Maxwell equations for electromagnetic waves
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Maxwell's Equations And Electromagnetic Waves
Electromagnetic waves are waves travelling in vacuum which are a couple of electric as well as magnetic fields. An ideal electromagnetic wave can be represented in three-directional space as a magnetic field in x direction and an electric field in y direction.
Hence, the direction of motion of the wave will be in z direction. Maxwell's equations are best way to represent electromagnetic waves. These are partial differential equations which represent the electric and magnetic fields in term of charge and fields.
The equations are,
1. Gauss' law of electricity is about the electric field and the charge enclosed. This is about the surface integral of electric field.
The differential form will give
2. Gauss' law of magnetism tells about the magnetic flux. This says about the surface integral of magnetic field.
The differential form will give
∇ · B =0
3. Using Faraday's law, the relationship between the electric field and magnetic field can be determined. According to Faraday's law
4. According to Ampere's law
To modify amperes law, Maxwell considered if the equation has to be correct, then there must be a displacement current between the capacitor plates since there is electric field between the capacitor plates and outside the plates the field is zero.
The Ampere law can hence be replaced as
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