A long solenoid of length

PHYSICS · Subjective · A Level · Physics · Fields and their consequences · Fields and their consequences

Problem

A long solenoid of length 0.80 m0.80\,\text{m}, radius 2.5 cm2.5\,\text{cm} and 20002000 turns carries a current that varies with time according to I(t)=5.0sin⁡(100 t)I(t)=5.0\sin(100\,t), where II is in amperes and tt in seconds. (a) Obtain an expression for the instantaneous magnetic field inside the solenoid as a function of time. (b) A small circular coil of radius 1.0 cm1.0\,\text{cm} and 2020 turns is coaxially placed at the centre of the solenoid. Derive an expression for the magnetic flux through the small coil as a function of time. (c) Hence calculate the maximum magnitude of the emf induced in the small coil. (d) If the resistance of the small coil is 0.50 Ω0.50\,\Omega, determine the maximum current induced in it.

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