How Does the Electromagnetic Wave Equation Represent Electric Fields?

[outclassed]

Hi I have a presentation tomorrow and have to explain a few wave equations. I am using a book to walk me through them but there is one point I don't understand:

At one point the book states:

Because k=(angular frequency)/c, we will represent the waves of the electric field as:

e^i (angular frequency ^ (x/c))

Now I am unsure what equation they used to get to this and also if its
e^i *(angular frequency ^ (x/c))
or
e^(i *(angular frequency ^ (x/c)))

Any help would be really great. I am sorry if this is a stupid question.
Thanks in advance,
Drew.

 

[lzkelley]

to derive that, you need to use maxwell's equations and then separation of variables in 4 dimensions (3space 1time). The spatial parts are much trickier as i recall, if your familiar with math methods it won't be TOO bad to derive the time dependence.

 

[outclassed]

Ok so the Maxwell equations, I am not familiar with those, I may just list it as a given and hope no one asks questions, do you know which of the two equations i listed it would be?
e^i * stuff or e^(i*stuff)?
Thanks again.

 

[lzkelley]

its e^(i*stuff) not (e^i)*stuff.
Maxwell's equations are some of the most important in all of physics; there are 4 (and a half... don't worry about that) and they describe the vast majority of all physical phenomena in the universe.