A uniform but time-varying magnetic field is present in a circular region of radius R . The magnetic field is perpendicular and into the plane of the paper and the magnitude of the field is increasing at a constant rate

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Correct answer: B. π R^ 2 α 4

Considering a square loop as shown, E.M.F. across the loop is given by

\text{e} = ∮ \text{E.dl} = - \dfrac{\text{d}ϕ}{dt} = - A\dfrac{dB}{dt}

& (where

A

= area =

\pi R^{2}

)

A uniform but time-varying magnetic field is present in a circular region of radius R . The magnetic field is

⇒ \text{e} = - \pi R^{2} \dfrac{\text{dB}}{\text{dt}} = - \pi R^{2} \alpha

∴

Magnitude of E.M.F. across one side

= \dfrac{\pi R^{2} \alpha}{4}

A uniform but time-varying magnetic field is present in a circular...

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