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A semicircular metallic strip of thickness t and resistivity rho has inner radius R1 and outer radius R2. A voltage V0 applied across its two flat ends drives a current I. A transverse potential difference DeltaV also appears between the inner and outer curved surfaces, arising purely from the kinetic (centripetal) effect on the moving electrons (neglect the magnetic field of the current). Which statement is correct?

1. I = V0 * t / (pi * rho) * ln(R2/R1)
2. the outer surface is at a higher voltage than the inner surface
3. the outer surface is at a lower voltage than the inner surface
4. DeltaV is proportional to I²

Correct answer: DeltaV is proportional to I²

Solution

The radial field providing centripetal force satisfies eE = m*v²/r, and since v (drift speed) is proportional to I, the transverse voltage DeltaV is proportional to I².

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