A particle of charge ' -q ' and mass ' m ' moves in a circle of radius ' r ' around an infinitely long line charge of linear charge density ' +λ '. Then time period will be given as: (Consider k as Coulomb's constant) (a) T² = (4π² m)/(2kλ q) r³ (b) T = (1)/(2π r)√((m)/(2kλ q)) (c) T = 1/2π√((2kλ q)/(m)) (d) T = 2π r√((m)/(2kλ q))

Answer: (d). Force from the line: qE = (2kλ q)/(r), which supplies mv²/r. v = √((2kλ q)/(m)) (same for every r). T = (2π r)/(v) = 2π r√((m)/(2kλ q)) So the answer is (d).

A particle of charge ' -q ' and mass ' m ' moves in a circle of… | JEE Main 2024 (30 Jan, Shift 2)

Q11JEE Main 2024 · 30 JAN · SHIFT 2Medium

Motion of Charges in an Electric Field

A particle of charge ' $-q$ ' and mass ' $m$ ' moves in a circle of radius ' $r$ ' around an infinitely long line charge of linear charge density ' $+\lambda$ '. Then time period will be given as:

(Consider $k$ as Coulomb's constant)

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Answer: (d)

Force from the line: $qE = \frac{2k\lambda q}{r}$ , which supplies $\frac{mv^2}{r}$ .
$v = \sqrt{\frac{2k\lambda q}{m}}$ (same for every $r$ ).
$T = \frac{2\pi r}{v} = 2\pi r\sqrt{\frac{m}{2k\lambda q}}$
So the answer is (d).

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Motion of Charges in an Electric Field question from JEE Main 2024 (30 Jan, Shift 2)

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