1. Natural Optics KM
Geise
Ampère’s Law

2. Ampère’s Law
Maxwell’s Equations

3. Ampère’s Law
Maxwell’s Equations

4. Mr. Ampere’s magical, mystical wonderful law

5. Mr. Ampere’s magical, mystical wonderful law

6. Mr. Ampere’s magical, mystical wonderful law
(Maxwell’s version)

7. Mr. Ampere’s magical, mystical wonderful law
(Ampère’s version)

8. Ampère’s Law… according to Ampère
The path integral of the magnetic field is equal to μ0 times the current passing through the region enclosed by the path.

9. Ampère’s Law… according to Ampère
The path integral of the magnetic field is equal to μ0 times the current passing through the region enclosed by the path.
The path need not be a circle.

10. Mr. Ampere’s magical, mystical wonderful law
On the left side, B of circulation
On the right side, μ0I

11. Mr. Ampere’s magical, mystical wonderful law
On the left side, B of circulation
On the right side, μ0I
Ampere’s law did not adequately describe physical phenomena such as a charging capacitor. Maxwell developed a nifty solution to the problem. Ampere’s Law (as adjusted by Maxwell) is the longest and strangest of all (of Maxwell’s equations).

12. How Maxwell Fixed Ampère’s Law
Maxwell added a displacement current to Ampère’s Law
The displacement current tells us that a changing electric field induces a magnetic field.
It is possible for a self-sustaining electromagnetic wave to propagate through a vacuum.
The wave moves at a particular speed.
Can you guess the speed?

13. The speed of light
Maxwell derived the speed at which an electromagnetic wave would propagate in a vacuum
Compared it against the known speed of light
And deduced that light must be an electromagnetic wave.

14. Credits Ampere’s Law song:
Floating frog:
The cover photo is an overhead view of a frog being levitated in a magnetic field. The upward magnetic force balances the downward force of gravity. The frog is diamagnetic. In essence, water can levitate. See HRW for more: Fundamentals of Physics, Part 3, Sixth Edition, pages Or,
Click picture for movie