Field and Force inside an Electron Gun

Since the voltage and plate separation are given, the electric field strength can be calculated directly from the expression $E=\frac{V_{\text{AB}}}{d}$. Once the electric field strength is known, the force on a charge is found using $\mathbf{\text{F}}\mathrm{<mo\; stretchy="false">=</mo>}q\mathbf{\text{E}}$. Since the electric field is in only one direction, we can write this equation in terms of the magnitudes, .

The expression for the magnitude of the electric field between two uniform metal plates is

Since the electron is a single charge and is given 25.0 keV of energy, the potential difference must be 25.0 kV. Entering this value for $V_{\text{AB}}$ and the plate separation of 0.0400 m, we obtain

The magnitude of the force on a charge in an electric field is obtained from the equation

Substituting known values gives

Note that the units are newtons, since $\text{1 V/m}=\text{1 N/C}$. The force on the charge is the same no matter where the charge is located between the plates. This is because the electric field is uniform between the plates.