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A neutral plasma consists of free electrons (number density N, each of mass m) among fixed positive ions. When the electrons are displaced and then released, they oscillate about the ions at the natural plasma angular frequency omegaₚ. Which expression gives omegaₚ?

1. sqrt(Ne / (m*epsilon0))
2. sqrt(m*epsilon0 / Ne)
3. sqrt(Ne² / (m*epsilon0))
4. sqrt(m*epsilon0 / Ne²)

Correct answer: sqrt(Ne² / (m*epsilon0))

Solution

Displacing the electron layer by x produces a uniform field E = (N e x)/epsilon0 (from the induced surface charge density sigma = N e x). The restoring force on each electron is F = -eE = -(N e²/epsilon0) x = m d²x/dt². This is SHM with omegaₚ² = N e²/(m epsilon0), so omegaₚ = sqrt(N e²/(m epsilon0)). Dimensionally only this option works.

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