Question

Write down Maxwell equations in integral form.

Answer 1

1. Electrodynamics can be summarized into four basic equations, known as Maxwell’s Equations.
2. First equation is Gauss Law, it relates net electric flux and net charge
   `oint vec"E" * "d"vec"A" = "Q"_"enclosed"/∈_0`
3. Second equation has no name but can be called Gauss Law in magnetism. It states that the surface integral of the magnetic field over a closed surface is zero.
   `vec"B" * "d"vec"A" = 0`
4. Third equation is Faraday’s Laws of electromagnetic induction.
   `oint vec"E" * "d"vec"l" = - "d"/"dt"`Φ_B 
5. The line integral of the electric field ground any closed path is equal to the rate of change of magnetic flux through the closed path bounded by the surface.
6. Fourth Equation is modified Ampere’s Circuital Law known as Ampere – Maxwell’s Law
   `oint vec"B"*"d"vec"l" = mu_0 "I"_"enclosed" + mu_0epsilon_0 "d"/"dt" int vec"SE" * "d"vec"A"`
7. This law relates the magnetic field around any closed path to the conduction current and displacement current through the path. These four equations are known as Maxwell’s Equation in electrodynamics.