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Osman123
#1
Feb19-12, 09:56 AM
P: 2
Hi, sorry for the childish title. But this problem is supposed to be solved quantitatively using Laplace's equation, so it's not so straightforward.

1. The problem statement, all variables and given/known data
(a) Explain why it is possible to keep a teaspoon in a cup of water heated in a microwave oven without spark formation, but if you place a piece of aluminium foil in the same microwave oven, you will see sparks.

(b) For a quantitative description, it is useful to calculate the electrical fields at the tip of a conductive wedge held at a potential V0 by solving the Laplace equation for this geometry.




2. Relevant equations

[itex]\nabla[/itex]2V=0




3. The attempt at a solution

I think I got it for part (a). Please help me check for incorrect physics.

In a microwave oven, the electromagnetic waves are tuned to coincide with the resonant frequency of water molecules. Hence, there is maximum transfer of energy from into the water, which gradually boils off as it dissipates the incident electromagnetic energy away into thermal energy. A metal teaspoon in the water is effectively shielded from exposure to the microwaves and thus does not acquire the energy requisite to spark formation.

For a free aluminium foil, the situation is very different. Electromagnetic micro waves pass through food, plastic and glass, but reflect off metal. The electrons on the surface of the metal will jump off of the metal object and into the air, which causes a spark in the microwave oven.

Another critical factor is the existence of numerous pointed, sharp edges on a foil; the local electric field at a sharp edge may be strong enough to ionize the adjacent air and cause an electric discharge through it. Whilst the current is passing through the air, various electronic transitions may occur in the visible electromagnetic spectrum which manifests in the form of sparks.




(b) I really need help for this part. Currently I am using the Griffiths’ Intro. To Electrodynamics book at university, and have completed Chapter 3 on solving Laplace’s equation in Cartesian, spherical and cylindrical coordinates. However I genuinely can’t see how all these things can help to find the e-field of a conductive wedge in a microwave oven!
My assignment is due on Friday, so any prompt help is greatly appreciated.

Thanks so much.
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