Question

The instantaneous electric field inside a source free, homogeneous , isotropic , and linear medium is give by

Answer 1

\[E=[ax*A(x+y)+ay*B(x-y)]*\cos(wt)\]

Answer 2

Determine the relations between A and B

Answer 3

my doubt is when i calculate the magnetic field i find the magnetic field i find\[H=(B-A)*\sin(wt)/(w*\mu0)*az\]

Answer 4

And since its source free \[Div(\epsilon E )=0 \] will wich leads A=B, but then if i dont forgot anything in previously calculation the magnetic field will be zero

Answer 5

Is the magnetic field wrong? if its not it can be zero?

Answer 6

i never really got to this in my physics classes ....

Answer 7

@experimentX

Answer 8

what are a_x and a_y?? are they different components?

Answer 9

unitary vectors in x and y directions

Answer 10

and A and B some arbitrary function?

Answer 11

No A isjust a coef

Answer 12

and B too

Answer 13

taking divergence you get
\[ A - B \cos(\omega t) = 0\]

Answer 14

\[\nabla · \bar E=0\rightarrow \frac{ \delta E_x }{ \delta x}+\frac{ \delta E_y }{ \delta y }=0\rightarrow (A-B)\cos(\omega t)=0\rightarrow A=B\]

Answer 15

@CarlosGP i know that but my doubt is if we have a electrical field like this there is no magnetic one, see all my question

Answer 16

@RaphaelFilgueiras in complex notation 3rd Maxwell´s equation is:\[\nabla \times \bar E=-i \omega \bar B \]. If you calculate with A=B\[\nabla \times \bar E=0\rightarrow \bar B=0\]

Answer 17

that wired dosen't it how can i have a electrical field without a magnetic one?

Answer 18

that weird dosen't it how can i have a electrical field without a magnetic one?

Answer 19

yep!!,,,, I am also confused in it!!,,, just like how a polarised light can propogate???,,,, because the magnetic vector is canceled from it!!!,,, does any one knows the answer??? :)

Answer 20

Hi! I think this problem is just here to make you use Maxwell-Gauss equation.
If you write that in the absence of sources \(\vec \nabla .\vec E=0\), then you end up with A = B.

Now, if you go further, you can prove by Maxwell-Faraday's equation that that B = 0, as you already remarked in your earlier posts.

Why not go on? Let's use Maxwell-Ampère's equation:
\(\vec \nabla \times\vec B=\Large \frac{1}{c^2}\;\normalsize
\partial \vec E/\partial t\)

It will prove that A = B = 0

So you are right: no fields of this structure can actually exist !