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If you're trying to simulate a 2D solution of the Laplace equation (which is the only unambiguous reading of your post as currently stated; if that's not what you're doing then you should clarify your question with exactly what it is you're doing and how), then your code is wrong. The reason is that your results don't obey the maximum principle: a harmonic ...

3

I believe the answer to your question lies in the Gauss theorem itself $$\oint \textbf{E}d\textbf{S} \sim Q$$ and the symmetry of the system, which defines the shape of equipotential surfaces. In case of a point charge there is a rotational symmetry about any axis going through the charge, so the equipotential surfaces are spheres whose area is ...

3

I don't like the "you can't get away" explanation. There is a simple explanation with field lines: In all three cases, the field lines are straight lines from the point charge to infinity. You can easily calculate the density of the field lines for each object. For a point charge, the "number" of field lines through any sphere around the point charge is ...

3

The principle of relativity: The laws of physics are the same in all inertial frames of reference. Since the Lorentz force is a valid law of physics, it will not change when we pass from one reference frame to another. First frame, wire is moving. There is no $\mathbf E$ field. Lorentz force $\mathbf F = q\mathbf v\times\mathbf B$. Apparently, you were OK ...

3

The excess charge carriers in the conduction/valence band of Silicon (delocalized so that around silicon atoms there is a slight excess of local charge) are neutralized by the equal opposite charge of the randomly scattered dopants. Thus, the total charge remains zero, and this is actually the only way that an infinite crystal can have a finite ...

2

1) This means that interaction between charged entities or matter takes place by the mediation of some force. According to standard particle theory, virtual photons are the mediators of electromagnetic interaction. Electric field is a certain region around a charge distribution, where it could influence a force on another charge. This means, the existence of ...

2

1) The electric field is not fundamental to the description of electrodynamics with point charges, one can take the point of view that electric charges simply interact at a distance with a force law proportional to the value of the electric field. 2) This is a bit of a loaded question in that any answer can normally be refuted, but the idea they're trying ...

2

$dl'$ is equivalent to "$d|\mathbf{r}|$", it is essentially a "scalar length measure". The electrodynamics integral you wrote here is a vector-valued integral, so no dotting happens. If you use a linear coordinate system, it may be evaluated as three scalar line integrals, one for each coordinate. Vector valued integrals cannot really be evaluated using a ...

2

"Water capacitors", where water is the dielectric, are commonly used in very high voltage pulse systems. For example, high-power nitrogen lasers commonly use water capacitors as their energy storage component. When used in these applications, a resin deionizer is used to dramatically reduce the conductivity of water. A great advantage of using water as a ...

2

If electrons obeyed classical mechanics, they would rearrange in a new configuration in order to maximize the distance between them. They would not stay still because of thermal motion, as pointed out by CuriousOne, but on average they will still maximize this distance. However, electrons don't obey classical mechanics, but quantum mechanics. The behavior ...

1

Electrons in metals have states which people call Bloch states. If we want to describe these states we should bear in mind that electrons have wave like behavior. Bloch states are a subset of the many infinite wave states which electrons can have in general. They're such that when an electron is in a Bloch state, it somehow fills everywhere in the metal. If ...

1

When you put +ve charge on a conductor, you are really removing the same amount of -ve charge, because only the electrons move. Gauss' Law assumes that charge is infinitely divisible, and can be spread uniformly throughout a volume or over a surface. This is a good approximation when the charge is on the order of $1 \mu C$, corresponding to about $10^{13}$ ...

1

For an INFINITE parallel plate capacitor, the electric field has the same value everywhere between the 2 plates. An intuitive reason for that is: suppose you have a small test charge +q at a distance $x$ away from the +ve plate and a distance $d-x$ away from the -ve plate. The +ve plate will repel the charge and the -ve plate will attract it. Now if the ...

1

In classical mechanics, all physical interactions are said to happen through collusions. According to Coulomb's law, the force seems to be magically acting from a distance, i.e: a charge at one location influences another charge far away from it without coming into contact with it. For the early scientific age, this seemed to be impossible and there was a ...

1

Doping introduces allowed energy states within the band gap of the material, and these energy states are very close to the energy band that corresponds to the dopant type. For example electron donor impurities create states near the conduction band while electron acceptor impurities create states near the valence band. The gap between these energy ...

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