Poynting's theoremtheorem
Sunlight carries energy across the void of space. Poynting's theorem reveals the balance: the energy of the electromagnetic field doesn't disappear, but either leaves across an imaginary boundary of a volume or heats the charges inside. Poynting presented the energy flow as a vector, always perpendicular to the electric and magnetic fields — like the direction of wind blowing leaves away.
How it works
Any wireless energy transfer — from cellular communications to Wi-Fi — obeys this theorem. It also describes how light heats water in solar collectors and how electromagnetic waves push charges in laser accelerators.
💡 If you point an antenna at a blank wall, the energy of radio waves reflects back, and the Poynting vector turns around. And in a microwave oven, this vector points straight into your food!
\frac{\partial u}{\partial t} + \nabla \cdot \mathbf{S} = -\mathbf{J} \cdot \mathbf{E}
u — volume energy density of the electromagnetic field (in vacuum u = ε₀E²/2 + μ₀H²/2), S — Poynting vector (energy flux), J — electric current density, E — electric field strength, ∇· — divergence operator, ∂/∂t — partial derivative with respect to time.
\mathbf{S} = \mathbf{E} \times \mathbf{H}
S — Poynting vector, electromagnetic energy flux density (W/m²), E — electric field vector, H — magnetic field vector, × — cross product.