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A long cylindrical volume contains a uniformly distributed charge of density $ρ$ . The radius of cylindrical volume is R. A charge particle (q) revolves around the cylinder in a circular path. The kinetic of the particle is :

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$\frac{ρ q R^{2}}{4 ε_{0}}$

$\frac{ρ q R^{2}}{2 ε_{0}}$

$\frac{q ρ}{4 ε_{0} R^{2}}$

$\frac{4 ε_{0} R^{2}}{q ρ}$

answer is A.

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Detailed Solution

$E = 2 π r ℓ = \frac{ρ π r^{2} ℓ}{ε_{0}}$
$qE = \frac{q ρ R^{2}}{2 ε_{0} r} = \frac{{mv}^{2}}{r}$
${mv}^{2} = \frac{q ρ R^{2}}{2 ε_{0}}$

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