A positive point charge is released from rest at a distance r₀ from a positive line charge with uniform density. The speed v of the point charge, as a function of the instantaneous distance r from the line charge, is proportional to

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(2) v∝√ln (r/(r₀)). The field of an infinite line charge of density λ is E=λ/(2πε₀ r), directed radially outward. Work done on the charge q as it moves from r₀ to r: W=q∫_r₀^rλ/(2πε₀ r') dr'=(qλ)/(2πε₀)ln (r/(r₀)). The charge starts from rest, so 1/2mv²=W. v=√(qλ)/(πε₀ m)ln (r/(r₀)), i.e. v∝√ln (r/(r₀)).

A positive point charge is released from rest at a distance r₀ from a positive line charge with uniform density. The speed v of the point charge, as a function of the instantaneous distance r from the line charge, is proportional to

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