JEE Mains · Physics · STD 12 - 1. Electric charges and fields
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
- A \(\frac{\rho q R^{2}}{4 \varepsilon_{0}}\)
- B \(\frac{\rho q R^{2}}{2 \varepsilon_{0}}\)
- C \(\frac{q \rho}{4 \varepsilon_{0} R^{2}}\)
- D \(\frac{4 \varepsilon_{0} R^{2}}{q \rho}\)
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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