# Using divB as a condition for wave

1. Nov 9, 2009

### HPRF

1. The problem statement, all variables and given/known data

By considering divergence, show whether the expression

B=kBzei(kzz-wt)

is a valid function for an electromagnetic plane wave.

2. Relevant equations

divB=0

3. The attempt at a solution

I have found divB=ikzBzei(kzz-wt).

Does this satisfy divB=0 because it is imaginary?

2. Nov 9, 2009

### gabbagabbahey

The field you give is usually denoted as

$$\tilde{\textbf{B}}=\hat{\mathbf{k}}\tilde{B}_ze^{i(k_z z- \omega t)}$$

and is itself complex-valued... The actual magnetic field $\textbf{B}$ is taken to be the real part of $$\tilde{\textbf{B}}[/itex] and so [tex]\mathbf{\nabla}\cdot\textbf{B}=\mathbf{\nabla}\cdot\text{Re}\left[\tilde{\textbf{B}}\right]=0$$

So, only if the divergence of the real part of the field you gave vanishes, can it be a valid magnetic field (The fact that the magnetic field is polarized in the same direction as the propagation should give you a little bit of hesitation here).

Last edited: Nov 9, 2009