Maxwell Equation

Creator
Creator
Seonglae Cho
Created
Created
2020 Jul 21 13:12
Editor
Edited
Edited
2025 Jan 28 16:12
Refs

4 partial differential equations

  • B=0\nabla \cdot \mathbf{B} = 0 (
    Gauss's Law for Magnetism
    ) The second equation indicates that there is no magnetic charge monopole that generates
    Magnetic Field
    while making a loop
  • ×E=Bt\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t} (
    Faraday’s law of induction
    ) The derivation per time of Magnetic Field generates Electric Field which has a circular symmetry and makes rotation to the charge.
  • ×B=μ0J+μ0ε0Et\nabla \times \mathbf{B} = \mu_0 \mathbf{J} + \mu_0 \varepsilon_0 \frac{\partial \mathbf{E}}{\partial t} (
    Ampere’s law
    ) The derivation per time of Electric Field generates Magnetic Field which has a circular symmetry
Based on third and forth laws, we could predict there might be a wave (
Light
) with interaction.
Maxwell Equations
 
Maxwell Equation
could not perfectly explain the effect of a magnetic field on a moving charge passing through a static magnetic field.
Hendrik Lorentz
showed that while stationary charges are only affected by electric fields, moving charges experience a force from the cross product of their velocity and the magnetic field direction (
Lorentz force
).
 
 
 
 
 
 
 
 

 

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