# Use Poynting's Theorem to show E and B fields are out of phase

• freesnow
In summary, the conversation discusses the use of Poynting's theorem in explaining why the waves of magnetic and electric field are 90 degrees out of phase in a Fabry-Perot interferometer. The attempt at a solution involves using equations to calculate the Poynting vector and showing that theta is 90 degrees, but the correct approach is to use the law of conservation of electromagnetic energy.

## Homework Statement

In a Fabry-perot interferometer, light is reflected back and forth between 2 highly reflecting parallel mirrors, with a nonconducting medium inside. The waves of magnetic and electric field are 90o out of phase, unlike the case of a wave in free space where they in phase. Develop an argument using Poynting's theorem for why this should be so.

## The Attempt at a Solution

I've thought of using E to calculate H and then say that they're out of phase, but then this method isn't based on Poynting's theorem.
Then I've thought of using the eq.:
E = E0exp((-kapper)z+i(kz-wt))
B = B0exp((-kapper)z+i(kz-wt+theta))
to calculate the Poynting vector, S = 1/mu * (E x B), then somehow show that theta is 90o, but then I don't really know how to do it.

I was under the impression that Poynting's theorem was the law of conservation of electromagnetic energy,
$$\vec{J}\cdot\vec{E} + \frac{1}{2}\frac{\partial}{\partial t}\left(\epsilon_0 E^2 + \frac{1}{\mu_0}B^2\right) + \frac{1}{\mu_0}\vec{\nabla}\cdot(\vec{E}\times\vec{B}) = 0$$

Does that give you any ideas?

Thanks. I just realized that I was in the wrong direction from the start, I've just now finished the argument using the law of conservation of electromagnetic energy instead.

## What is Poynting's Theorem?

Poynting's Theorem is a fundamental law in electromagnetism that relates the electric and magnetic fields to the flow of energy in an electromagnetic wave.

## How does Poynting's Theorem show that E and B fields are out of phase?

Poynting's Theorem states that the direction of energy flow in an electromagnetic wave is perpendicular to both the electric and magnetic fields. Since the electric and magnetic fields are perpendicular to each other, this means that the energy flow and the fields are also perpendicular. This results in the E and B fields being out of phase.

## Why is it important to understand the phase relationship between E and B fields?

Understanding the phase relationship between E and B fields is important because it helps us understand the behavior of electromagnetic waves. It also allows us to predict how electromagnetic waves will interact with different materials and how they will propagate through space.

## Can Poynting's Theorem be used to show the phase difference between E and B fields in other situations?

Yes, Poynting's Theorem can be used to show the phase difference between E and B fields in a variety of situations, such as in the presence of conductors or dielectrics. It is a general law that applies to all electromagnetic waves.

## How is Poynting's Theorem derived to show the phase relationship between E and B fields?

Poynting's Theorem is derived from Maxwell's equations, specifically the equations for the electric and magnetic fields. By combining these equations and manipulating them, we can arrive at the expression for the Poynting vector, which describes the direction and magnitude of energy flow and thus shows the phase relationship between E and B fields.