Solutions of maxwells equations in Vaccum

In summary, the conversation discusses deriving the relations between the magnitudes and phases of Eo, Bo, ω, k, and c using Maxwell's equations in vacuum. The solution involves finding the electric and magnetic fields, and a hint is given to start with the fact that Del (k.r) = k.
  • #1
wgdtelr
9
0

Homework Statement



Show that the Fields E= Eo exp{i (k.r-ωt)} and B= Bo exp{i(k.r-ωt) are solutions of Maxwell's Equations in source free vaccum.Starting with maxwells equations in vaccum.
And there by Derive the relations between the Magnitudes & Phases of
Eo, Bo, ω, k, & c. And the directions of Unit vectors Eo,Bo,& k.

Hint( Should only need the fact that Del (k.r) = k .

Homework Equations



Div E = 0.

Div B = 0.

Curl E= - (1/c)d/dt(B)

curl B = (1/c) d/dt(E).

atempt at a solution[/b]

How to solve these Equations. to obtain the Electric & Magnetic Feilds.

Atleast give me Hint.. how to start this..

iam really trying hard on this...
 
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  • #2
wgdtelr said:
iam really trying hard on this...
Really? I couldn't tell from your post :biggrin:

Here's your first hint: read the question. (I've found that to be pretty useful myself) "Show that the fields [tex]\vec{E} = \vec{E}_0 e^{i(\vec{k}\cdot\vec{r} - \omega t)}[/tex] and [tex]\vec{B} = \vec{B}_0 e^{i(\vec{k}\cdot\vec{r} - \omega t)}[/tex] are solutions of Maxwell's equations..." Surely you can do that? Just plug them in and see what you get.
 
  • #3
thank U very much diazona...
 

FAQ: Solutions of maxwells equations in Vaccum

What are Maxwell's equations?

Maxwell's equations are a set of four fundamental equations in electromagnetism, named after the physicist James Clerk Maxwell. They describe the relationship between electric and magnetic fields and their sources, such as charges and currents.

What is a "solution" of Maxwell's equations in vacuum?

A solution of Maxwell's equations in vacuum is a set of mathematical equations that describes the behavior of electric and magnetic fields in a vacuum, without any external sources. It is a theoretical concept that helps us understand and predict the behavior of electromagnetic waves.

Why is it important to study solutions of Maxwell's equations in vacuum?

Studying solutions of Maxwell's equations in vacuum allows us to understand and predict the behavior of electromagnetic waves, which are essential for various technological applications. It also helps us understand the fundamental laws of electromagnetism and how they govern the behavior of electric and magnetic fields.

What are some real-life applications of solutions of Maxwell's equations in vacuum?

Solutions of Maxwell's equations in vacuum are used in many practical applications, such as radio and television broadcasting, satellite communications, radar systems, and medical imaging. They also play a crucial role in the development of technologies like wireless charging, fiber optics, and GPS systems.

How do scientists find solutions of Maxwell's equations in vacuum?

Scientists use various mathematical techniques, such as differential equations and vector calculus, to solve Maxwell's equations in vacuum. They also use computer simulations and experiments to validate and improve their solutions. Additionally, advancements in computer technology have allowed for more complex and accurate solutions to be found.

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