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42

Get together a collection of charges. As many different ways to generate a charge as you can think of. Go ahead and invite your friends so they can think of some more. (As a practical matter you make static charges just before you use them, but still...) Now, test them pair wise to see if they attract or repel one-another. Keep careful records. Find the ...


25

I agree with DanielSank that the question is asking (wholly, not partly) about the historical development of the concept of electrical charge, not our modern description of it - "how did they know?" not "how can we know?" The latter (answered by dmckee) is the end result of more than two centuries of observation, experiment, theorising and debate, and ...


16

The Hall Effect shows that negative charge is moving. In the Hall effect, one passes a current through a wide strip of metal exposed to a perpendicular magnetic field. If positive charges moved, we'd expect the positive charges to be travelling in the same direction as $\vec{I}$, and the magnetic force $q\vec{v}\times\vec{B}$ would be to the right. Thus, ...


11

Physics's don't know that only negatively-charged particles move. We can create ion currents on demand in many environments. We do know that the current flowing in a metal wire is negatively charged particles in motion. As for how to determine that, you do a Hall effect measurement. The measurement works by subjecting a current in a relatively wide bar to ...


8

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 ...


6

Initially, when first glass rods were systematically being rubbed, the "charging" phenomena was observed. The electric charges were hypothesized to be positive and negative, and the pioneer (Franklin? forgot the name...) pretty much arbitrarily decided to call one positive and the other negative. Further experiments helped him deduce that two like charges ...


5

There are some good answers here, but I think I want to try to abstract Franklin's work a little bit. Because Franklin found just two options - "repel" and "attract", he was forced to consider only two kinds of charges. Consider the experiment, where glass-glass repels, plastic-plastic repels, and glass-plastic attracts. If all glass is the same, the glass ...


4

For point sources of a field or energy source, such as a charged particle, a gravitational body (which acts like a point source), or a loudspeaker on top of a tall column, the geometry of the problem controls how energy and fields distribute themselves in space. At all points that are an equal distance from a point source, the energy or field strength is ...


4

Technically "potential difference" is the difference in electrical potential, i.e. $\Delta V$, not the difference in electrical potential energy, $\Delta U$. Potential difference ($\Delta V$) is also called voltage, in certain contexts. However, many people and sources are sloppy about their terminology, and they will say just "potential" when they really ...


4

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 ...


4

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

The boundary conditions by themselves can't tell you anything about a conductor. The boundary conditions can't even tell which side of the surface has the conductor! One way to model a conductor is as an Ohmic conductor where there is a constant $\sigma$ (different than the surface charge density listed in your boundary conditions) and then you assert the ...


3

Let's assume we don't know how many types of charges exist. But we know that there are bodies which either attract or repel each other. Now we perform an experiment We find all such bodies that repel each other and put them in separate categories. After extensive experimentation we observe that they only belong to two piles. Furthermore we also observe ...


3

As such there is no real theoretical proof to the inverse square dependence of the electric field in classical electrodynamics. It is an experimental fact famously known as the Coulomb's law. When combined with the superposition principle, it gives us the Gauss's law of classical electrodynamics: $$\nabla \cdot\mathbf E = \frac{\rho}{\epsilon_0}.$$ But, ...


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 ...


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 ...


2

You can prove it using the concept of electric flux. For instance. If you surround a point charge with a sphere if r=1, or a sphere with r =10, you know that the electric flux ( field strength times area) must be the same. A sphere is easy because every point is equidistant to the charge.


2

You're trying to understand how a point charge is represented in the charge density $\rho(r)$. The concept you need is the Dirac delta function $\delta(r)$, which can describe the density of a finite amount of stuff packed into an infinitesimal point: $$\delta(r) = \left\{ ^{\infty \text{ if } r=0 }_{0 \text{ if } r\ne0} \right\} $$ $$\int_{-\infty}^{+\...


2

I sort of doubt the blue jet explanation by Xeren is probable (although it is a possibility). It's just too rare and too faint. Much more likely, it's lightning far away near the horizon. Just because there are no clouds doesn't mean the light wont scatter. Sunlight makes the sky very bright blue during the day, and in the brief moment when lightning ...


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

Brief Summary Numerically, the mean value property of harmonic functions allows you to get an approximate solution to boundary value problems relatively quickly. Often you can improve convergence to a solution with a good initial guess, however, so analytical approaches can still be useful. Consider the limit of an infinitely long cylinder. There is a ...


2

Among competing hypotheses, the one with the fewest assumptions should be selected. Some electrified objects repel, some attract. This can be explained by two kinds of charge. Nothing that cannot be explained by two charges can be explained by adding a third kind of charge. So we continue to describe electricity as occurring in two kinds.


2

You need to use Ohms law: $J = \sigma E$ which has to be added to Maxwell's equations as a bulk observation, as explained by this answer. You can then conclude that the electric field is zero in a conductor for: perfect conductor where $\rho = 1/\sigma = 0$ and $J$ is finite static case where $J = 0$ and $\sigma$ is finite


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

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

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

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

By analogy, you are comparing the properities of a solid material, in your first paragraph, to a gas mixture, the atmosphere, in the second. So the path taken would flow through the "weakest" or most conductive sections of air. No matter how small a volume of air you take, the conductivity/ionisation path is very unlikely to be consistent enough to ...


1

No. The battery is already neutral, and remains neutral during operation. (-ve charge leaving one terminal has to be replaced at the other terminal.) If some -ve charge flowed to Earth the battery would become +ve, attracting electrons back to it.


1

Technically, you can neutralize the electrostatic potential of the entire battery this way. However, batteries do not primarily work by electrostatics. They work by creating a potential difference between the two terminals which encourages electrons to flow out of one (the negative side) and into the other (the positive side). This encouragement is ...



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