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)`

Explanation

Consider a small element of length `dL` of the wire of radius R, as shown in figure.

Force on the element: `BI(dL)=2T sin theta`
`BI(R2theta)=2Ttheta` (`:' theta` is small)
or `T=BIR=BI(L)/(2pi) ( :' L=2piR)`