# Allowed EM waveforms

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1. Apr 18, 2017

### Rahulrj

1. The problem statement, all variables and given/known data
which of the following proposed space-time dependent electric fields in vacuum is/are allowed by the equations of EM theory?
a) $$E_x=E_1\sin(kz-wt),E_y=E_2\sin(kz-wt),E_z=0$$
b) $$E_x=E_1\sin(kz-wt),E_y=2E_1\cos(kz-wt),E_z=0$$
c) $$E_x=E_1\sin(kz-wt),E_y=0,E_z=E_2\sin(kz-wt)$$

2. Relevant equations
$$E = E_0\sin(kz-wt)$$

3. The attempt at a solution
I think all the three equations are allowed according to the normal waveform. However I do not know what exactly to look for in such case that does not make it an allowed waveform. I would appreciate if someone could show an example that is not a waveform if my answer turns out to be correct.

2. Apr 18, 2017

### BvU

Hello Rahulrj,

What are
?

I'm afraid your relevant equation doesn't mean much in the context of this problem. Anyway: what are all those symbols referring to ? You write vectors and scalars the same way ?

3. Apr 18, 2017

### Rahulrj

I do not know how to identify the allowed wave form and 'the equations of EM theory' idea doesn't help me much since I do not know what I require to distinguish an allowed waveform. $$E_x E_y$$and$$E_z$$ are electric field components,that's how the question itself is given.

4. Apr 18, 2017

### BvU

The equations of EM theory are called the Maxwell equations, as I suspect you are supposed to know (from the fact you are given this exercise)...

5. Apr 18, 2017

### Rahulrj

I do know Maxwell equations but I am not sure how to make use of them to know the allowed waveform which is why I said that it doesn't help me much.

6. Apr 18, 2017

### BvU

Do you now how to transform the maxwell equations into a wave equation ? Then you can check if the given $\vec E$ can satisfy such equations...

7. Apr 18, 2017

### Rahulrj

I don't think I understand that could please provide an example?
$$\nabla.D = \rho$$
How do i transform this?

8. Apr 19, 2017

### BvU

In vacuum $\rho = 0$...