Maxwell's Equations

Discussion

introduction

integral forms

∯ E · dA =  Q   (Gauss's Law)
ε0  
∯ B · dA =  0   (No One's Law)
 
E · ds =  −  dΦ B   (Faraday's Law)
dt  
B · ds =  μ0ε0  dΦB  + μ0I   (Ampère's Law)
dt  

differential forms

∇ · E =  ρ   (Gauss's Law)
ε0  
∇ · B =  0   (No One's Law)
 
∇ × E =  −  dB   (Faraday's Law)
dt  
∇ × B =  μ0ε0  E  + μ0 J   (Ampère's Law)
t  

tensor notation

μFμν = jν

text

  1. Gauss's Law
    • There are two types of charge, positive and negative, just as there are two types of real numbers, positive and negative.
    • Electric field lines diverge from positive charge and converge on negative charge
  2. No One's Law
    • There is no magnetic monopole
    • Magnetic field lines neither converge nor diverge (have no beginning or end)
  3. Faraday's law
    • Electric field lines don't curl
    • … except when the magnetic field changes.
  4. Ampère's law
    • Magnetic field lines curl around electric current
    • … and also curl when the electric field changes.