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A large thin non-conducting plate carries a uniform surface charge density sigma and moves with constant velocity v in its own plane. The magnetic field at a small distance above or below the plate in the middle region is
- mu₀ * sigma * v in magnitude
- mu₀ * sigma * v / 2 in magnitude
- Perpendicular to the plate
- Parallel to the plate
Correct answer: mu₀ * sigma * v / 2 in magnitude
Solution
The moving charged plate acts like an infinite sheet with surface current density K = sigma * v. By Ampere's law for an infinite current sheet, the magnetic field on each side has magnitude B = mu₀ * K / 2 = mu₀ * sigma * v / 2, directed parallel to the plate and perpendicular to v.
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