Maxwell Equation Teardown

Created: 06/04/2020Last Upated: 06/04/2020

Definition: Maxwell equation governs the foundation electromagnetism

Overview

    1. Gauss's Law:
      • Electric field radiates either inward or outward from a charge and the sum of electric field cutting through any enclosed imaginary sphere is equal to the electric charge.
      • Magnetic field makes a complete loop around the a current carrying wire or magnet (i.e magnetic field ends where it starts) . Summing the magnetic field lines cutting through any enclosed imaginary sphere is equal to 0. This also implies that there is no magnetic charge if we make a deduction using the same logic for electric field.
        • Note: if you are familiar with surface integral, you can see that magnetic field will sum to zero because the field at one end of the surface is going outward and at the other end, the magnetic field is going inward of the surface. The dot product for surface normal vector and magnetic field direction is opposite at two end of this imaginary sphere and sums to zero.
    2. Faraday's Law: changing in magnetic flux induces a voltage.
    3. Ampere's Law: current carrying wire induces a magnetic field

In practice:

  • Faraday's law is the governing principle for induction used transformer for energy transfer and the why we see back electromagnetic force (EMF) voltage on motor coils.
  • Ampere's law is how you make electromagnets.