A particle of charge -q and mass m moves in a circle of radius r around an infinitely long line charge of linear density +λ. Then the time period will be given as (consider k as Coulomb's constant)

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(1) T=2π r√m/(2kλ q). Field of the line charge at distance r: E=(2kλ)/r, pointing away from it, so the negative particle is pulled inwards. Centripetal balance: (mv²)/r=(2kλ q)/r, so v²=(2kλ q)/m — the speed does not depend on r. v=√(2kλ q)/m. T=(2π r)/v=2π r√m/(2kλ q).

A particle of charge -q and mass m moves in a circle of radius r around an infinitely long line charge of linear density +λ. Then the time period will be given as (consider k as Coulomb's constant)

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