Santa's Sleigh

Level pending

It's Christmas Eve and this year Santa has attached a highly conductive metal bar on his sleigh to act as his foot rest. He decides to start delivering presents to houses along the Equator where the vertical component of the magnetic field of the Earth is approximately 31 μ T 31\mu\text{T} . His sleigh travels at a speed of 1000 kmh − 1 1000\text{kmh}^{-1} and the length of his foot rest is 3 m 3\text{m} . The foot rest has a resistance of 1 0 − 4 Ω 10^{-4} \, \Omega . The sleigh's velocity is perpendicular to the vertical component of the Earth's magnetic field at all times. You may assume that the sleigh does not twist and that the sleigh remains upright. What is the induced current in the foot rest in Amperes to three significant figures?


The answer is 258.

Cole Coupland by Cole Coupland , 24, Canada

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2 solutions

Ahaan Rungta
Jun 6, 2014

Note that the induced emf is ε = B ℓ v = I R , \varepsilon = B\ell v = IR, so I = B ℓ v R = 258 A I = \frac {B \ell v}{R} = \boxed {\text {258 A}} .

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emf produced across the two ends of the sleigh=Blv current(I)=emf/resist=E/R=(Blv)/R=258.3A

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