An electrton beam is widely used in all kinds of vacuum tubes. The electrons decrease the potential in and around the beam. The electrical force courses the beam to expand in the cavity. The main step to obtain the potential is as follows:
Step 1 Use Gauss’s low to find the electric field in the cavity.
Step 2 Integrate the electric field to get the potential.
Step 3 Obtain the electron speed by the energy conservation.
Step 4 Get the charge density by I=Q/t
Step 5 Subsitude the charge density to the potential formula.
