Topic: Self and mutual inductance· Electromagnetic Induction and Alternating Currents

A long solenoid of diameter 0.1 m has 2×10^4 turns per meter. At the centre of the solenoid, a coil of 100 turns and radius 0.01 m is placed with its axis coinciding with the solenoid axis. The current in the solenoid reduces at a constant rate to 0A…

A long solenoid of diameter 0.1 m has \(2\times10^4\) turns per meter. At the centre of the solenoid, a coil of 100 turns and radius 0.01 m is placed with its axis coinciding with the solenoid axis. The current in the solenoid reduces at a constant rate to 0A from 4 A in 0.05 s. If the resistance of the coil is \(10\pi^2\,\Omega\), the total charge flowing through the coil during this time is :

1. 16 \(\mu\)C

2. 32 \(\mu\)C

3. 16\(\pi\) \(\mu\)C

4. 32\(\pi\) \(\mu\)C

Doubtly Asked 30 Oct 2026 NEET UG 2017 Practice test neet Save WhatsApp Report

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Answer: 2. 32 \(\mu\)C

Key idea: charge \(q=\dfrac{\Delta\Phi}{R}\) (independent of the time taken).

Field inside solenoid \(B=\mu_0nI\). Change: \(\Delta B=4\pi\times10^{-7}\times2\times10^4\times4=0.032\pi\) T.

The coil radius is 0.01 m, so area \(=\pi\times10^{-4}\) m\(^2\). \(\Delta\Phi=N\,\Delta B\,A=100\times0.032\pi\times\pi\times10^{-4}=3.2\pi^2\times10^{-4}\) Wb.

\(q=\dfrac{3.2\pi^2\times10^{-4}}{10\pi^2}=3.2\times10^{-5}\) C \(=32\ \mu\)C.

Doubtly AI · 30 Oct 2026 AI-generated · not yet verified Report

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A long solenoid of diameter 0.1 m has 2×10^4 turns per meter. At the centre of the solenoid, a coil of 100 turns and radius 0.01 m is placed with its axis coinciding with the solenoid axis. The current in the solenoid reduces at a constant rate to 0A…

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