR2
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C
Tension in the threads is BIR
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D
Tension in the threads is BIR2
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Solution

The correct option is C Tension in the threads is BIR
FBD:


From the FBD of quarter circle wire, magnetic force on it
FB=Il×B

|FB|=IlBsin90

Here, l=effective length so,l=R2+R2=R2

FB=2RIB

Since, the wire is held at rest, so the net force on the wire must be zero.

F1=T=FBcos45

T=FB2

T=2RIB2=RIB

Hence, options (a) , (b) and (c) are the correct answers.

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