A circular coil of radius \( 1 \) m and \( 1000 \) turns is placed perpendicular to the horizontal component of earth’s magnetic field \( 7\times10^{-5} \) T. An induced emf of \( 4 \) mV develops when the coil is rotated about its vertical diameter through \( 180^\circ \). The time taken during rotation is :
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( 110 \) s
By Faraday’s law the average induced emf is the change in flux linkage divided by the time taken. The coil’s plane is perpendicular to the horizontal field, so the flux through it is maximum, \( NBA \). Turning it through \( 180^\circ \) reverses the flux, so the change is \( 2NBA \). (The vertical component of the earth’s field lies in the plane of the coil throughout, so it adds no flux.)
\( N = 1000 \)
\( r = 1\,\mathrm{m} \Rightarrow A = \pi r^{2} = 3.14\,\mathrm{m^{2}} \)
\( B = 7\times10^{-5}\,\mathrm{T} \)
\( \varepsilon = 4\,\mathrm{mV} = 4\times10^{-3}\,\mathrm{V} \)
\( \Delta\Phi = 2NBA = 2\times1000\times(7\times10^{-5})\times3.14 = 0.44\,\mathrm{Wb} \)
\( \displaystyle \Delta t = \frac{\Delta\Phi}{\varepsilon} = \frac{0.44}{4\times10^{-3}} = 110\,\mathrm{s} \)