Figure shows a conducting rod of length l $$=$$ $$l0$$ cm, resistance R and mass m $$=$$ $$100$$ mg moving vertically downward due to gravity. Other parts are kept fixed. Magnetic field is B $$=$$ $$1$$ T. MN and PQ are vertical, smooth, conducting rails. The capacitance of the capacitor is C $$=$$ $$10$$ mF. The rod is released from rest. Find the maximum current (in$$ $$mA) in the circuit.

Question

Infinity Learn · Accepted Answer

By Newton's law,Using KVL $$Blv=iR+qC$$    $$----(ii)Differentiating$$ equation (ii) w.r.t. time, we $$getBldvdt=Rdidt+iC$$    $$----(iii)Eliminating$$ dvdt from equations (i) and (iii), we $$getmg-ilB=mBlRdidt+iC$$⇒$$mgBl-iB2l2=mRdidt+miC$$   $$---(iv)I$$ will be maximum when $$didt=0$$. use this in equation (iv)⇒$$mgBlC=iB2l2C+m$$⇒$$imax=mgBlCm+B2l2C$$

Magnetic flux and induced emf

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