CHAPTER 28 : MAXWELL'S FIELD EQUATIONS AND ELECTROMAGNETIC WAVES
In our discussion earlier, it has been pointed out that the four basic experimental laws on which the
science of Electromagnetism 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 ElectroStatic is based on Coulomb's law of force between stationary charges
Similar as above in Magnetism, but free monopoles do not exist.
Modified Ampere's law for magnetic fields formed due to timedependent currents.
Faraday's Law of electromagnetic 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, Electromagnetic field propagates in vacuum with the speed of light; and light therefore must be
an electromagnetic wave.
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