# Tag Info

15

Because it was defined by measurements (the force between to wire segments) that could be easily made in the laboratory at the time. The phrase is "operational definition", and it is the cause of many (most? all?) of the seemingly weird decision about fundamental units. It is why we define the second and the speed of light but derive the meter these days.

14

It's not a mistake, and conventional current is not wrong or backwards. The labeling of one polarity of charge as "positive" and the other as "negative" is totally arbitrary. It could be done either way and everything would still work out the same. Franklin didn't choose wrong; he just chose. Labeling protons as negative and electrons as positive wouldn't ...

12

Let me add two references to points already mentioned in this discussion: Today, there is no reason known why the electric charge has to be quantized. It is true that the quantization follows from the existence of magnetic monopoles and the consistency of the quantized electromagnetic field, which was shown first by Dirac, you'll find a very nice exposition ...

12

The maximum charge a capacitor stores depends on the voltage $V_0$ you've used to charge it according to the formula: $$Q_0=CV_0$$ However, a real capacitor will only work for voltages up to the breakdown voltage of the dielectric medium in the capacitor. So in reality, for every capacitor there is a maximum possible charge $Q_{max}$ given by: $$... 10 It seems you are contrasting the speed of propagation of current with the speed of the individual charge carriers. These two things are clearly separate. There are many examples. Consider sound. A fire cracker goes off at the other end of a football field from you. You hear the sound a few 100 ms later. The air molecules that were by the firecracker ... 9 Charge comes from discrete symmetries and is countable and additive. Mass comes from continuous 4d space, is exchangeable with energy and, in quantum mechanical dimensions not linearly additive, thus not countable. Suppose you have an elementary quantum of mass, m_q. In the world we know two such quanta would not end up as 2m_q. One would add the ... 9 James Clerk Maxwell thought about this one and showed the following. Suppose we have two concentric conducting spheres and we charge one up to a potential \Phi relative to some grounding plane. Then the voltage of the inner sphere relative to the same ground is:$$\Phi_{inner} = \Phi \,q\, ...

9

I believe that the "roughly" term is applied because of the associated experimental error when measuring its charge. The same cannot be said to the electron because "we" decided to make the electron the reference charge. So, the reference charge is definitely -1. However the muon charge must be measured. According to this paper, Muon Mass and Charge ...

8

Actually, mass and charge are only superficially similar. Yes, they both appear in inverse square force laws, namely Newton's law of gravitation and Coulomb's law of electrostatic force, but both of those are approximations. Coulomb's law ignores quantum effects, which is a very slight approximation, but Newton's law ignores all of relativity, which makes a ...

8

Dear asmailer, the reason is simple and completely understood: the electric charge is the generator of a $U(1)$ symmetry which is compact and may be parameterized by an angle, $\phi$. So wave functions may only depend on the angle $\phi$ in a periodic way, $\exp(iQ\phi)$ where $Q$ is integer (or an integer multiple of $e/3$, if I look at the elementary ...

8

Coulomb repulsion it is. Specifically, if a black hole has a lot of charge, then particles with a high charge-to-mass ratio will be repelled. Anything that falls in will contribute "more mass than charge," heuristically, keeping the charge-to-mass ratio of the black hole from getting too big.

8

In fact, an electric charge at rest on the Earth's surface is accelerated and this actually poses a challenge to the idea that uniformly accelerated charge radiates. I believe this is still an open question. For example: One of the most familiar propositions of elementary classical electrodynamics is that "an accelerating charge radiates". In fact, ...

7

In quantum field theory and its extensions including string theory, the electric charge is a generator of a $U(1)$ symmetry which should be promoted to a local symmetry i.e. gauge symmetry. In string theory, the $U(1)$ symmetry and the gauge field often appear as parts of the low-energy effective action. This could be enough to answer the question: we ...

6

There is a limit on how much charge a black hole may have: http://en.wikipedia.org/wiki/Extremal_black_hole In general, rotating, charged black holes is described by a Kerr-Newman metric. Intuitively, eventually the Coulumb repulsion is enough that a charged particle which does not contribute more mass than charge will be repelled.

