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Question

A capacitor of capacitance 100 μF is connected to a battery of 20 volts for a long time and then disconnected from it. It is now connected across a long solenoid having 4000 turns per metre. It is found that the potential difference across the capacitor drops to 90% of its maximum value in 2.0 seconds. Estimate the average magnetic field produced at the centre of the solenoid during this period.

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Solution

Given that,
C=100μf,
V=20V,
Q=CV=2×103C,
V=18V,
Q=CV=1.8×103C,
t=2sec,
i=QQt
=2×1042=104A
No. of turns per metre, n=4000
Thus, The average magnetic field at the centre of the solenoid is given by
B=μ0ni
=4π×107×4000×104
=16π×107T

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