Electromagnetic waves

A charge at rest makes an electric field. A charge moving steadily also makes a magnetic field. An accelerated (shaking) charge sends out electromagnetic waves: changing E and B fields that keep regenerating each other and travel outwards.

A charge oscillating at frequency ν radiates waves of the same frequency ν. Hertz first made and detected such waves in 1887 with sparks; Bose and Marconi later used them for signalling.

The shape of an em wave:

• E and B are perpendicular to each other and both perpendicular to the direction of travel. So em waves are transverse.
• E and B rise and fall together, in phase.
• The wave travels in the direction of E × B. If E is along x and B along y, the wave goes along z.

Their sizes are linked: E₀ = c B₀. Example: E₀ = 30 V/m gives B₀ = 30 / (3 × 10⁸) = 10⁻⁷ T. The magnetic part looks tiny in tesla, but it carries as much energy as the electric part.

The speed in vacuum is fixed by two constants:

c = 1/√(µ₀ε₀) = 3 × 10⁸ m/s

Maxwell calculated this and found it equal to the measured speed of light. So light is an electromagnetic wave. In a medium, em waves travel more slowly.

For all waves, c = νλ. An FM station at 100 MHz broadcasts with λ = 3 × 10⁸ / 10⁸ = 3 m.

Em waves need no medium: they cross empty space, which is how sunlight reaches us. They carry energy and momentum, so light exerts a tiny pressure on whatever it falls on.