Show that the plane wave is a general solution to the electromagnetic wave eqatuion

In summary, the "plane wave" E=Eocos(k.r-\omegat) is a general solution of the electromagnetic wave equation in a continuous, homogeneous medium with no explicit charges or currents. This is derived by using the Maxwell equations and the wave equation for the electric field in a continuous, homogeneous medium. The wave equation is given by \nabla2E= \muo\mur\epsilono\epsilonr*d2E/dt^2 and the general solution is in the form of a plane wave.
  • #1
rayray2216
5
0
Show that the "plane wave" is a general solution to the electromagnetic wave eqatuion

Homework Statement



Show that the "plane wave" E=Eocos(k.r-[tex]\omega[/tex]t)
is a general solution of the electromagnetic wave equation. (you must derive this first)

Homework Equations



we were given Maxwell equations in a continuous, homogeneous medium, (no explicit charges or currents) and no other information

The Attempt at a Solution



ive got as far as deriving the wave equation in a continuous homogenous medium, i got this to be:
[tex]\nabla[/tex]2E= [tex]\mu[/tex]o[tex]\mu[/tex]r[tex]\epsilon[/tex]o[tex]\epsilon[/tex]r*d2E/dt
 
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  • #2


had issues entering the formula but its just the wave equation for the electric field in a continuous homogeneous medium .
 
  • #3


OK, so what do you know about differential equations and their solutions?
 

1. What is the electromagnetic wave equation?

The electromagnetic wave equation is a mathematical representation of the behavior of electromagnetic waves in free space. It is derived from Maxwell's equations, which describe the fundamental principles of electromagnetism.

2. What is a plane wave?

A plane wave is a type of electromagnetic wave that has a constant amplitude and wavelength, and travels in a single direction. It is a simplified model used to understand the behavior of electromagnetic waves in free space.

3. How is the plane wave derived from the electromagnetic wave equation?

The plane wave is derived by solving the electromagnetic wave equation for a specific set of boundary conditions. This results in a solution with a constant amplitude and wavelength, and a direction of propagation that is perpendicular to the electric and magnetic fields.

4. What makes the plane wave a general solution to the electromagnetic wave equation?

The plane wave is a general solution to the electromagnetic wave equation because it satisfies the equation for all possible values of the parameters (such as amplitude, wavelength, and direction of propagation). This means that any other solution to the equation can be expressed as a combination of plane waves.

5. How is the plane wave used in practical applications?

The plane wave is a useful tool for understanding the behavior of electromagnetic waves in free space, and is often used in theoretical and experimental studies. It is also used in the development of technologies such as antennas, satellite communications, and radar systems.

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