An airliner is flying due east from the USA to France. The Earth's magnetic field acts at \( 60^{\circ} \) to the horizontal and has a strength of \( \sqrt{3}\times10^{-4}\,\mathrm{T} \), and the aircraft speed is \( 300\,\mathrm{m\,s^{-1}} \). The wing span of the aircraft is 60 m. The potential difference induced between the tips of the wings is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 2.7 V
The wings are a conductor moving through a magnetic field, so a motional emf \( \varepsilon = B_{\perp}\,v\,l \) appears between the tips. The aircraft flies east and the wings lie along the north–south line, so only the vertical component of the field is cut by the wings.
The field makes \( 60^{\circ} \) with the horizontal, so its vertical component is \( B\sin60^{\circ} \).
\( \displaystyle B_V = \sqrt{3}\times10^{-4}\times\frac{\sqrt{3}}{2} = 1.5\times10^{-4}\,\mathrm{T} \)
\( \varepsilon = B_V\,v\,l = 1.5\times10^{-4}\times300\times60 \)
\( \varepsilon = 2.7\,\mathrm{V} \)