A planar loop made of wire is rotating in a uniform magnetic field. At time \(t=0\), the plane of the loop is perpendicular to the magnetic field. If the loop is rotating about an axis passing through its plane with a period of \(10\) seconds, at which of the following times will the induced electromotive force (emf) be maximum and minimum, respectively?

Pick an option to check your answer.

Verified Solution

Answer & Solution

Correct Answer

(D) \(2.5\; s\) and \(5.0 \;s\)

Detailed explanation

\(\operatorname{Fiux} \phi=\overline{B} \cdot \overline{A}=\mathbf{B A} \cos \theta=\mathbf{B A} \cos \omega t\)

\(|\) Induced emf \(|=| \mathrm{e}|=| \frac{\mathrm{d} \phi}{\mathrm{dt}}|=| \mathrm{BA} \omega \sin \omega t |\)

le \(|\) will be maximum at \(\omega t=\frac{\pi}{2}\)

\(\left(\frac{2 \pi}{\mathrm{T}}\right) \mathrm{t}=\frac{\pi}{2}\)

\(\left(\frac{2 \pi}{10}\right) \mathrm{t}=\frac{\pi}{2} \Rightarrow \mathrm{t}=2.5 \mathrm{sec}\)

\(|\mathrm{e}|\) will be minimum at \(\omega \mathrm{t}=\pi\)

\(\left(\frac{2 \pi}{10}\right) t=\pi \Rightarrow t=5 \sec\)

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