The surface charge density of a uniformly charged infinite plane is σ. A simple pendulum is suspended vertically near it, and a charge q₀ is placed on its metallic bob. If the string then makes an angle θ with the vertical,

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(2) σ∝(tan θ)/(q₀). Given: sheet of charge density σ; bob of mass m carrying q₀; string at angle θ to the vertical. Field of an infinite sheet: E=σ/(2ε₀), perpendicular to the sheet, so horizontal here. Forces on the bob: weight mg down, electric force q₀E sideways, tension T along the string. Balance: T cos θ=mg and T sin θ=q₀E, so tan θ=(q₀E)/(mg)=(q₀σ)/(2ε₀mg). σ=(2ε₀mg)/(q₀)tan θ, that is σ∝(tan θ)/(q₀) for a given bob.

The surface charge density of a uniformly charged infinite plane is σ. A simple pendulum is suspended vertically near it, and a charge q₀ is placed on its metallic bob. If the string then makes an angle θ with the vertical,

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