Is the Plane Wave a General Solution to the Electromagnetic Wave Equation?

AI Thread Summary
The discussion focuses on demonstrating that the plane wave equation E=Eocos(k·r - ωt) is a general solution to the electromagnetic wave equation derived from Maxwell's equations in a continuous, homogeneous medium. Participants have successfully derived the wave equation for the electric field, which is expressed as ∇²E = μ₀μᵣε₀εᵣ(d²E/dt²). The conversation emphasizes understanding the relationship between differential equations and their solutions, particularly in the context of electromagnetic theory. The derivation process and the characteristics of plane waves are central to the discussion. Ultimately, the goal is to confirm that the plane wave satisfies the conditions set by the wave equation.
rayray2216
Messages
4
Reaction score
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-\omegat)
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:
\nabla2E= \muo\mur\epsilono\epsilonr*d2E/dt
 
Physics news on Phys.org


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


OK, so what do you know about differential equations and their solutions?
 
Thread 'Help with Time-Independent Perturbation Theory "Good" States Proof'

Thread 'Help with Time-Independent Perturbation Theory "Good" States Proof'

(Disclaimer: this is not a HW question. I am self-studying, and this felt like the type of question I've seen in this forum. If there is somewhere better for me to share this doubt, please let me know and I'll transfer it right away.) I am currently reviewing Chapter 7 of Introduction to QM by Griffiths. I have been stuck for an hour or so trying to understand the last paragraph of this proof (pls check the attached file). It claims that we can express Ψ_{γ}(0) as a linear combination of...
View full post »

Similar threads

General solution of the spherical wave equation
Replies
20
Views
3K
Help with a calculation about gravitational waves
Replies
1
Views
1K
Why Do Electromagnetic Waves Propagate Independently of Their Source?
Replies
5
Views
2K
Are longitudinal magnetic waves possible?
Replies
7
Views
2K
What are electromagnetic waves really
Replies
5
Views
2K
I Dispersion Relation in Different Media
Replies
3
Views
1K
Charge/current density inside rectangular wave guide?
Replies
6
Views
3K
Plane Wave Equation Propagation and Oscillation Directions
Replies
5
Views
2K
Direction of travel of a plane wave given direction of electric field
Replies
8
Views
1K
E and B Fields of Monochromatic Plane Waves
Replies
5
Views
2K

Hot Threads

Recent Insights

Back
Top