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  4. A short circuited coil is placed in magnetic field at any time. Power loss in coil occurs due to generated induced current. If number of turns becomes 4 times and radius of wire becomes half, then the loss of electric power will be

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Q. A short circuited coil is placed in magnetic field at any time. Power loss in coil occurs due to generated induced current. If number of turns becomes $4$ times and radius of wire becomes half, then the loss of electric power will be

Rajasthan PETRajasthan PET 2002

Solution:

Power $ P=\frac{{{e}^{2}}}{R} $ and $ e=-\frac{d\phi }{dt} $
Here, $ \phi =NBA $
$ \therefore $ $ e=-NA\left( \frac{dB}{dt} \right) $ and $ R\propto \frac{1}{{{r}^{2}}} $
$ P\propto {{N}^{2}}{{r}^{4}} $
$ \therefore $ $ \frac{{{P}_{1}}}{{{P}_{2}}}=1 $