A boat is moving due east in a region where the Earth's magnetic field is \( 5.0 \times 10^{-5}\,\mathrm{N\,A^{-1}\,m^{-1}} \) due north and horizontal. The boat carries a vertical aerial 2 m long. If the speed of the boat is \( 1.5\,\mathrm{m\,s^{-1}} \), the magnitude of the induced emf is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 0.15 mV
A conductor moving through a magnetic field has a motional emf \( \varepsilon = B l v \) across it when the field, the conductor and the velocity are mutually perpendicular. Here the field is horizontal towards north, the velocity is horizontal towards east and the aerial is vertical, so all three are at right angles. The unit \( \mathrm{N\,A^{-1}\,m^{-1}} \) is the tesla.
\( \displaystyle \varepsilon = B\,l\,v = 5.0\times10^{-5}\,\mathrm{T} \times 2\,\mathrm{m} \times 1.5\,\mathrm{m\,s^{-1}} \)
\( \displaystyle \varepsilon = 1.5\times10^{-4}\,\mathrm{V} = 0.15\,\mathrm{mV} \)