A conducting circular loop is placed in a uniform magnetic field of 0.02 T with its plane perpendicular to the field. After that the radius of the loop starts shrinking at a constant rate of 2 mm/s. The induced emf in the loop at the instant when the radius is 7 cm will be
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 17.6 μV
The flux through the loop is \( \phi = B\pi r^{2} \). B is constant, but the area shrinks, so by Faraday’s law an emf equal to the rate of change of flux is induced.
\( \displaystyle \varepsilon = \left|\frac{d\phi}{dt}\right| = B \times 2\pi r \times \left|\frac{dr}{dt}\right| \)
\( r = 7\,\mathrm{cm} = 0.07\,\mathrm{m} \)
\( |dr/dt| = 2\,\mathrm{mm\,s^{-1}} = 2\times10^{-3}\,\mathrm{m\,s^{-1}} \)
\( \displaystyle \varepsilon = 0.02\,\mathrm{T} \times 2\pi \times 0.07\,\mathrm{m} \times 2\times10^{-3}\,\mathrm{m\,s^{-1}} \)
\( \varepsilon \approx 1.76\times10^{-5}\,\mathrm{V} = 17.6\,\mu\mathrm{V} \)