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133

As you said, it's probably not magnetism if the balls are free to rotate; there is no reason they wouldn't just flip over and stick together, north to south. You can test this by buying some of those toy magnetic balls. The repulsive configurations are highly unstable and turn attractive with the slightest touch. I'm going to go out on a limb and say it's ...

112

Well it has nothing to do with the Higgs, but it is due to some deep facts in special relativity and quantum mechanics that are known about. Unfortunately I don't know how to make the explanation really simple apart from relating some more basic facts. Maybe this will help you, maybe not, but this is currently the most fundamental explanation known. It's ...

105

The title of the question asks if Maxwell's equations are mathematically precise. The answer is certainly yes. Maxwell's equations are well-posed differential equations. There is no ambiguity about the symbols, and one can unambiguously check if a given set of fields and charge/current distributions satisfy the equations. In fact, Maxwell's equations enjoy ...

62

You're right that CERN gets its protons by ionizing matter and collecting them. But the number of electrons & protons CERN deals with is far smaller than you might think. They get about 600 million collisions a second at CERN. So call it 1.2 billion protons used per second. $1.2 \times 10^9$. That'd be a large number in dollars, but it's not much ...

56

The electron and proton aren't like pool balls. The electron is normally considered to be pointlike, i.e. has no size, but what this really means is that any apparent size we measure is a function of our probe energy and as we take the probe energy to infinity the measured size falls without limit. The proton has a size (about 1fm) but only because it's made ...

51

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 ...

45

As far as we know, electrons are fundamental particles and have no internal structure or components. Also, an electron cannot decay into other particles (unless it has a very high kinetic energy) because there is no lighter charged lepton for it to decay into. It can, however, annihilate with a positron to produce gamma rays.

42

Gauss's law applies to situations where there is charge contained within a surface, but it doesn't cover situations where there is a finite amount of charge actually on the surface - in other words, where the charge density has a singularity at a point that lies on the surface. For that, you need the "Generalized Gauss's Theorem" [PDF], which was published ...

41

The answer is that it doesn't matter. The distance at which fields resemble that from a point charge is also the distance at which it does not matter where that point is located within the structure. The change of field due to switching the origin within the conductor will be comparable to the corrections to the point charge approximation, both arising from ...

41

Yes, potential energy can be negative: consider Newton’s law of gravitation $$V = -\frac{GMm}{r}$$ Where $G$ is Newton’s constant, $M$ and $m$ are masses, and $r$ is the distance between them. It can clearly be seen that this is always negative. The key thing is that the absolute value of potential energy is not observable; there is no measurement that can ...

37

If something is 'Electrically neutral' this means that the algebraic sum of its electric charges, however distributed, is zero. This does not imply that there is no electric field in its vicinity. Plenty of neutral bodies – even, it is believed, the neutron – have electric fields, for just the reason you have pointed out.

