A long cylindrical volume contains a uniformly distributed charge of density \(\rho\). 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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Answer & Solution

Correct Answer

(A) \(\frac{\rho q R^{2}}{4 \varepsilon_{0}}\)

Step-by-step Solution

Detailed explanation

\(E\cdot 2 \pi r \ell=\frac{\rho \pi r ^{2} \ell}{\varepsilon_{0}}\)

\(qE =\frac{ q \rho R ^{2}}{2 \varepsilon_{0} r }=\frac{ mv ^{2}}{ r }\)

\(mv ^{2}=\frac{ q \rho R ^{2}}{2 \varepsilon_{0}}\)

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