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  • 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 loop and the magnitude of field is increasing at

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 loop and the magnitude of field is increasing at a constant rate \mathrm{\alpha } . There is a straight conducting rod of length 2R placed as shown in figure. The magnitude of induced emf across the rod is:

Option: 1

\mathrm{\pi \mathrm{R}^2 \alpha}


Option: 2

\mathrm{\frac{\pi \mathrm{R}^2 \alpha}{2}}


Option: 3

\mathrm{\frac{\mathrm{R}^2 \alpha}{\sqrt{2}}


Option: 4

\mathrm{\frac{\pi R^2 \alpha}{4}}


Answers (1)

best_answer

Induced emf,\mathrm{V}_{\mathrm{BA}}=\int \mathrm{E} \cdot \mathrm{dI}=\frac{1}{4}\left(\frac{\mathrm{d} \phi}{\mathrm{dt}}\right)

\mathrm{=\frac{1}{4}\left(\pi \mathrm{R}^2\right) \cdot \frac{\mathrm{dB}}{\mathrm{dt}}=\frac{\pi \mathrm{R}^2 \alpha}{4} \quad\left[\because \phi=\mathrm{B} \cdot \mathrm{A} \text { and } \frac{\mathrm{dB}}{\mathrm{dt}}=\alpha\right]}

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