1. Chapter 23
EM Waves

2. Electromagnetic Waves
Solution of Maxwell's Equations
Simple Idea:
Changing Electric field creates Magnetic field
Changing Magnetic field creates Electric field
Both happen simultaneously and propagate

3. Characteristics of EM waves
The wave is transverse: Both and are perpendicular to the direction of propagation of the wave and to each other.
All EM waves move with speed c when in vacuum
Require no medium.
Definite ratio between E and B
E=cB

4. Formed from E and B field orthonormal to each other, propagating in direction
E x B at speed of light c (in vacuum).
Direction of propagation: 𝑘 =𝛼 𝐸 × 𝐵

8. Electromagnetic Waves
They carry energy
This follow from the fact that electric and magnetic fields have energy
Electric energy density
Magnetic energy density

9. Electromagnetic Waves
In an electromagnetic wave propagating through a vacuum or air, the electric field and the magnetic field carry equal amounts of energy per unit volume of space.
It is possible to rewrite the equation for total energy density,
, in two additional, but equivalent, forms:

10. Electromagnetic Waves
The fact that the two energy densities are equal implies that the electric and magnetic fields are related. To see how, we set the electric energy density equal to the magnetic energy density and obtain
In 1865, Maxwell determined theoretically that electromagnetic waves propagate through a vacuum at a speed given by
Hence, from equation (1) it follows that

11. Electromagnetic Waves
There are 2 ways of calculating the intensity:
From the electric and magnetic fields
𝐼= 𝑢 𝑡 ×𝑐= 𝜀 𝑜 𝐸 𝑐= 1 2 𝜇 0 𝑐 𝐵 0 2

12. Electromagnetic Waves
From the power emitted by a source
I: intensity, P: power emitted, A: surface area the waves propagate over
The intensity of an EM wave tells you the average energy flowing across a surface in a span of time

14. Electromagnetic Waves
They carry momentum
Without considering this, Newton’s laws would fail in the presence of electromagnetic waves
𝑝= 𝐸 𝑡𝑜𝑡𝑎𝑙 𝑐
Since they carry momentum, they can apply pressure to an object
Prad: radiation pressure, I: Intensity, c: vacuum speed of light, α: ratio of light reflected
P 𝑟𝑎𝑑 =(1+𝛼) 𝐹 𝐴 =(1+𝛼) 𝐼 𝑐

15. Polarization
Polarization occurs with all transverse waves (e.g., wave on a string).
When a wave has only y displacements, we say that it is linearly polarized in the y direction ; similarly, a wave with only z displacements is linearly polarized in the z direction.
For mechanical waves, we can build a polarizing filter that permits only waves with a certain polarization direction to pass.
In figure c, the string can slide vertically in the slot without friction, but no horizontal motion is possible.

16. POLARIZED ELECTROMAGNETIC WAVES
Linearly polarized wave
on a rope.

17. In polarized light, the electric field
fluctuates along a single direction.

18. Polarized light may be produced from unpolarized light with
the aid of polarizing material.

19. MALUS’ LAW
intensity before
analyzer
intensity after
analyzer

20. Example 7 Using Polarizers and Analyzers
What value of θ should be used so the average intensity of the polarized
light reaching the photocell is one-tenth the average intensity of the
unpolarized light I_0?

22. The electromagnetic Spectrum
All these electromagnetic waves have the general characteristics, including the common propagation speed c = 3.00 x 108 m/s (in vacuum). All are the same in principle; they differ in frequency f and wavelength , but the relation holds for all.

23. Quiz Question 1
Look at projector. +x -x +y -y +z

24. Quiz Question 2