Discussion
A circular coil of radius 10 cm with 200 turns is placed perpendicular to a uniform magnetic field of 0.4 T. If the magnetic field is reduced to zero uniformly in 0.2 s, then the average induced emf (in volt) is
Answer: A
The average induced emf is \(4\pi\) volt.
By Faraday's law the average emf is the change in flux linkage divided by the time:
\[ \begin{aligned} \varepsilon &= \frac{NBA}{t} = \frac{200 \times 0.4 \times \pi(0.1)^{2}}{0.2} \\ &= \frac{0.8\pi}{0.2} = 4\pi\ \text{V} \end{aligned} \]
The radius must be in metres; leaving it in centimetres makes the answer far too large. \(40\pi\) is ten times the correct value.
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