An infinitely long positively charged straight wire has a linear charge density $\lambda$. An electron is in uniform circular motion around the wire in a plane perpendicular to the wire. Quantities associated with the electron's motion, which are independent of the radius of the circular path, are:

Coulomb force provides the necessary centripetal force for the circular motion of the particle. Thus

$\frac{\lambda e}{2\pi {\epsilon }_{0}r}=m\frac{v^2}{r}$

$\Rightarrow v=\sqrt{\frac{\lambda e}{2\pi {\epsilon }_{0}m}}\Rightarrow v$ is independent of $r$

Frequency of revolution $=\frac{v}{2\pi r}\text{ depends on }r$

Kinetic energy $=\frac{1}{2}m{v}^2$  independent of $r$

Linear momentum $=mv$ independent of $r$

Angular momentum about the wire $=mvr$ depends on$r$