Question 158: Electromagnetic Induction

Question

A coil of 200 turns and area $0.20 \mathrm{~m}^2$ is rotated at half a revolution per second and is placed in uniform magnetic field of $0.01 \mathrm{~T}$ perpendicular to axis of rotation of the coil. The maximum voltage generated in the coil is $\frac{2 \pi}{\beta}$ volt. The value of $\beta$ is _______.

Accepted Answer

$\begin{aligned} & \phi=\mathrm{NAB} \cos (\omega \mathrm{t}) \\ & \varepsilon=-\frac{\mathrm{d} \phi}{\mathrm{dt}}=\mathrm{NAB} \omega \sin (\omega \mathrm{t}) \\ & \varepsilon_{\max }=\mathrm{NAB} \omega \\ & =200 	imes 0.2 	imes 0.01 	imes \pi \\ & =\frac{4 \pi}{10}=\frac{2 \pi}{5} \mathrm{volt}\end{aligned}$

Electromagnetic Induction

A coil of 200 turns and area 0.20 \mathrm{~m}^2 is rotated at half a revolution per second and is placed in uniform magnetic field of 0.01 \mathrm{~T} perpendicular to axis of rotation of the coil. The maximum voltage generated in the coil is \frac{2 \pi}{\beta} volt. The value of \beta is _______.

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