Maxwell's equations

Maxwell’s equations are:

Maxwell’s equations are linear equations and the principle of superposition holds.

(SI units)		(Gaussian units)

(SI units)		Gaussian units)


Define the flux and the electromotive force . Then :

Any induced emf tries to oppose the flux changes that produces it. This is Lenz’s rule.

Consider N filamentary circuits. Then the flux through the ith circuit is where (SI units), (Gaussian units).

is the coefficient of mutual induction and is the coefficient of self inductance. We have

For a single filamentary circuit we have . To change the current in a circuit we need an external emf, V_ext, to overcome the induced emf e. .

The energy stored in the circuit is . For a system of N circuits we have:

Poynting’s theorem, is a statement of energy conservation.

(SI units), (Gaussian units)

is the energy density and

(SI units), (Gaussian units)

is the energy flux in the electromagnetic field. We define the momentum density as

(in SI and Gaussian units).

If in electrodynamics we choose the Lorentz gauge defined through

(SI units)		(Gaussian units)

then f and each Cartesian component of A satisfy the inhomogeneous wave equation

Choosing is called choosing the Coulomb gauge.