Maxwell's electromagnetic wave equation confusion

[Legion81]

I'm not understanding something here. Maxwell's wave equation is:

Laplacian of E = (1/c^2) * second partial of E
(sorry, I don't know how to write symbols)

But the second partial derivative is the Laplacian. So how can you scale the laplacian of E by a number and get the laplacian of E as a result? Is there some fundamental rule of EM that allows this? What is physically happening? Thanks in advance.

 

[vela]

Partial with respect to what variable on the right-hand side?

 

[Legion81]

Partial with respect to what variable on the right-hand side?

time

Laplacian of E = (1/c^2)* second partial of E with respect to t.

 

[vela]

Does that answer your question?

 

[Legion81]

No. Should it?

 

[vela]

Well, perhaps I don't understand your question, but there's no Laplacian on the right-hand side.

 

[Legion81]

Well, perhaps I don't understand your question, but there's no Laplacian on the right-hand side.

Since the laplacian is the second partial derivative, you can write the expression as:

Laplacian of E = (1/c^2)*Laplacian of E

I don't see how you can multiply by a scalar and still get the Laplacian of E back or why it is written as a second derivative instead of the Laplacian. That is what my question is.

 

[jtbell]

(sorry, I don't know how to write symbols)

For an introduction,

https://www.physicsforums.com/showthread.php?t=8997

For your specific equation:

$$\nabla^2 \vec E = \frac{1}{c^2} \frac {\partial^2 \vec E}{\partial t^2}$$

Click on the equation and you get a popup window that shows the code.

 

[Legion81]

I just realized what my problem was. The RHS is JUST with respect to time, not x or y or anything. That's not the laplacian...

Lets just imagine this thread never happened, haha! Thanks for your help.

 

[moj20062001]

there is a simble in physics that is due to the special relativity that u can show the second derivative of time combined with the laplacian of x,y and z.

u can find it in the "electromagnetic theory" book that is written by,milford,rits and cristy.(i'm not sure at all,about the spelling of the writers and the name of the book.)
u can search in the last chapters and find it.