Physics

Problem

A long solenoid of length

0.80\,\text{m}

, radius

2.5\,\text{cm}

and

2000

turns carries a current that varies with time according to

I(t)=5.0\sin(100\,t)

, where

I

is in amperes and

t

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\,\text{cm}

and

20

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\,\Omega

, determine the maximum current induced in it.

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