JEE Advanced · PhysicsMedium

$A circular loop of radius r is placed in a uniform magnetic field B that is perpendicular to the plane of the loop. If the magnetic field changes with time according to B = B_{0} sin (ω t), what is the maximum induced electromotive force in the loop?$

Show correct answer & step-by-step solution

Correct answer: A — $π r^{2} B_{0} ω$

Solution

$The magnetic flux through the loop is Φ = B A = B_{0} sin (ω t) \cdot π r^{2} .$
$The induced EMF is given by Faraday's law as ε = - d Φ/ d t .$
$Differentiating gives ε = - π r^{2} B_{0} ω cos (ω t) .$
$The maximum value of the EMF is the amplitude of this expression, which is π r^{2} B_{0} ω .$
$Hence the answer is (A).$