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 kineti

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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 energy of the particle is :

TestHub · Accepted Answer

Electric field due to a long cylinder is,

$E = \frac{λ}{2 π ε_{0} r} = \frac{ρ A}{2 π ε_{0} r}$

If a charge $q$ is rotating in a circle of radius $r$

$\frac{m v^{2}}{r} = q E$ $\Rightarrow \frac{m v^{2}}{r} = q \frac{ρ A}{2 π ε_{0} r} \Rightarrow \frac{1}{2} m v^{2} = \frac{q ρ π R^{2}}{4 π ε_{0}} = \frac{q ρ R^{2}}{4 ε_{0}}$

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