36

Field lines draw all of their validity from Gauss's law for the electrostatic field, $$\nabla\cdot \mathbf{E}=\frac1{\epsilon_0}\rho,\ \text{or equivalently}\ \oint_{\partial\Omega}\mathbf{E}\cdot\text d\mathbf{S}=\frac1{\epsilon_0}Q_\Omega,$$ where $Q_\Omega=\int_\Omega\rho\,\text d\mathbf{r}$ is the electric charge in a volume $\Omega$ whose surface is $... 36 Electro-magnetism is a good guess, simply because it's the only force you commonly see that's powerful enough. It's not very useful as an explanation, though, because almost everything you see around you is due to electro-magnetism (e.g. the way the spoon holds together in the first place, or the light that allows you to see the sugar, or the way the water "... 36 Based on some of the back-and-forth I see, I think you're asking the wrong question. I think the question you want to ask is "Given a charge distribution$\rho(\mathbf{r})$, where should I place a point source so that the exact potential$\phi(\mathbf{r}) = \int \rho(\mathbf{r}')/|\mathbf{r}-\mathbf{r}'| dv'$is most closely approximated by the potential ... 36 If you suddenly removed all the electrons from a piece of material, or even just the valence electrons, you would be left with a huge concentration of positive ions in a small volume, which would exert a huge electrostatic repulsion on each other. Since you no longer have the bonding influence of the electrons to counteract this repulsion, the material would ... 34 It is said that atoms with the same number of electrons as protons are electrically neutral, so they have no net charge or net electric field. This is a great over-simplification, which I am sure you have already determined (based on why you are asking this question). You can have objects that are polarized where, overall, they have no "net charge", yet the ... 34 An electron is an elementary particle in the standard model of particle physics. . The table axiomatically assumes that elementary particles are point particles in the QFT of the model, i.e. have no constituent parts. Depending on the quantum number conservation rules and if there exist consistent lower mass particles to decay to, elementary particles can ... 33 Your analysis doesn't make sense because the units don't match up.$1100 \, \text{kV}$is not more than twice$510 \, \text{keV}/c^2$, because the two quantities can't be compared at all. It's like saying$4$meters is twice as big as$2$minutes. It's indeed possible to create electron-positron pairs, but you need a tremendously large electric field, given ... 29 In general the answer is "yes it is possible" - but in your case the answer is "that is not a Faraday cage". Radio waves are (partially) reflected by any discontinuity in dielectric constant of the medium they propagate through. The ones that propagate (through walls etc) will also experience attenuation. A faraday cage is a continuous conducting structure ... 28 Permittivity$\varepsilon$is what characterizes the amount of polarization$\mathbf{P}$which occurs when an external electric field$\mathbf{E}$is applied to a certain dielectric medium. The relation of the three quantities is given by $$\mathbf{P}=\varepsilon\mathbf{E},$$ where permittivity can also be a (rank-two) tensor: this is the case in an ... 28 Consider the flux through a tiny segment of a sphere. Since the electric field is parallel to the normal of the surface at all points, the flux is simply the electric field at that distance multiplied by the area of the element. Now imagine tilting the top of the cone by an angle$\theta$so that the corners still lie on the conical section, as seen below: ... 27 You can use a high vertical tube to store water in it (fill it from the bottom by pushing the water in) How much water can you store? It obviously depends on the pressure you apply to push it in. If you push harder, there will be more water stored. The tube is characterized not the amount of water, but by how easy it is to store the water. Its "capacity" ... 27 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 ... 27 if I take out some electrons from a neutral body, it would become positively charged. So didn't I just create some charge You didn't create anything. The electrons were already there (and so were the protons that make up the positive charge). All you did was move them. When you talk about conservation laws you have to include the whole system. If you're ... 26 Electric field lines are a visualization of the electrical vector field. At each point, the direction (tangent) of the field line is in the direction of the electric field. At each point in space (in the absence of any charge), the electric field has a single direction, whereas crossing field lines would somehow indicate the electric field pointing in two ... 26 In the centre of a bowl there is equilibrium. Put a ping pong ball in it. If this ball is ever shaken slightly away from equilibrium, it will immediately roll back. A "shake-proof" equilibrium is called stable. Now, turn the bowl around and put the ball on the top. This is an equilibrium. But at the slightest shake, the ball rolls down. This "non-shake-... 26 It's true that a point particle with finite charge is problematic in electromagnetism because of the infinite field and associated energy near such a particle. However, we don't need that concept in order to make a defining statement about the electric field. Rather, we can use $${\bf E} = \lim_{r \rightarrow 0} \frac{\bf f}{q}$$ where$\bf f\$ is the force ...

25

Neutral charge just means there is no net charge when considering the entire atom/molecule. It doesn't mean there can't be a non-zero or non-symmetric electric field. This is especially true for molecules that are neutral yet still polar, such as water. you would think that there is more negative charge concentrated at the 'perimeter' of the atom, and the ...

24

This comment It was a "one-sided" fridge magnet. is a key piece of information. Your magnet is not a single dipole bar magnet; instead, it is a Halbach array, i.e., a carefully-engineered arrangement of individual dipole magnets which has been optimized to have a strong magnetic field near the magnet which becomes weak as you go away from it. ...

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