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Physics-

General

Easy

Question

A circular metal plate of radius $R$ is rotating with a uniform angular velocity $omega$ with its plane perpendicular to a uniform magnetic field B. Then the emf developed between the centre and the rim of the plate is

$π ω B R^{2}$
$ω B R^{2}$
$π ω B R^{2} / 2$
$ω B R^{2} / 2$

The correct answer is: $omega B R to the power of 2 end exponent divided by 2$

From Faraday’s law of electromagnetic induction, the emf induced between center and rim is equal to rate of change of magnetic flux.

$e equals negative fraction numerator d ϕ over denominator d t end fraction$
Where, $d ϕ equals B d A comma$ where $B$ is magnetic field and $d A$ the area.
$therefore blank e equals negative fraction numerator B not stretchy integral from 0 to R of d A over denominator T end fraction$
$e equals negative fraction numerator B cross times pi R to the power of 2 end exponent over denominator T end fraction$
Also, $omega equals fraction numerator 2 pi over denominator T end fraction comma$ where $T$ is periodic time,
$e equals negative fraction numerator B pi R to the power of 2 end exponent over denominator 2 pi divided by omega end fraction$
$blank equals blank minus fraction numerator B R to the power of 2 end exponent omega over denominator 2 end fraction$

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