The electric third rail in a subway system is made of steel, measures h=0.1m hig

Question

The electric third rail in a subway system is made of steel, measures h=0.1m high, w=0.02m wide, and carries a current I=130A. Calculate the Hall potential difference across the rail from corner to opposite corner due to the Earth's magnetic field with components Bhoriz=3e-05T and Bverti=2.7e-05T. Steel has 8e+28 conducting electrons per cubic meter, or a conducting charge density of 12800000000C/m3. You can relate this conducting charge density to the speed of the electrons and the current density through the rail.

Vmax = V
Vmin = V

Please show your work!

Explanation / Answer

Use V = I * B / n * e * d to solve for Vhoriz and Vvert Vvert = I * Bhoriz / n * e * w Vvert = 170 * (3e-05) / (8e28) * (1.6e-19) * (0.02) = 1.99e-11 then Vhoriz = I * Bvert / n * e * h so Vhoriz = 170 * (2.7e-05) / (8e28) * (1.6e-19) * (0.1) = 3.58e-12 Vmax = Vvert + Vhoriz = 2.34e-11 Vmin = Vvert - Vhoriz = 1.63e-11

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