Electric dipole radiation
An accelerating charge — in the simplest case, one oscillating back and forth like a dipole antenna — radiates electromagnetic waves whose intensity is not the same in every direction: it is zero along the dipole's own axis and greatest in the plane perpendicular to it, following a sin²θ pattern with θ measured from that axis.
Practise this conceptA charge sitting still, or moving at constant velocity, doesn't radiate — its electric field just moves along with it. Radiation only happens when a charge accelerates, and the simplest accelerating-charge system worth studying is a dipole: two opposite charges (or one charge sloshing back and forth, as in a wire antenna) oscillating along a line. That oscillation is a continuous acceleration, reversing direction twice per cycle, and it's strongest — not the speed, the acceleration — at the two ends of the swing where the charge momentarily stops and reverses, not in the middle where it's moving fastest.
The radiation this produces doesn't spread out equally in every direction the way light from a point source does. Look along the dipole's own axis — straight along the direction it's oscillating — and you'll find no radiation there at all, no matter how strong the oscillation. Look from the side, in the plane perpendicular to that axis, and you'll find the radiation at its strongest. Everywhere in between follows a sin²θ pattern, where θ is the angle measured from the dipole's axis: maximum at 90° (side-on), falling smoothly to exactly zero at 0° and 180° (along the axis).
This is why real antennas are shaped and oriented deliberately rather than arbitrarily: a vertical dipole antenna radiates well out to the horizon in every horizontal direction (all of which sit at 90° to the vertical axis) but sends essentially nothing straight up or straight down. It's also why calculating the total power radiated in every direction requires integrating that sin²θ pattern over the full sphere around the dipole, rather than just multiplying one direction's intensity by 4πr² as you would for a source that really does radiate equally everywhere.
Key ideas
Requires: Electromagnetic waves, The wave equation
Formulas
| Symbol | Name | Unit |
|---|---|---|
| intensity | W/m^2 (watt per square metre) | |
| angle | deg (degree) | |
| intensity | W/m^2 (watt per square metre) |
Common misconceptions
- Believing an oscillating dipole radiates equally in all directions, like a point source, rather than the radiation pattern depending on the angle from the dipole's oscillation axis and vanishing along that axis entirely.
- Believing a charge only radiates while it is actually moving fastest (as it crosses the centre of its oscillation), rather than radiation being tied to acceleration — the charge radiates most strongly at the turning points, where its speed is momentarily zero but its acceleration is greatest.
- Believing the radiated intensity varies with angle as a simple 1/r² fall-off only, with no additional angular dependence — the 1/r² decrease with distance is separate from, and multiplied by, the sin²θ dependence on direction.
Resources
Part of these UT courses
This concept is mapped as covering part of the following course(s) in the University of Tartu curriculum.
- OpticsLOFY.01.008
- Microscopic electrodynamicsLOFY.04.040