What is the Fault in My Derivation of the Wave Equation in a Conductor?

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SUMMARY

The discussion centers on the derivation of the wave equation in a conductor, specifically addressing problem 2a from the TFY4240 exam. The user initially derived a result from Maxwell's equations that led to the conclusion that the Laplacian of the electric field, ##\nabla^2 \vec{E} = 0##, which is incorrect in the context of an ideal conductor. The fault identified in the derivation is the assumption of zero charge density, which invalidates the resulting equation. This highlights the importance of considering material properties when applying electromagnetic theory.

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Nikitin
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Homework Statement


http://web.phys.ntnu.no/~ingves/Teaching/TFY4240/Exam/Exam_Dec_2008_tfy4240.pdf
problem 2a)

Homework Equations

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?
 
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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?
 

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