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 energy of the particle is :

Options

A. `(rho qR^(2))/(4 epsilon_(0))`
B. `(rhoqR^(2))/(2epsilon_(0))`
C. `(qrho)/(4 epsilon_(0)R^(2))`
D. `(4epsilon_(0)R^(2))/(qrho)`

Explanation

To solve the problem, we need to find the kinetic energy of a charged particle \( q \) revolving around a long cylindrical volume with a uniform charge density \( \rho \) and radius \( R \).

### Step-by-Step Solution:

1. **Determine the Total Charge in the Cylinder**:
The volume \( V \) of the cylinder can be expressed as:
\[
V = \pi R^2 L
...