(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Suppose we know that [tex]B(\vec x ,t)[/tex] is a solution to Maxwell's equations in vacuum and furthermore we know that [tex]E(\vec x , 0)=E_0[/tex].

How do we find [tex]E(\vec x , t)[/tex]?

2. Relevant equations

[tex]\nabla \cdot E = 0[/tex].

[tex]\nabla \cdot B =0[/tex].

[tex]\vec \nabla \times \vec B = \left ( \frac{-1}{c} \right ) \cdot \frac{\partial E}{\partial t}[/tex]

[tex] \vec \nabla \times \vec E = \left ( \frac{1}{c} \right ) \cdot \frac{\partial B}{\partial t}[/tex].

I'm using Gaussian's units.

3. The attempt at a solution

I think I could work with the 2 lasts equations I posted to find E but I don't reach anything. I'd like a very small guidance like if I'm in the right direction + a hint if possible.

Thanks.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Finding a solution to Maxwell's equations from initial datas

**Physics Forums | Science Articles, Homework Help, Discussion**