Maxwell's electromagnetic wave equation confusion

1. Jan 9, 2010

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.

2. Jan 9, 2010

vela

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

3. Jan 9, 2010

Legion81

time

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

4. Jan 9, 2010

vela

Staff Emeritus
Does that answer your question?

5. Jan 9, 2010

Legion81

No. Should it?

6. Jan 9, 2010

vela

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

7. Jan 9, 2010

Legion81

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.

8. Jan 9, 2010

Staff: Mentor

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.

9. Jan 9, 2010

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.

10. Oct 14, 2011

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.

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook