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  • A conducting circular loop is placed in a uniform magnetic field of 0.4 T with its plane perpendicular to the field. Somehow, the radius of the loop starts expending at a constant rate of 1 mm/s. T

A conducting circular loop is placed in a uniform magnetic field of 0.4 T with its plane perpendicular to the field. Somehow, the radius of the loop starts expending at a constant rate of 1 mm/s. The magnitude of induced emf in the loop at an instant when the radius of the lop is 2 cm will be ______  \muV .

Option: 1

50


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

best_answer

\mathrm{B}=0.4 \mathrm{~T}\\ Rate \ \frac{\mathrm{dr}}{\mathrm{dt}}=1 \mathrm{~mm} / \mathrm{sec} \quad \\ E_{induced} = ?

\begin{aligned} & \mathrm{r}=2 \mathrm{~cm} \\ & \phi=\mathrm{B} \pi \mathrm{r}^2 \quad((\phi=\mathrm{B} . \mathrm{A}) \\ & \varepsilon=\frac{\mathrm{d} \phi}{\mathrm{dt}}=\mathrm{B} \pi(2 \mathrm{r}) \frac{\mathrm{dr}}{\mathrm{dt}} \\ & \text { Ein }=0.4 \times \pi \times 4 \times 10^{-2} \times 10^{-3} \\ & \text { Ein }=16 \pi \times 10^{-6} \\ & \text { Ein }=50 \mu \mathrm{V} \end{aligned}

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