A thin flexible wire of length $\mathrm{L}$ is connected to two adjacent fixed points and carries a current $\mathrm{I}$ 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
IIT 2010, Advanced
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$ 2 \mathrm{~T} \sin \frac{\mathrm{d} \theta}{2}=\mathrm{BiRd} \theta $
$ \mathrm{Td} \theta=\mathrm{BiRd} \theta $ (for $\theta$ small)
$ \mathrm{T}=\mathrm{BiR}=\frac{\mathrm{BiL}}{2 \pi}$
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