A boat is moving due east in a region where the earth's magnetic field is 5.0 × 10⁻⁵ 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 1.50 ms⁻¹, the magnitude of the induced emf in the wire of aerial is: (a) 0.75 mV (b) 0.50 mV (c) 0.15 mV (d) 1 mV

Answer: (c). Aerial is vertical, velocity east, B north: all three mutually perpendicular, so ε = Blv. ε = 5×10⁻⁵ × 2 × 1.5 = 1.5×10⁻⁴ V = 0.15 mV. So the answer is (c).

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Motional EMF

A boat is moving due east in a region where the earth's magnetic field is $5.0 \times 10^{-5}\text{ N A}^{-1}\text{ m}^{-1}$ due north and horizontal. The boat carries a vertical aerial $2\text{ m}$ long. If the speed of the boat is $1.50\text{ ms}^{-1},$ the magnitude of the induced $\text{emf}$ in the wire of aerial is:

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Answer: (c)

Aerial is vertical, velocity east, $B$ north: all three mutually perpendicular, so $\varepsilon = Blv$ .
$\varepsilon = 5\times10^{-5} \times 2 \times 1.5 = 1.5\times10^{-4}$ V
$= 0.15$ mV. So the answer is (c).

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