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

[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?

 

[weirdoguy]

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.

 

[vanhees71]

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

 

[sophiecentaur]

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.

 

[A.T.]

Doesn't the Energy Conservation law apply here?

That's basically what the Poynting's theorem is.

 

[Dale]

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.

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.

 

[hutchphd]

Cavity resonators
https://www.feynmanlectures.caltech.edu/II_23.html

Transmission Lines
https://www.feynmanlectures.caltech.edu/II_24.html