# Is the amplitude of an EM wave the combination of the electric AND magnetic fields added together?

For instance, to get the TOTAL energy of an EM wave(s) or intensity you square the amplitude. But do you first add or combine the strengths of the e and m fields?

• you cannot combine E and B because they have different dimensions and point in different directions. – hyportnex Nov 8 '18 at 20:48

Suppose you have two sources of Electric field, $$E_1$$, and $$E_2$$

Then $$\vec{E_{tot}}=\vec{E_1}+\vec{E_2}.$$

So the total intensity is $$E^2_{tot}=(\vec{E_1}+\vec{E_2})^2=E^2_1+E_2^2+2\vec{E_1}\cdot\vec{E_2}$$

So the intensity of the sum of two electric fields is not the sum of their intensities individually.

The same thing applies to a magnetic field.

Now both the E field and the B field can carry energy. Not only is there the complexity of the above, summing the associated intensities has it's own complications.

Are you familiar with the Poyting Vector?

$$\vec{S}=\frac{1}{\mu_0}\vec{E}\times\vec{B}$$

It satisfies the energy conservation equation of electro magnetic waves.

$$\nabla\cdot \vec{S}+\frac{\partial u}{\partial t}=0$$

$$u=\frac{1}{2}\epsilon_0E^2+\frac{1}{2\mu_0}B^2$$

$$u$$ is the energy desnity of the fields. The Poyting Vector indicates the direction of the flow of energy of the EM field.

So the energy density is a linear combination of the sum of their intensities, but neither exactly the sum of their intensities nor the intensities of their sums.

• I would lose the last section on adding electric and magnetic fields together as it's both confusing and physically meaningless. – Punk_Physicist Nov 8 '18 at 22:36