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This is a guess about what the author was thinking.
We have the fundamental SI units for length (m), mass (kg), and time (s), which were originally defined as one 40-millionth of the circumference of the earth, the mass of 0.001 m3 of water, and 1/86400 of a day. This is the MKS system. There is no natural way of integrating electromagnetism in this MKS ...
6
Under the current understanding of the Standard Model, there are only three possible charge magnitudes for fundamental particles: $e$ (for leptons such as electrons), $\frac23 e$, and $\frac13 e$ (for various types of quarks). There are also uncharged fundamental particles (neutrinos). So if we restrict ourselves to fundamental particles, the answer is that ...
6
It’s not circular at all. The early chapters are concerned with charges at rest; here their electric fields are given by Coulomb’s law.
The chapter where this new definition appears is about the fields of moving charges, a topic which has not yet been covered. In this more general context, Coulomb’s law doesn’t work anymore, so we start over with new ...
5
The quantity that you are thinking of is called current density. It is charge per area per time (you were forgetting the time).
Current and current density have different purposes. Current is more useful for circuit theory and current density is more useful for Maxwell’s equations. In circuit theory we use a lumped element approximation which eliminates all ...
4
I think it can be justified because we can only know that there are charges there due to the effect in other charges. And that effect is expressed mathematically by the electric field.
So, using test charges outside at several distances, it is possible to evaluate the field. While the charges are the source of the field, and on this way more fundamental so ...
3
To pass a current through the conductor, you connect a source of electrons and a place deficit of electrons, and electrons flow from one to the other.
When you do that, the charge on the conductor will spread throughout the circuit. It will leak some.
If the circuit is grounded, then the charge will all escape.
If there is a switch that can prevent or stop ...
3
I'm quite sure the answer is
$$\hat{U}(f) = e^{iq\int d^3x\ f(\vec{x})\hat{\psi}^\dagger(\vec{x})\hat{\psi}(\vec{x})}$$
But I wasn't able to prove it. So it is only a conjecture.
For the special case of $f(\vec{x})=f=\text{const}$, the above reduces to
$$\begin{align}
\hat{U}(f) &= e^{iq\int d^3x\ f\ \hat{\psi}^\dagger(\vec{x})\hat{\psi}(\vec{x})} \\
&...
3
No, at least in the standard model the highest charge of any elementary particle is $\pm e$. You can of course find composite particles with higher net charge.
3
Contrary to what science fiction may tell us, quantum teleportation does not involve the physical teleportation of matter. It only teleports the state of matter. In that sense, it teleports the information that is associated with a particle and not the particle itself. So, electric charge remains where it is.
In response to the comment: the spin is a degree ...
2
There should be no "should" in
Either it should be that E.F acts on the charge (if at rest) or M.F (if in motion).
Namely as mentioned in the comments, any particle which is electrically charged feels a force due to an electric field $\vec{E}$, equal to
$$\vec{F} = q \vec{E}$$
whether it is moving or not. At the same time a charged particle which ...
2
Charge conservation can be stated as a continuity equation
$$\frac{\partial \rho}{\partial t}+\nabla\textbf{j}=0 \tag{1}$$
where $\rho$ is charge density (measurable in Coulomb/m$^3$)
and $\textbf{j}$ is current density (measurable in Ampere/m$^2$).
On the other hand, from the magnetostatic equation
$$\nabla \times \textbf{B} = \mu_0\textbf{j} \tag{2}$$
you ...
2
The $\Delta^{++}$ baryon, which is a member of the isospin $\frac 3 2 $ delta-quadruplet.
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Yes, an example of an elementary particle with mass but without electric charge is the Z boson or the Higgs boson.
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Let at time $t$ charge on a area $A$ of the sheet be $Q$. charge density on one face will be $\sigma_{t}$ and on the other face will be -$\sigma_{t}$. the net field inside the conducting sheet will be $$E_{tot}=E-\frac{Q}{A\epsilon_{o}}=E-\frac{\sigma_{t}}{\epsilon_{o}}$$Current Density, $J=\eta E_{tot}$
Due to this current a charge $JAdt$ flows from one ...
2
The entanglement is the coupling of different quantum systems. The experimenters bring entangled systems to their own journies. And when a quantum system is measured, the other quantum system is collapsed at the same time because they are entangled. While this process, no material is transferred.
It is the non-locality of the world which makes this possible ...
