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  • A perfectly conducting straight rigid rod of mass m and length L is suspended symmetrically from two identical perfectly conducting springs as shown in the figure. The springs stretch a distance of

A perfectly conducting straight rigid rod of mass m and length L is suspended symmetrically from two identical perfectly conducting springs as shown in the figure. The springs stretch a distance of\mathrm{x_{0}} due to the weight of the wire. The circuit has a total
resistance of \mathrm{R\Omega }. When the magnetic field perpendicular to the plane of the paper is switched on, springs are observed to extend further by the same distance. The magnetic field strength is

Option: 1

\mathrm{\frac{m g R}{\varepsilon L}} directed outward from the plane of the paper


Option: 2

\mathrm{\frac{m g R}{2 \varepsilon x_0}}; directed outward from the plane of the paper


Option: 3

\mathrm{\frac{m g R}{\varepsilon L}}; directed into the plane of the paper


Option: 4

\mathrm{\frac{m g R}{\varepsilon x_0}}; directed into the plane of the paper


Answers (1)

\mathrm{\begin{aligned} & 2\left(\mathrm{k} 2 \mathrm{x}_0\right)=\mathrm{mg}+\mathrm{iBL} \\ & \mathrm{mg}=2 \mathrm{kx}_0 \\ & \mathrm{i}=\frac{\varepsilon}{\mathrm{R}} \\ & \therefore \mathrm{B}=\frac{\mathrm{mgR}}{\varepsilon \mathrm{L}} . \end{aligned}}

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Kshitij

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