A coil of 200 turns and area 0.20 is rotated at half a revolution per second and is placed in a uniform magnetic field of 0.01T perpendicular to the axis of rotation of the coil. The maximum voltage generated in the coil is volt. The value of is

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Solution

Q.
A coil of 200 turns and area 0.20 $m^{2}$ is rotated at half a revolution per second and is placed in a uniform magnetic field of 0.01T perpendicular to the axis of rotation of the coil. The maximum voltage generated in the coil is $\frac{2 π}{β}$ volt. The value of $β$ is ______. [2024]

Ans.
(5)

$ϕ = N B A \cos θ$

$ε = - \frac{d ϕ}{d t} = - \frac{d}{d t} (N B A \cos θ)$

$ε = N B A \sin θ \cdot \frac{d θ}{d t} = (N B A ω) \sin θ$

$ε_{\max} at θ = 90 °, ε_{\max} = N B A ω$

$ε_{\max} = 200 \times 0.01 \times 0.2 \times π = 200 \times \frac{1}{100} \times \frac{2}{10} \times π$

$ε_{\max} = \frac{4 π}{10} = \frac{2 π}{5}, ε_{\max} = \frac{2 π}{β} so β = 5$

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