A rod of 20 cm lying along the horizontal East-West direction falls freely from the roof of a building of height 3 m. If the horizontal component of the Earth's magnetic field is 0.36 G over the region, find the magnitude of Induced emf when it reaches the bottom of the building (take \( g=10\,\mathrm{m\,s^{-2}} \) at that place)
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( 0.56\times10^{-4}\,\mathrm{V} \)
A rod of length l moving with velocity v perpendicular to a field B has a motional emf \( \varepsilon = Blv \). Here the rod is horizontal along East-West, it falls vertically, and the horizontal component of the earth’s field points North-South, so the three directions are mutually perpendicular.
Speed at the bottom (free fall from rest through 3 m)
\( v = \sqrt{2gh} = \sqrt{2\times10\times3} = \sqrt{60} = 7.75\,\mathrm{m\,s^{-1}} \)
Induced emf (\( B = 0.36\,\mathrm{G} = 0.36\times10^{-4}\,\mathrm{T} \), \( l = 0.20\,\mathrm{m} \))
\( \varepsilon = Blv = 0.36\times10^{-4}\times0.20\times7.75 \)
\( \varepsilon = 5.58\times10^{-5}\,\mathrm{V} = 0.56\times10^{-4}\,\mathrm{V} \)