# Plane wave approximation

Consider a proton in harmonic motion along vertical direction.

Near a point source, direction of electric field is along the curve.

But at greater distance from point source, in plane wave approximation, electric field is not along the sinusoid but it is perpendicular to axis.

How the direction of electric field is determined in plane wave approximation?

• the Coulombic part is generally directed away from the charge, and it goes down as $1/r^2$ with the distance from the center of the oscillations.
• the radiative part is generally transversely polarized, and it goes down as $1/r$ with the distance from the charge.
When we're considering radiation, we keep the $1/r$ component, because it dominates completely over the $1/r^2$ Coulombic near-field when you're far away from the charge. This explains the discrepancy you observe.