operations and physics

Electrons are accelerated towards the plate.

Each electron has this Kenetic Energy:

v
where V = Electron Velosity (Scalar Speed)

Simple newtonian physics apply to tubes that have electron velosities less than a few percent of the velosity of light.

M
Electron Rest Mass = 9.11E-31 Kg

The mass of the electron is a small quantity. But remember, we are dealing with huge numbers. Each amp is a qoulomb/sec. And each qoulomb is 6E18 electrons. That is a huge quantity.

---

The electric field Electric field inside the tube is determined by the plate volts Volts and separation distance Distance between Plate and Filament. The electric field would be isometric and linear if the field was produced by two parallel plates. However, the construction of two concentric grid structures, as in the depicted tube, comes close to such an electric field.

E
E=Electric Field in newtons/coulomb volts/meter

...By deffinition

Notice that the energy that hits the plate is NOT dependent upon separation distance D: And only depends upon voltage.

(Distance cancels)

---

V
V=Voltage in Volts

---

As a side note to emphasize the point: The energy is invariant of distance for currents q (large number of e) but also for a single electron. In which case the energy can be conveniently equated directly to voltage, as in electron volts eV. This eliminates large exponents. 1 eV = qV = q = 1.6 10^-19 joule. As an engineer this is too small a value to work with, but does show that tube energy is invariant of separation distance.

And total power will depend upon voltage and current in the tube.