A beam of electrons has radius $r$and contains $\text{'}n\text{'}$ electrons per cubic meter moving with velocity $\overrightarrow{v}$ along the beam (figure). Assume that a beam that is much longer than its diameter forms a cylindrically symmetric distribution of charge and current. The beam expand if the electric force exceeds the magnetic force. So long as the expansion is slow, the approximations of cylindrical symmetry and static fields
remain valid.