Chapter 24 Electromagnetic Waves
24.4 Energy in Electromagnetic Waves
- Explain how the energy and amplitude of an electromagnetic wave are related.
- Given its power output and the heating area, calculate the intensity of a microwave oven’s electromagnetic field, as well as its peak electric and magnetic field strengths
Anyone who has used a microwave oven knows there is energy in electromagnetic waves. Sometimes this energy is obvious, such as in the warmth of the summer sun. Other times it is subtle, such as the unfelt energy of gamma rays, which can destroy living cells.
Electromagnetic waves can bring energy into a system by virtue of their electric and magnetic fields. These fields can exert forces and move charges in the system and, thus, do work on them. If the frequency of the electromagnetic wave is the same as the natural frequencies of the system (such as microwaves at the resonant frequency of water molecules), the transfer of energy is much more efficient.
The behavior of electromagnetic radiation clearly exhibits wave characteristics. But we shall find in later modules that at high frequencies, electromagnetic radiation also exhibits particle characteristics. These particle characteristics will be used to explain more of the properties of the electromagnetic spectrum and to introduce the formal study of modern physics.
Another startling discovery of modern physics is that particles, such as electrons and protons, exhibit wave characteristics. This simultaneous sharing of wave and particle properties for all submicroscopic entities is one of the great symmetries in nature.
But there is energy in an electromagnetic wave, whether it is absorbed or not. Once created, the fields carry energy away from a source. If absorbed, the field strengths are diminished and anything left travels on. Clearly, the larger the strength of the electric and magnetic fields, the more work they can do and the greater the energy the electromagnetic wave carries.
A wave’s energy is proportional to its amplitude squared (E2E2 size 12{E rSup { size 8{2} } } {} or B2B2 size 12{B rSup { size 8{2} } } {}). This is true for waves on guitar strings, for water waves, and for sound waves, where amplitude is proportional to pressure. In electromagnetic waves, the amplitude is the maximum field strength of the electric and magnetic fields. (See [link].)
Thus the energy carried and the intensity II size 12{I} {} of an electromagnetic wave is proportional to E2E2 size 12{E rSup { size 8{2} } } {} and B2B2 size 12{B rSup { size 8{2} } } {}. In fact, for a continuous sinusoidal electromagnetic wave, the average intensity IaveIave size 12{I rSub { size 8{“ave”} } } {} is given by
where cc size 12{c} {} is the speed of light, ε0ε0 size 12{ε rSub { size 8{0} } } {} is the permittivity of free space, and E0E0 size 12{E rSub { size 8{0} } } {} is the maximum electric field strength; intensity, as always, is power per unit area (here in W/m2W/m2 size 12{“W/m” rSup { size 8{2} }