1. Maxwell’s Equations (so far)
Gauss’s law
Gauss’ law for magnetism
Faraday’s law
Ampere’s law*

2. Parallel-Plate Capacitor Revisited
B=0 ? Not experimentally!
For surface S1, Is = I, but for surface S2, Is = 0 Q -Q
Wait, LHS is the same (because C is the same)! ??
You could make this work if a fictitious current Id is added to Is in such a way that Id is zero for S1 but is equal to I for S2.
will work.

3. James Clerk Maxwell proposed that a changing electric field
Displacement Current
James Clerk Maxwell proposed that a changing electric field
induces a magnetic field, in analogy to Faraday’s law: A
changing magnetic field induces an electric field.
Ampere’s law is revised to become Ampere-Maxwell law
is the displacement current.
where
The direction of the displacement current is the same as that of the electric flux, if the flux increases, and is opposite, if the flux decreases.

4. Basis for electromagnetic waves!
Maxwell’s Equations
Basis for electromagnetic waves!
The equations are often written in slightly different (and more convenient) forms when dielectric and/or magnetic materials are present.

5. ©2008 by W.H. Freeman and Company

6. DOCCAM 2

7. Electromagnetic Waves From Faraday’s Law

8. ©2008 by W.H. Freeman and Company

9. Electromagnetic Waves From Ampère’s Law

10. ©2008 by W.H. Freeman and Company

11. Electric Dipole Radiation

12. ©2008 by W.H. Freeman and Company

13. WARM UP QUIZ 1
Light is an electromagnetic wave where the wavelength λ in meters times the frequency f in Hz is equal to the velocity of light c = 3 x 108 meters/second in vacuum. Which of the following statements is correct?
λ = 100 meters, f = 1x106 Hz
(b) λ = 105 meters, f = 3x104 Hz
λ = 10-6 meters, f = 3x1014 Hz
λ = 1 meter, f = 3/2 x 108 Hz

14. Electromagnetic Wave Propagation in Free Space
So, again we have a traveling electromagnetic wave
speed of light in vacuum
Ampere’s Law
Faraday’s Law
Wave Equation
Speed of light in vacuum is currently defined rather than measured (thus defining meter and also the vacuum permittivity).

15. Plane Electromagnetic Waves
where c
Transverse wave
Plane wave (points of given phase form a plane)
Linearly polarized (fixed plane contains E) x

16. Energy Density of Electromagnetic Waves
Electromagnetic waves contain energy. We know already expressions for the energy density stored in E and B fields:
EM wave
So Total energy density is

17. Energy Propagation in Electromagnetic Waves
Energy flux density
= Energy transmitted through unit time per unit area
Intensity I
= Average energy flux density (W/m2)
Define Poynting vector
Direction is that of wave propagation
average magnitude is the intensity

18. If radiation is totally absorbed:
Radiation Pressure
Electromagnetic waves carry momentum as well as energy. In terms of total energy of a wave U, the momentum is U/c.
During a time interval Δt , the energy flux through area A is ΔU =IA Δ t .
If radiation is totally absorbed:
If radiation is totally reflected: x2
momentum imparted
radiation pressure EXERTED

19. Light is an Electromagnetic Wave
Maxwell’s Rainbow
Light is an Electromagnetic Wave

20. x The direction of travel
Physics :30 Quiz 2
An electromagnetic wave is traveling in +x direction and the electric field at a particular point on the x-axis points in the +z direction at a certain instant in time. At this same point and instant, what is the direction of the magnetic field?
a) -z
b) -x
c) -y
d) +y
e) None of the above z E y
x The direction of travel
is that of E x B.

21. z a) +x E y b) -x c) -y B x d) -z e) None of the above
Physics :30 Quiz 2
An electromagnetic wave is traveling through a particular point in space where the direction of the electric field is along the +z direction and that of the magnetic field is along the +y direction at a certain instant in time. Which direction is this wave traveling? z E y B x
The direction of travel
is that of E x B.
a) +x
b) -x
c) -y
d) -z
e) None of the above

22. z -z B -x y c) -y x d) +x e) None of the above
Physics 241 – Quiz 21c – April 2, 2009
An electromagnetic wave is traveling in +y direction and the magnetic field at a particular point on the y-axis points in the +z direction at a certain instant in time. At this same point and instant, what is the direction of the electric field? z B y x
The direction of travel
is that of E x B. -z -x
c) -y
d) +x
e) None of the above

23. READING QUIZ 1
The extended Amperes law involves a displacement current which was added to the real currents as a source of the magnetic (B) fields. Which of the following statements is correct? A| the displacement current has a constant magnitude ie not a frequency dependent magnitude. B| The displacement current does not involve the constant εO= 1/4πk. C| The displacement current is proportional to εO. D| The displacement current was introduced by Faraday.