6

Four possibilities come to mind, in decreasing order of feasibility: Is barefoot an option? I'm willing to bet it will significantly mitigate the buildup of charge. The two of you only experience a shock on contact because you are at different electric potentials. If you can't keep him at your potential, why not try to join his? Before helping him down, ...

6

Your intuition for the first one is correct; the extra charges are held to the surface by the electrostatic force, which is many orders of magnitude stronger than the gravitational force. The second one (and part of the first one): You're confusing free electrons with "extra" electrons. In a conductor, the highest energy electrons are not bound to any ...

5

There is a way of seeing this more explicitly with the Reissner-Nordstrom (RN) metric $$ds^2~=~-F(r)dt^2~+~F(r)^{-1}dr^1~+~r^2d\Omega^2$$ where the $F(r)~=~1~-~r_0/r~+~(Q/r)^2$, $r_0~=~2GM$ and $Q$ the charge in length units. The metric has two critical points $$r_\pm~=~\frac{r_0}{2}~\pm~\frac{r_0}{2}\sqrt{\frac{4Q^2}{r_0^2}}$$ These are the outer ...

5

Moving mass does generate gravitation different from stationary mass. This is the ''gravitomagnetic'' effect predicted by Lens and Thirring in the 20's and measured by Gravity Probe B: http://en.wikipedia.org/wiki/Gravitoelectromagnetism It is related to the ''frame dragging'' effect that you hear about with respect to spinning black holes. There, there ...

5

General Relativity is a mathematical model that relates the curvature of spacetime to an object called the stress-energy tensor. In many cases the stress-energy tensor is dominated by mass and you can simply consider the curvature as being related to the mass. However this isn't always true as I'll mention below. Anyhow, we can put any numbers we want into ...

5

As the two charged bodies attract, they have unlike charges. So, Assuming your two charged bodies as conductors and charged equally, the system may be considered as a Capacitor. If you place a dielectric like glass of some Relative permittivity $\epsilon_r$ (3.7 to 10) which fills the empty space between the bodies, then the capacitance would be ...

5

If you followed the arguments carefully and checked what is demonstrably right and what is not, you would agree that what the argument actually does is to prove that a uniform electric charge density cannot have a uniform electric field. Your original task was to solve Maxwell's equations (well, Gauss's law), so if you find out that the equations aren't ...

5

A charged particle circulating in a magnetic field does radiate energy, and it is called synchrotron radiation. All circular particle accelerators have energy losses due to this radiation.

5

The nature (and glory) of the dirac delta function is that the volume integral $$\int_{\Delta V} dV' \delta ( \boldsymbol{r-r'} ) = \left\{ \begin{array}{cc} 1 & \text{if } \Delta V \text{ contains } \boldsymbol{r}\\ 0 & \text{if } \Delta V \text{ does not contain } \boldsymbol{r} \end{array} \right.$$ Using this function, you can write the ...

5

If it is in air (or any other substance), there is a limit where the electric field of the object is going to be enough to ionize the surrounding medium, and the resulting current will drain the object of its charge. Similarly, if the object is immersed in vacuum, you will eventually have an electric field sufficient to "polarize the vacuum" by creating ...

5

The cross-section for $$e^+ + e^- \to q + \bar{q}$$ goes by the square of the quark charge (times the number of colors). Now, the quarks can not be observed in isolation because they hadronize. However the cross-section for $$e^+ + e^- \to \mu^+ + \mu^-$$ is identical except for going by the muon charge squared. So, a measurement of  R = ...

5

This is because the neutrality of polarity can be changed by electric field in this case. When you create - charge in the comb and you expose the pieces of paper to the electric field created by the charge, you will polarise them so that the part closer to the comb will be + and the other will be -. Here, see the electric field. The same polarities do not ...

5

It's not intuition.It's a problem which can be solved. First we identify the sign of the charges. By seeing the direction of field lines we can see that the sign of charges. Field lines originate from $+ve$ and end at $-ve$ charges. Next by Definition of Flux, The number of field lines cutting per unit surface surface . And Gauss' Law The flux ...

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