Electromagnetic Waves: How Radiation is Generated

An electromagnetic wave is a coupled disturbance of electric and magnetic fields that propagates through space.

With Maxwell’s equations we discovered that electric and magnetic fields can travel together through a vacuum at the speed of light. But knowing that they can travel is one thing, and knowing how to create them is quite another.

A static charge or a steady current does not radiate continuously. To create a radio wave we need accelerated charges and a distribution capable of radiating.

The Key Idea: Accelerated Charges Radiate

Let’s review the hierarchy of motion for an electric charge:

Zero Velocity (At Rest): Creates only an Electric Field. (This is Electrostatics). No waves.

Steady Current: Produces electric and magnetic fields that extend through space around the circuit, but does not by itself generate continuous radiation to infinity.

Changing Velocity (Acceleration/Braking): Radiation appears.

• When the velocity changes, the electromagnetic field experiences a “jolt”.
• Part of the disturbance can propagate as radiation if the geometry and frequency of the system allow it.

We have created Electromagnetic Radiation.

How an Antenna Works

If we want to emit radio, we need to “shake” electrons furiously. How do we do it? With a high-frequency Alternating Current (AC) Circuit.

Let’s take the simplest antenna in the world: the Dipole (two metal rods).

1. The transmitter pushes electrons toward the top rod. (They accelerate upward).
2. The transmitter pulls them toward the bottom rod. (They decelerate and accelerate downward).
3. This alternating current produces varying fields; part of the energy detaches from the near region and propagates as an electromagnetic wave.

We call this radiation a radio wave. In a vacuum, the electric and magnetic fields jointly satisfy Maxwell’s equations and carry energy and momentum without needing a material medium.

The Electromagnetic Spectrum

Depending on how quickly we shake the electrons in the antenna, the wave will have a different wavelength. But physically, it is exactly the same thing: photons traveling.

The faster you shake (higher frequency), the more energy the wave carries. That’s why WiFi doesn’t harm you, but X-rays (extremely high frequency) can ionize your cells.

The Limit of the Classical Atomic Model

And here we reach the end of Classical Physics. Maxwell’s equations worked so well for antennas and light that physicists in 1900 tried to apply them to the Atom.

Rutherford’s model imagined the atom as a mini solar system:

• The positive nucleus at the center.
• The negative electron orbiting around it.

The Big Problem #15

1. An object moving in a circle, even at constant speed, experiences Centripetal Acceleration (it constantly changes the direction of its velocity).
2. According to Maxwell: Accelerated Charge = Emission of Radiation.
3. If the electron emits radiation (light/energy), it loses its own kinetic energy.
4. If it loses energy, it should slow down and spiral into the nucleus.

According to Maxwell’s equations, a hydrogen atom should collapse in approximately 10⁻¹¹ seconds. All the matter in the universe should have imploded in an instantaneous flash of light.

Why Doesn’t It Happen?

Because the classical planetary model of the atom is incorrect. Bohr’s model introduced quantized stationary states as an intermediate step, and quantum mechanics replaced defined orbits with states and orbitals.

Maxwell’s equations still describe the classical electromagnetic field, but they are not sufficient by themselves to describe an atom.

That is a story for another course. In applied electricity, the classical model works very well within its range of validity.