# 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

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,

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

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.