A vacuum tube, in its simplest conceptual form, is a parallel- 12 plate capacitor enclosed in a glass tube so that all the air can be pumped out. A potential difference is applied, and if the negative plate is heated, some electrons will spontaneously pop out of the metal and be accelerated across the gap. The density of the electrons in flight is nonuniform because of their acceleration, and an analysis by Richardson around 1901 showed that the potential would have the form o = cr*/3, where c is a constant. Find the electric field.

A vacuum tube, in its simplest conceptual form, is a parallel- 12 plate capacitor enclosed in a glass tube so that all the air can be pumped out. A potential difference is applied, and if the negative plate is heated, some electrons will spontaneously pop out of the metal and be accelerated across the gap. The density of the electrons in flight is nonuniform because of their acceleration, and an analysis by Richardson around 1901 showed that the potential would have the form o = cr*/3, where c is a constant. Find the electric field.