Explain Maxwells equations and its four elegant equation?
Maxwell's equations (J.C. Maxwell; 1864):
The four elegant equations that explain classical electromagnetism in its entire splendor. They are:
Gauss law:
The electric flux via a closed surface is proportional to the arithmetical sum of electric charges encompassed within that closed surface; in its differential form,
div E = rho,
Here rho is the charge density.
Gauss law for magnetic fields:
The magnetic flux via a closed surface is zero (0); no magnetic charges exist. In the differential form,
div B = 0
Faraday's law:
The line integral of the electric field about a closed curve is proportional to the instant time rate of change of the magnetic flux via a surface bounded by that closed curve; in its differential form,
curl E = -dB/dt,
Here d/dt here symbolizes partial differentiation.
Ampere's law, modified form:
The line integral of the magnetic field about a closed curve is proportional to the addition of two terms: first, the arithmetical sum of electric currents flowing via that closed curve; and second, the instant time rate of change of the electric flux via a surface bounded by that closed curve; in its differential form,
curl H = J + dD/dt,
Here d/dt here symbolizes partial differentiation.
In addition to explaining electromagnetism, his equations too predict that waves can propagate via the electromagnetic field, and would for all time propagate at similar speed -- these are electromagnetic waves; the speed can be found by evaluating (epsilon0 mu0)-1/2, that is c, the speed of light in vacuum.