- #1
Raioneru
- 83
- 3
1. Consider the fields:
[tex]\vec{E}[/tex] = E0 * cos(kx-wt)[tex]\vec{e}[/tex]1
[tex]\vec{B}[/tex] = B0 * cos(kx-wt)[tex]\vec{e}[/tex]1
Do these fields solve the maxwell equations? if so, what do they describe?
2. Homework Equations
[tex]\vec{E}[/tex] = E0 * cos(kx-wt)[tex]\vec{e}[/tex]1
[tex]\vec{B}[/tex] = B0 * cos(kx-wt)[tex]\vec{e}[/tex]1
if these functions holds for the maxwell equations then,
[tex]\nabla[/tex].[tex]\vec{B}[/tex]=0
[tex]\nabla[/tex].[tex]\vec{E}[/tex]=0
that is
[tex]\nabla[/tex].[tex]\vec{B}[/tex]=-[tex]\vec{B}[/tex]0.[tex]\vec{K}[/tex]*Sin(kx-wt)
this equation is equal to zero only if and only if B0.K = 0 that means, they are perpendicular vectors. that is the constraint.
I guess the [tex]\vec{e}[/tex] means that the wave propagates only in the x direction? since e1=<1,0,0>
hum, I really can't tell if that's the appropriate answer, so could you help please ?
thanks in advance
so the question what do they describe, I wrote the propagation of the electromagnetic wave in the x-direction as time increases.
[tex]\vec{E}[/tex] = E0 * cos(kx-wt)[tex]\vec{e}[/tex]1
[tex]\vec{B}[/tex] = B0 * cos(kx-wt)[tex]\vec{e}[/tex]1
Do these fields solve the maxwell equations? if so, what do they describe?
2. Homework Equations
[tex]\vec{E}[/tex] = E0 * cos(kx-wt)[tex]\vec{e}[/tex]1
[tex]\vec{B}[/tex] = B0 * cos(kx-wt)[tex]\vec{e}[/tex]1
The Attempt at a Solution
if these functions holds for the maxwell equations then,
[tex]\nabla[/tex].[tex]\vec{B}[/tex]=0
[tex]\nabla[/tex].[tex]\vec{E}[/tex]=0
that is
[tex]\nabla[/tex].[tex]\vec{B}[/tex]=-[tex]\vec{B}[/tex]0.[tex]\vec{K}[/tex]*Sin(kx-wt)
this equation is equal to zero only if and only if B0.K = 0 that means, they are perpendicular vectors. that is the constraint.
I guess the [tex]\vec{e}[/tex] means that the wave propagates only in the x direction? since e1=<1,0,0>
hum, I really can't tell if that's the appropriate answer, so could you help please ?
thanks in advance
so the question what do they describe, I wrote the propagation of the electromagnetic wave in the x-direction as time increases.