# Why can the electric and magnetic field be separated in spatial and time components?

I was reading the Jackson and suddenly in one line they wrote the electric field as:

$$E(x,t)=E(x)e^{-iwt}$$

why is this valid?

• Please type in the necessary information into the question. Pasting images is not encouraged as they don't allow the content to be searchable. Also please consider using MathJax for mathematical expressions – ohneVal Oct 22 at 9:07

$$e^{\boldsymbol{i} z} = \cos z + \boldsymbol{i}\sin z$$
With $$z=-\omega t$$
Note, the imaginary unit $$\boldsymbol{i}$$ is missing in what you wrote. They are just saying that the solution being sought is a plane wave.