JEE MAIN - Physics (2006 - No. 11)
In an $$AC$$ generator, a coil with $$N$$ turns, all of the same area $$A$$ and total resistance $$R,$$ rotates with frequency $$\omega $$ in a magnetic field $$B.$$ The maximum value of $$emf$$ generated in the coil is
$$N.A.B.R.$$$$\omega $$
$$N.A.B$$
$$N.A.B.R.$$
$$N.A.B.$$$$\omega $$
Explanation
$$e = - {{d\phi } \over {dt}} = - {{d\left( {N\overrightarrow B .\overrightarrow A } \right)} \over {dt}}$$
$$ = - N{d \over {dt}}\left( {BA\,\cos \,\omega t} \right) = NBA\omega \sin \,\omega t$$
$$ \Rightarrow {e_{\max }} = NBA\omega $$
$$ = - N{d \over {dt}}\left( {BA\,\cos \,\omega t} \right) = NBA\omega \sin \,\omega t$$
$$ \Rightarrow {e_{\max }} = NBA\omega $$
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