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A thin flexible wire of length L is conn...

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

A

IBL

B

`(IBL)/pi`

C

`(IBL)/(2pi)`

D

`(IBL)/(4pi)`

Text Solution

Verified by Experts

The correct Answer is:
C
Let an elemental length dl subtending an angle de at the centre of the circle
Force `F_B = BI(dI)`
`F_B = BI(R"d"theta)`
`=BI (L/(2pi))"d" theta`

Now, 2T sin `("d" theta)/(2)` add up to balance `F_B`
At equilibrium -
`2T sin""("d" theta)/(2) = BI(L)/(2pi)"d" theta`
`implies2 T ("d" theta)/2 =BI =(L)/(2pi)"d" theta` [For small angle sin `("d" theta)/2 ~~ ("d" theta)/2` ]
`implies T = (BIL)/(2pi)`
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