A train is moving due north with a speed of \( 30\,\mathrm{m\,s^{-1}} \) on rails 2 m apart. If the vertical component of the earth’s magnetic field there is \( 8\times10^{-5}\,\mathrm{T} \), the emf induced across the axle of the train (between the rails) is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( 0.0048\,\mathrm{V} \)
The axle is a straight conductor of length \( l \) moving with velocity \( v \). A conductor moving perpendicular to a magnetic field and to its own length has a motional emf \( \varepsilon=Blv \) across its ends. The axle lies horizontally across the rails and moves horizontally northward. So only the vertical component of the earth’s field is perpendicular to both. The horizontal component lies along the motion and adds nothing.
\( \begin{aligned} \varepsilon &= B_Vlv \\ &= 8\times10^{-5}\,\mathrm{T}\times2\,\mathrm{m}\times30\,\mathrm{m\,s^{-1}} \\ &= 4.8\times10^{-3}\,\mathrm{V} \\ &= 0.0048\,\mathrm{V} \end{aligned} \)