1. Electromagnetic waves
Bringing It All Together

2. This Week Today- The rest of the week: FINAL EXAMS
No Clickers – sell them back to the bookstore unless you are planning to take my section of the course next semester. Bad idea!
We tie the stuff together and do the candle trick right in front of you. (Remember the video??)
The rest of the week: FINAL EXAMS

3. My schedule Tuesday – Not on Campus Wednesday – Friday
Giving exams
Grading Papers
In foul mood! Stop by if you need to.
Grades will be completed as fast as I can.
Grader has finals this week to, so it may be a slow process.

4. The Last Lecture Covering 5 Additional Chapters
We have been looking at the properties of Electric Fields.
We have been looking at the properties of Magnetic Fields
We looked at a few situations where there was some kind of connection between the two.
We saw that ALL of what we discussed could be explained by one set of equations.
MAXWELL’s Equations

5. James Clerk Maxwell 1831 – 1879 Scottish physicist
Provided a mathematical theory that showed a close relationship between all electric and magnetic phenomena
His equations predict the existence of electromagnetic waves that propagate through space
SMART DUDE

6. Almost Maxwell
Gauss
Bindell
Faraday
Ampere
E&B Together
Problem

7. Remember the Lowly Capacitor?
AC Current=I
But there MUST be a magnetic field
present around the gap - even if it is small!

8. Ampère’s Law is used to analyze magnetic fields created by currents:
But this form is valid only if any electric fields present are constant in time
Maxwell modified the equation to include time-varying electric fields
Maxwell’s modification was to add a term

9. Maxwell Fixed the Problem!
The additional term included a factor called the displacement current, Id
This term was then added to Ampère’s Law
Now sometimes called Ampère-Maxwell Law
This showed that magnetic fields are produced both by conduction currents and by time-varying electric fields

10. MAXWELL’S EQUATIONS

11. Vacuum There ain’t nuttin there. Maxwell’s equations say YES
No Charges
No Currents
Can there be electric or magnetic fields present??
Maxwell’s equations say YES
And they add some serious requirements to what is there.

12. Sorry it’s crooked!

13. Propagation
Direction

14. Back to Maxwell
E & M fields can propagate from a region where there are charges/currents to regions far away where they do not contain these sources.
The fields propagate as WAVES
Shape moves at the speed of the wave.
Because the E field is changing (moving charge example), there will be a B field there as well.

15. Enter: Heinrich Rudolf Hertz
1857 – 1894
German physicist
First to generate and detect electromagnetic waves in a laboratory setting
The most important discoveries were in 1887
He also showed other wave aspects of light

16. Hertz Experiment

17. So far we can assume:

18. Extended View – Sine Shape

19. The Magic From M’s 4
Mathematically these equations describe waves traveling thought space.
E and B are perpendicular to each other and to the direction of propagation.
The velocity of the wave must be

20. The Velocity is “c:
This must describe light waves …..

21. It can be shown that the wave carries energy and momentum,
Receiver!

22. How??

23. FINAL DEMO!