How Is the Energy Density of EM Waves Related to Capacitors and Inductors?

• cg0303
In summary, the energy density of an EM wave is derived from the energy density of the electric and magnetic fields of capacitors and inductors, respectively. This is based on Poynting's theorem, which is derived from Maxwell's equations. This explains why the energy density of these components is the same as that of an EM wave, as they all follow the same principles and laws.
cg0303
The energy density of an EM wave is given as (1/2) ϵ E^2 + (1/(2μ)) B^2.

This is derived from the energy density of the electric and magnetic fields of capacitors and inductors, respectively.

But why should the energy density of the fields of capacitors and inductors be the same as that of the fields of an EM wave?

cg0303 said:
This is derived from the energy density of the electric and magnetic fields of capacitors and inductors, respectively.

No, it's not. Which book are you learning from? I mean, the book can say something like "let's assume it works also for EM waves" if it's not too advanced, but certainly there are textbooks that derive it the proper way.

cg0303
Check for the key word "Poynting's theorem"!

cg0303
Doesn't the Energy Conservation law apply here? The (ideal) passive components in a transmitter output network must be passing on the same Power as is being radiated.

sophiecentaur said:
Doesn't the Energy Conservation law apply here?
That's basically what the Poynting's theorem is.

vanhees71 and sophiecentaur
cg0303 said:
This is derived from the energy density of the electric and magnetic fields of capacitors and inductors, respectively.
No. It is derived from Poynting’s theorem, as I see several others have pointed out. Poynting’s theorem is derived directly from Maxwell’s equations.

cg0303 said:
But why should the energy density of the fields of capacitors and inductors be the same as that of the fields of an EM wave?
Because capacitors, inductors, and EM waves all obey Maxwell’s equations, therefore Poynting’s theorem describes the conservation of energy in all of them.

vanhees71

1. What is energy density of an EM wave?

The energy density of an electromagnetic (EM) wave is the amount of energy per unit volume carried by the wave. It is a measure of the energy present in the electric and magnetic fields of the wave.

2. How is energy density of an EM wave related to its frequency and amplitude?

The energy density of an EM wave is directly proportional to its frequency and the square of its amplitude. This means that as the frequency or amplitude of the wave increases, so does its energy density.

3. What are the units of energy density for an EM wave?

The units of energy density for an EM wave are Joules per cubic meter (J/m3). This is the same unit used to measure the energy density of any type of electromagnetic radiation.

4. What is the significance of energy density in EM waves?

The energy density of an EM wave is important because it determines the intensity of the wave, which can have various effects on matter. For example, high energy density waves can cause damage to living cells, while low energy density waves are used in communication and technology.

5. How is the energy density of an EM wave related to its speed?

The energy density of an EM wave is not directly related to its speed. However, the speed of an EM wave is determined by the properties of the medium it is traveling through, which can also affect its energy density. In a vacuum, the speed of an EM wave is constant and its energy density remains the same.

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