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There is a horizontal cylindrical uniform but time varying magnetic field increasing at a constant rate
P \( \frac{\mathrm{dB}}{\mathrm{dt}} \) as shown. A charged particle is having charge \( q \) is attached to spring of constant \( \mathrm{K} \), in such a way that it is on the horizontal line passing through the centre of magnetic field as shown. The compression in the spring will be:
(1) \( \frac{1}{\mathrm{~K}}\left[\mathrm{mg}-\frac{\mathrm{qR}^{2}}{2 l} \frac{\mathrm{dB}}{\mathrm{dt}}\right] \)
(3) \( \frac{1}{\mathrm{~K}}\left[\mathrm{mg}+\frac{2 \mathrm{qR} \mathrm{R}^{2}}{l} \frac{\mathrm{dB}}{\mathrm{dt}}\right] \)
(2) \( \frac{1}{\mathrm{~K}}\left[\mathrm{mg}+\frac{\mathrm{qR}^{2}}{l} \frac{\mathrm{dB}}{\mathrm{dt}}\right] \)
(4) \( \frac{1}{\mathrm{~K}}\left[\mathrm{mg}+\frac{\mathrm{qR}^{2}}{2 l} \frac{\mathrm{dB}}{\mathrm{dt}}\right] \)
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