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
    • 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.

The Physics Hypertextbook

  • No condition is permanent.