CHAPTER 28 : MAXWELL'S FIELD EQUATIONS AND ELECTRO-MAGNETIC WAVES
In our discussion earlier, it has been pointed out that the four basic experimental laws on which the
science of Electro-magnetism is based, can be represented in the form of differential equations. This was
obtained for the first time by Maxwell. These are
Gauss's law in Electro-Static is based on Coulomb's law of force between stationary charges
Similar as above in Magnetism, but free mono-poles do not exist.
Modified Ampere's law for magnetic fields formed due to time-dependent currents.
Faraday's Law of electro-magnetic induction.
For simplicity and for the purpose of illustration the discussion
is restricted to Electro magnetic field in Vacuum. If there are
no free changes and the free currents are in the vacuum then the
above equations become.
Equation (5) is a wave equation, the solution to which, propagates as a wave i.e. E propagates as a
wave in vacuum with velocity
Likewise for the field , it is easy to show that
Thus, Electro-magnetic field propagates in vacuum with the speed of light; and light therefore must be
an electro-magnetic wave.