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  4. A coil whose diameter is 0.40 m is in a variable magnetic field. As the magnetic induction of the field changes by 127.4 T during 2 s, an emf of 200 V is induced in the coil. Then the number of turns in the coil is approximately

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Q. A coil whose diameter is $0.40\, m$ is in a variable magnetic field. As the magnetic induction of the field changes by $127.4\, T$ during $2\, s$, an emf of $200\, V$ is induced in the coil. Then the number of turns in the coil is approximately

Electromagnetic Induction

Solution:

$ \phi=N B A$
$|\varepsilon|=\frac{\Delta \phi}{\Delta t}=N\left(\frac{\pi d^{2}}{4}\right) \cdot \frac{\Delta B}{\Delta t}$
$200 V =N \cdot\left(\frac{\pi(0.4)^{2} m ^{2}}{4}\right) \cdot\left(\frac{127 \cdot 4 \, T }{2 s }\right)$
$\Rightarrow N=24.98 \approx 25$