Ch 32 Maxwell’s Equations 1)Gauss’ Law for Electrostatics 2)Gauss’ Law for Magnetostatic 3)Faraday's Law 4)Maxwell-Ampere Law They predict that light is an E&M Wave propagating at speed =3x10 8 m/s (Edinburgh, Scotland) The first Unification of Physical Laws. The pursuit has never stopped….

Can you ever just get a north pole or a south pole ???

Gauss’s Law for Magnetism Reminder of the definition of magnetic flux As of today 4/21/05 there is no evidence of magnetic monopoles See :Phys.Rev.Lett.85:5292,2000

Gauss’s Law for Magnetism Only magnetic dipoles exist

The Search for magnetic monopoles Goes ON! Null result sets the lower bound on a monopole mass to be about m= GeV

Carl Friedrich Gauss The total flux passing through a closed surface is proportional to the charge enclosed within that surface.

KEY TO USING Gauss’s Law The shape of the surrounding surface is one that MIMICS the symmetry of the charge distribution …..

Faraday: Changing Flux due to moving permanent magnet British Physicist

Induced EMF produced by a changing Magnetic Flux!

Induced electric fields We will assume here that B is increasing into the page

Electric Field circulates about a changing magnetic field (into the page here)

Maxwell thought is there a symmetry here? Can there be a circulating magnetic field around a changing electric field? Maxwell’s Law of Induction WAIT!!! Didn’t we already see that B circulates around a current carrying WIRE ?!!?

Recall Ampere’s Law Andre Marie Ampere ( )

For r>R, radius of wire the magnetic field must have cylindrical symmetry Long Straight Wire with a constant current

Ampere-Maxwell Law and Maxwell’s Displacement current

Displacement Current

Maxwell’s Equations Gauss’s Law Gauss’s Law for Magnetism Ampere’s Maxwell’s Law Ampere’s Maxwell’s Law Faraday’s Law

Information AGE, Medicine, Engineering …. Based on the physics of E&M waves T.V. telecommuncations, radio transmission, radar … Challenge of today’s engineers to try to envision what global interconnections will be in 20 years (Halliday and Resnick 04) Starting point understanding Electro-mag waves which is summarized by Maxwell’s rainbow!

E&M Waves and Maxwell Crowning achievement was to show that light is a traveling E&M wave The basis for the study of optics! Phys. 213 and Dr. Romberger Phys. Science 440 In mid 1800s only infrared, visible and ultraviolet forms of light were only E&M waves know Heinrich Hertz later showed that what we call radio waves also..

Maxwell’s Rainbow

Human Eye Sensitivity

Traveling Waves Consider a transformer: A generating LC circuit which establishes a frequencey and a secondary coil with a dipole antenna. You have a changing E and B field coupled together!!! However, changes don’t appear instantaneously, they happen a the speed of light with the disturbance traveling outward at that speed. Will see

Looking toward the wave front the amplitudes are related by the cross product Wave is transverse/perpendicular to the direction of travel Field vary sinusoidally At speed of light!!

Traveling E&M wave No need for a medium on wave generates the other. Prediction of Maxwell’s equation and proved by Einstein with a little bit of symmetry 1905

Faraday’s Law of Induction Maxwell’s Law of Induction Faraday’s Law Ampere’s Maxwell’s Law Ampere’s Maxwell’s Law

Faraday’s Law of Induction Applying Faraday’s law to the loop above

Maxwell’s Law of Induction Applying Maxwell’s law of induction to the loop above

The Wave Equation Source free region ie no wires and no charges Solution

Spherical Wave Energy John Henry Poynting ( ): E&M waves transport energy! From which we define intensity

Looking toward the wave front the amplitudes are related by the cross product Wave is transverse/perpendicular to the direction of travel Field vary sinusoidally At speed of light!!