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• Oscillations in Mechanical Systems

• Partial Derivatives

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Course by: Paul Padley. E-mail the author

The Electromagnetic Wave Equation

Module by: Paul Padley. E-mail the author

Summary: We derive the electromagnetic wave equation from Maxwell's equations.

The E&M Wave Equation

Lets recall Maxwell's equations in differential form × E = B t × B = μ 0 ( J + ε 0 E t ) E = ρ ε 0 B = 0 × E = B t × B = μ 0 ( J + ε 0 E t ) E = ρ ε 0 B = 0 In free space there are no charges or currents these become: × E = B t × B = μ 0 ε 0 E t E = 0 B = 0 × E = B t × B = μ 0 ε 0 E t E = 0 B = 0 Lets take the time derivative of × E = B t × E = B t × E t = 2 B t 2 × E t = 2 B t 2 × × B = μ 0 ε 0 2 B t 2 × × B = μ 0 ε 0 2 B t 2 but recall × × C = ( C ) ( ) C × × C = ( C ) ( ) C so using that and B = 0 B = 0 we get 2 B = μ 0 ε 0 2 B t 2 2 B = μ 0 ε 0 2 B t 2 This is the 3d wave equation! Note that is a second time derivative on one side and a second space derivative on the other side It is left as an exercise to show that 2 E = μ 0 ε 0 2 E t 2 2 E = μ 0 ε 0 2 E t 2 we also see from this equation that the speed of light in vacuum is c = 1 μ 0 ε 0 c = 1 μ 0 ε 0

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Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

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Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

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