A circular loop of radius \( \mathrm{R} \) is bent along a diameter and given a shape as shown i...

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A circular loop of radius \( \mathrm{R} \) is bent along a diameter and given a shape as shown in the figure. One of the semicircles (KNM) lies in the \( \mathrm{x}-\mathrm{z} \) plane and the other one (KLM) in the \( y \)-zplane with their centers at the origin . Current \( \mathrm{I} \) is flowing through each of the semicircles as shown in figure .
(i) A particle of charge \( q \) is released at the origin with a velocity \( v=-v_{0} \hat{i} \). Find the instantaneous force F on the particle. Assume that space is gravity free.
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(ii) If an external uniform magnetic field \( \mathrm{B} \hat{\mathrm{j}} \) is applied, determine the forces \( \mathrm{F}_{1} \) and \( \mathrm{F}_{2} \) on the semicircles KLM and KNM due to this field and the net force F on the loop .
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