Physics

Problem

A single circular loop of wire lies in a region where a uniform magnetic field

B

is perpendicular to the plane of the loop. If only the area

A

of the loop is changing with time at a rate

\dfrac{dA}{dt}

while

B

and the orientation remain constant, which one of the following gives the magnitude of the induced emf

\mathcal E

in the loop? a)

\mathcal E = A\,\dfrac{dB}{dt}

\mathcal E = \dfrac{B}{2}\,\dfrac{dA}{dt}

\mathcal E = B\,\dfrac{dA}{dt}

\mathcal E = B\,A\,\dfrac{d\theta}{dt}