Maxwell’s Equations are Lorentz Invariant

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# Maxwell’s Equations are Lorentz Invariant - PowerPoint PPT Presentation

Maxwell’s Equations are Lorentz Invariant. Maxwell’s Equations. Charge current obeys continuity eqn. continuity equation, or charge conservation. charge current density density. Charge current 4-vector. Divergence operator is invariant under Lorentz transformations.

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## Maxwell’s Equations are Lorentz Invariant

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Presentation Transcript

### Maxwell’s EquationsareLorentz Invariant

Charge current obeys continuity eqn.

continuity equation,

or charge conservation

charge current

density density

Charge current 4-vector

Divergence operator

is invariant under

Lorentz transformations

Define charge current 4-vector

E&M potentials

Define scalar and vector potentials, and .

this works because

this works because

and

The Lorenz condition

How are and related?

Lorenz condition:

Its divergence is Lorentz invariant

Define potential 4-vector

Wave equation for

Use the first inhomogeneous eqn to show that obeys

the wave equation, travelling at c.

Wave equation for

Use the second inhomogeneous eqn to show that obeys

the wave equation, travelling at c.

Maxwell’s Equations

Used and to make a charge current 4-vector,

Used and to make a scalar and vector potentials, and

Used and to make a 4-potential,