Question

Non-relativistic protons accelerated by a potential difference U form a round beam with current I. Find the magnitude and direction of the Poynting vector outside the beam at a distance r from its axis.

Answer 1

Here n e v   

where R = radius of cross section of the conductor and n = charge density (per unit volume)

Thus, the moving protons have a charge per unit length

This gives rise to an electric field at a distance r given by

This is the Poynting vector.