Maxwell's Equations

Discussion

introduction

integral vs. differential

Integral Form
∯ E · dA =  Q   (Gauss's Law)   E · ds =  −  dΦ B       (Faraday's Law)
ε0   dt  
   
∯ B · dA =  0   (No Name Law)   B · ds =  μ0ε0  dΦB  + μ0I   (Ampère's Law)
  dt
 
Differential Form
∇ · E =  ρ   (Gauss's Law)   ∇ × E =  −  dB       (Faraday's Law)
ε0   dt  
   
∇ · B =  0   (No Name Law)   ∇ × B =  μ0ε0  E  + μ0 J   (Ampère's Law)
  t

tensor notation

μFμν = jν

text

  1. Gauss's Law
  2. No One's Law
  3. Faraday's law
  4. Ampère's law