May/June 2026 Paper 43

A hydrogen atom consists of a proton and an electron separated by distance $2x$, as shown in Figure 4.1.

Point P is at the midpoint of the line joining the centres of the proton and the electron. For point P, compare the electric field due to the proton with the electric field due to the electron.

For point P, compare the electric potential due to the proton with the electric potential due to the electron.

The elementary charge is $e$ and the permittivity of free space is ${\epsilon }_0$. State an expression, in terms of $x$, $e$ and ${\epsilon }_0$, for the magnitude of the electric force $F$ between the proton and the electron.

Determine an expression, in terms of $F$ and $x$, for the electric potential energy $E_{\text{P}}$ of the proton and the electron.