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

Options

A. `IBL`
B. `(IBL)/(pi)`
C. `(IBL)/(2pi)`
D. `(IBL)/(4pi)`

Answer

C

Explanation

`L = 2pi R, :. R = (L)/(2pi), 2T sin (d theta) = d theta`
For small angles, `sin (d theta) = d theta`
`:. 2T(d theta) = I(dL)B sin 90^(@), = I (2R. d theta).B`
`:. T = IRB = (ILB)/(2pi), :.` Correct option is (c )