Faraday's Paradox — Rotating DiskHardQuestion 20232
Question
A conducting disk rotates about its axis in a uniform axial magnetic field. The EMF between the centre and the rim is non-zero because:
- AThe flux through the circuit changes
- BThe motional EMF formula qv×B gives radial force on charge carriers even with constant total fluxCorrect
- CThe resistance of the disk changes
- DFaraday's law cannot apply to rotating conductors
Correct answer
The motional EMF formula qv×B gives radial force on charge carriers even with constant total flux
Explanation
Total flux through the disk doesn't change as it rotates in a uniform axial field. However, each radial element of the disk moves with velocity v = ωr, experiencing a Lorentz force qvB along the radius. Integration gives EMF = ½BωR². This is the homopolar generator and demonstrates that Faraday's flux rule needs careful application to rotating conductors.