2
The answers will differ, because the charge distribution on each sphere will not be uniform. Effectively, each sphere will have an induced dipole moment due to the presence of the other, which will change the force between them.
This effect of the charge distribution, however, will generally be smaller than the basic effect from treating the spheres as ...
2
I don't blame you at all for your confusion. It seems that he's attempting to scientifically demonstrate or argue something on the basis of electromagnetism, but his assertion is rather unprofessional; I've read many scientific research papers, and not once have I encountered one that appeared so paranoid about people accusing the author of "trickery&...
2
Conservation of electric charge
If your capacitor starts out uncharged, then unless you add or remove charge to it, it will always remain net neutral. Charging a capacitor simply applies a voltage to both sides (i.e. it doesn't add or remove charge), so the capacitor must remain net neutral. In other words, the two plates must store equal amounts of charge.
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The current is directly proportional to the voltage and inversely proportional to the resistance. This means that increasing the voltage will cause the current to increase, while increasing the resistance will cause the current to decrease
Conclusion: it depends upon whether voltage is fixed or resistance is fixed
2
resistance is defined as R=U/I, so is it not very good to say: the current is inversely proportional to resistance, if you do not complete your sentence with: if voltage is constant.
2
Actually, we indeed take the minus sign. But, the direction of electric field due to the negative plate will be in the opposite direction of that of positive plate. Mathematically understanding, we have $$\begin{align}\vec E&=\vec E_1+\vec E_2\\ &=\frac{\sigma}{2\epsilon_0}\ \hat i+\frac{(-\sigma)}{2\epsilon_0}\ (-\hat i) \\ &=\frac{\sigma}{\...
2
Electrons have to overcome the so called work function. Even conduction electrons have some probability of being found near and even at the nucleus of the atoms making up the metal. This is what causes metallic bonding and keeps the metallic structure stable.
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To answer two of your questions:
We're interested in what happens inside the sphere, not outside it, since the sphere will fill all of space as $ R\rightarrow \infty $. Inside the sphere, both the electric field and the gravitational field are proportional to $R$. "Increase" is correct.
The main difference is not that the electric field and the ...
1
The circuit is presumably built from electrically neutral wire, containing the same number of positive and negative charges. When the circuit is switched on and current starts to flow, new negative charges can't appear from nowhere. The average spacing of charges (measured in the lab frame) is the same before and after the current is switched on, because it'...
1
How does an Ion Thruster work?
An ion thruster basically just ionizes (generally) Xenon atoms to produce ions by electron bombardment, in this process , a highly energetic electron is made to collide with a neutral propellant atom (e.g. Xenon), which knocks out electrons from the atom, and leaves a net positive charge on the Xenon atoms. The resultant ...
1
You need to provide more details on the circuit. I'm going to assume you have two equal initially charged capacitors of capacitance $C$ in parallel which are then connected across a resistor $R$ by a switch initially in the open position. Of interest is then the equivalent time constant for the equivalent circuit that dictates the current in the circuit and ...
1
Not sure how helpful it will be, but this comes from my notes on GUT charge quantisation:
In the Standard Model, the electric charge is the quantum number related to the $U(1)$ of $SU(3)\times SU(2) \times U(1)$ symmetry. Strictly speaking it is a $U(1)$ subgroup of $SU(2)\times U(1)$, but that doesn't make a difference in this case. The Eigenvalues of $U(1)$...
1
Lorentz Force is given as:
$$\vec{F}=q\vec{E}+q\vec{v}×\vec{B}$$
The magnetic force will only act on the charge when $\vec{v} \neq 0$ and the angle between velocity and Magnetic field is not the integral multiple of $\pi$.
While Electric field will always act on the charge irrespective of its state of motion.
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It's the magnitude of the gradient of $F$.
$\operatorname{grad} F$ or $\nabla F$ denotes the gradient of the field F and thus $|\operatorname{grad} F|$ is the magnitude of the gradient of F.
It's common practise, but just a matter of taste, to use $\operatorname{grad} F$ over $\nabla F$ in order to guide the eye easier as to what is being done or used (...
1
The principle idea of a scanning electron microscope (SEM) is to use electrodes to raster the probe with a tiny focus: The electrodes shape the electric field lines (electric potentials) in such a way that the electrons propagating in $z$-direction are focussed onto a "small" spot in the $(x,y)$-plane. The "small" focus in the $(x,y)$-...
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