1. Trivia Question
James Clerk Maxwell ( ) was famous for showing that electric and magnetic fields travel through space at the speed of light. Which of the following are also his notable achievements? (a) Maxwell-Boltzman Distribution (used to describe kinetic theory of gases) (b) Description of color vision in humans. (c) Rigidity of trusses in bridges (d) Developed special relativity. (e) Started Maxwell House coffee company

2. Do not be afraid of the math in the Textbook!
As your doctor would say…. “this is going to pinch a bit…”
The math will be MUCH easier once we get the ‘formal’ calculus out of the way.

3. Gauss’s Law

4. Gauss’s Law for Magnetism
Compare with Gauss’s law for Electric Fields…..
What does this imply about ‘enclosed magnetic charge’?
“Magnetic Charge” does NOT exist!
You can not isolate a North pole of a magnetic from the South pole…. They both must exist together.
Magnetic field lines form CLOSED loops

5. Faraday’s Law Electromotive Force
Time varying B fields generate E fields

6. Ampere’s Law
Current (moving charges) generate magnetic fields

7. Ampere’s Law in a Capacitor
The contour C is the boundary of the surface S.
If the contour C is fixed, there are MANY surfaces which are bounded by that contour such as S1 and S2 in the figure.
If we evaluate current using S1, we calculate current I through that surface.
If we evaluate current using S2 (which is INSIDE the capacitor), current equals zero.
Why does evaluation of Ampere’s Law depend on WHICH surface one uses for the evaluation?
THERE IS A MISSING TERM IN THE EQUATION!

8. Symmetry in Electromagnetic equations?
Time dependent magnetic fields generate electric fields
What should happen if there are time dependent electric fields?

9. Symmetry in Electromagnetic equations?
Displacement CURRENT

10. Maxwell’s equations
Integral form
Differential form

11. Review of Dot and Vector Cross Products
Direction of cross product given by “Right Hand Rule”

12. Animations of Electromagnetic waves
E and B fields
E and B with another polarization