Wave equation in conductor

1. Dec 1, 2014

Nikitin

1. The problem statement, all variables and given/known data
http://web.phys.ntnu.no/~ingves/Teaching/TFY4240/Exam/Exam_Dec_2008_tfy4240.pdf
problem 2a)

2. Relevant equations

3. The attempt at a solution

Hi. In problem 2a I was supposed to find a wave equation, however while digging around in maxwell's equations, I found this result:

https://fbcdn-sphotos-f-a.akamaihd.net/hphotos-ak-xap1/v/t1.0-9/16410_10204393293009062_1155886601331102418_n.jpg?oh=44e1d9886a54e34274c00437ed952ca5&oe=5505B805&__gda__=1427040332_aace122d9214b5db9de482b3e631a490

which effectively implies that $\nabla^2 \vec{E} = 0$ if you insert it into the wave equation they want me to find (look in problem 2a to see what I mean), which obviously can't be right.

But where is the fault in my derivation?

2. Dec 1, 2014

Nikitin

Ahh, but of course, the charge density is zero in an ideal conductor, is it not? Then what I get out will be nonsense because of that?