Two long concetric cylindrical conductors of radii a and b `(b lt a)` are maintained at a potential difference V and carry equal and opposite currents l. Show that an electron with a particular velocity u parallel to the axis may travel underivated in the evacuated region between the conductors, and calculate u when a = 50 mm, b = 2.0 mm, V = 50 V and l = 100 A.
It is also possible for the electron to travel in a helical path. By regarding such a path as the combination of a circular motion perpendicular to the axis with a steady velocity parallel to the axis, indicate without detailed mathematics how this comes about.

Explanation

To solve the problem, we need to show that an electron can travel undeviated in the evacuated region between two concentric cylindrical conductors and calculate the specific velocity \( u \) given the parameters. Let's break this down step by step.

### Step 1: Understanding the Electric Field
The electric field \( E \) in the region between the two cylindrical conductors can be derived from the potential difference \( V \) and the geometry of the cylinders.

Using Gauss's law, the electric field at a distance \( r \) from the axis of the cylinders is given by:
\[
E = \frac{2k\lambda}{r}
...