Maxwell’s Equations
By: Scott Riggs
Divergence and Curl
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Divergence (scalar)
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∆ • A = δAx/dx + δAy/dy + δAz/dz
Measure of how much A spreads out from the point in
question
Curl (vector)
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∆ x A = (δAz/dy - δAy/dz)i + (δAx/dz δAz/dx)j + (δAy/dx + δAx/dy)k
How much A curls around the point in question. (How
rotational A is).
Gauss’s Law
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∆ • E = 4πρ (ρ is the charge density)
No MM Law
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ƥB=0
Faraday’s Law
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∆ x E = -(1/c)(δB/δt)
Ampere’s Law
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∆ x B = (1/c)(δE/δt) + (4π)J
J is the volume current density
Maxwell’s Equations
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With ρ and J = 0
ƥE=0
ƥB=0
∆ x E + (1/c)(δB/δt) = 0
∆ x B - (1/c)(δE/δt) = 0
// plate capacitor
Changing E induces a changing B and
can have a wave that lives forever
Electromagnetic waves in a Vacuum

Take the curl of ∆ x (∆ x E) + (1/c)(δ/δt)(∆ x B) = 0
2
 ∆(∆•E) -∆ E + (1/c)(δ/δt)(1/c)(δE/δt) = 0
2
2
2
2
 -∆ E + (1/c )(δ E/δt ) = 0
 Equation for a wave
 Can do the same thing for the magnetic field
 Propogation of Electromagnetic Wave