There is one long line charge with linear charge density `lambda`. One electron is moving in a circular path around this line charge. Plane of the circle is perpendicular to line charge and line charge passes through centre of circle. Prove that kinetic energy of electron is independent to the radius of a circle.

Explanation

To prove that the kinetic energy of an electron moving in a circular path around a long line charge with linear charge density \(\lambda\) is independent of the radius of the circle, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Electric Field due to the Line Charge**:
The electric field \(E\) at a distance \(r\) from an infinite line charge with linear charge density \(\lambda\) is given by:
\[
E = \frac{2k\lambda}{r}
...