Question

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. $\frac{\rho q{R}^2}{4{\epsilon }_0}$
• B. $\frac{\rho q{R}^2}{2{\epsilon }_0}$
• C. $\frac{q\rho }{4{\epsilon }_0{R}^2}$
• D. $\frac{4{\epsilon }_0{R}^2}{q\rho }$

Answer 1

Answer: (A)

$E=2\pi r\ell =\frac{\rho \pi r^2\ell }{{\epsilon }_0}$
$qE=\frac{q\rho R^2}{2{\epsilon }_{0}r}=\frac{m{v}^2}{r}$
$m{v}^2=\frac{q\rho R^2}{2{\epsilon }_0}$