Maxwell's equations wave equation

Maxwell’s equations

Time harmonic excitation Maxwell's equations Time harmonic excitation

boundary conditions for time varying fields tangential electric fields are continuous normal components of displacement flux density differ by a surface charge density

boundary conditions for time varying fields tangential magnetic field intensities differ by a surface current density normal components of magnetic flux density are continuous

Plane waves in a vacuum

Plane waves in a vacuum

Plane waves in a vacuum

Plane waves in a vacuum

units

Look at the dimensions

Look at the numbers

c is the speed of light vector wave equation

Galileo 1564-1642 1638 - Galileo attempts to measure the speed of light by a lantern relay between distant hilltops. He gets a very large answer.

Einstein 1879-1955

There was a young lady named Bright, Whose speed was far faster than light; She set out one day, In a relative way, And returned home the previous night.

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one dimensional wave equation vacuum infinite parallel planes polarization x y z Ey

one dimensional wave equation x y z Ey

MOST GENERAL SOLUTION!! Ey = a F(z - ct) + b G(z + ct) = a Fb G where F & G are arbitrary functions that depend on the excitation

Q. E. D. Ey = a F(z - ct) + b G(z + ct) = a Fb G is a solution of the wave equation!!!

Ey = aF(z - ct) + bG(z + ct) = aFbG t = T z Ey t = 2T

The solution consists of 2 waves F(z – ct) & G(z + ct)

Let c = 2 q = z - ct = 0 y = z + ct = 0 t zq zy 0 0 0 1 2 -2 2 4 -4 Ey = aF(z - ct) + bG(z + ct) = aFbG -10 10 z Let c = 2 q = z - ct = 0 y = z + ct = 0 t zq zy 0 0 0 1 2 -2 2 4 -4 3 6 -6 4 8 -8 5 t

Ey = aF(z - ct) + bG(z + ct) = aF() + bG() -10 10 z Let c = 2 q = z - ct = 0 y = z + ct = 0 t zq zy 0 0 0 1 2 -2 2 4 -4 3 6 -6 4 8 -8 5 t

Helmholtz 1821-1894

I was feeling a bit depressed the other day, so I called the Help Hotline. I was put through to a call-center in Ames. I explained that I was feeling suicidal. They were very excited at this news and wanted to know if I could play football.