A railway track running north-south has two parallel rails 1 m apart. Calculate the value of induced emf between the rails, when a train passes at a speed of \( 25\,\mathrm{m/s} \). The vertical component of earth's magnetic field at that place is \( 0.3\times10^{-4}\,\mathrm{Wb\,m^{-2}} \).
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( 7.5\times10^{-4}\,\mathrm{V} \)
The axle of the train is a conductor moving in a magnetic field, so it has a motional emf \( \varepsilon = B_{V}\,l\,v \). Here \( l \) is the separation of the rails, the train moves along the rails, and only the vertical component \( B_V \) of the earth's field is perpendicular to both the velocity and the axle.
\( \displaystyle \varepsilon = B_{V}\,l\,v = 0.3\times10^{-4} \times 1 \times 25 = 7.5\times10^{-4}\,\mathrm{V} \)