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A thin wire of length L is connected to ...

A thin 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`
Consider a small element of the wire of length dx The horizontal components `T` cos (d theta) cancel each other The vertical compoents add up to `2T` sin (d theta) because in the limit `dtheta rarr 0` they are collinear The magnetic force an element dx is `F=BI` dx vertically upward . For equilibrium
`2T sin (d theta) =BIR (2d theta)`
Where `R` is the radius of the ring For small `dtheta sin d theta = d theta`
Hence `2T d theta == 2BIR d theta`
` implies T =BIR = (BIL)/(2pi) (:' L =2pi R)`
.
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