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A circular coil of mean radius of 7 cm and having 4000 turns is rotated at the rate of 1800 revolutions per minute in the earth's magnetic field $(B=0.5$ gauss), the emf induced in coil will be
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The correct answer is:
0.58 V
Here: $n=4000, B=0.5 \times 10^{-4} \mathrm{~Wb} / \mathrm{m}^2$
Rate of rotation of coil $=1800 \mathrm{rev} / \mathrm{min}$ $=\frac{1800}{60}=30 \mathrm{rev} / \mathrm{sec}$
$\begin{aligned} & \omega=2 \pi f=2 \pi \times 30=60 \pi \mathrm{rad} / \mathrm{s}, \\ & r=7 \mathrm{~cm}=0.07 \mathrm{~m}\end{aligned}$
Now area of coil
$A=\pi r^2=\pi \times(0.07)^2=49 \pi \times 10^{-4} \mathrm{~m}^2$
Now the maximum energy induced is
$\begin{aligned}e & =B A n \omega \\& =0.5 \times 10^{-4} \times 49 \pi \times 10^{-4} \times 4000 \times 60 \pi \\& =0.58 \mathrm{~V}\end{aligned}$
Rate of rotation of coil $=1800 \mathrm{rev} / \mathrm{min}$ $=\frac{1800}{60}=30 \mathrm{rev} / \mathrm{sec}$
$\begin{aligned} & \omega=2 \pi f=2 \pi \times 30=60 \pi \mathrm{rad} / \mathrm{s}, \\ & r=7 \mathrm{~cm}=0.07 \mathrm{~m}\end{aligned}$
Now area of coil
$A=\pi r^2=\pi \times(0.07)^2=49 \pi \times 10^{-4} \mathrm{~m}^2$
Now the maximum energy induced is
$\begin{aligned}e & =B A n \omega \\& =0.5 \times 10^{-4} \times 49 \pi \times 10^{-4} \times 4000 \times 60 \pi \\& =0.58 \mathrm{~V}\end{aligned}$
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