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Question
Write down Maxwell equations in integral form.
Solution
- Electrodynamics can be summarized into four basic equations, known as Maxwell’s Equations.
- First equation is Gauss Law, it relates net electric flux and net charge
`oint vec"E" * "d"vec"A" = "Q"_"enclosed"/∈_0` - 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` - Third equation is Faraday’s Laws of electromagnetic induction.
`oint vec"E" * "d"vec"l" = - "d"/"dt"`ΦB - 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.
- 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"` - 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.
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