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  4. A square coil of side 25 cm having 1000 turns is rotated with a uniform speed in a magnetic field about an axis perpendicular to the direction of the field. At an instant t , the emf induced in the coil is e=200 text sin text 100 text π t . The magnetic induction is

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Q. A square coil of side $ 25\, cm $ having $ 1000 $ turns is rotated with a uniform speed in a magnetic field about an axis perpendicular to the direction of the field. At an instant $ t $ , the emf induced in the coil is $ e=200\text{ }sin\text{ }100\text{ }\pi t $ . The magnetic induction is

KEAMKEAM 2007Electromagnetic Induction

Solution:

$ e=200\,\sin \,100\pi t $
We have, $ {{e}_{0}}=200, $
$ \omega =100\,\pi $
$ \because $ $ BAN\omega ={{e}_{0}} $
$ \therefore $ $ B=\frac{{{e}_{0}}}{AN\omega } $
$ =\frac{200}{(0.25\times 0.25)\times 1000\times 100\pi } $
Or $ B=0.01\,T $