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Is it true that the Poynting theorem $P=E\times H$ is quite valid for DC circuits?

If something is stationary, it is a special case of being time-varying (with time derivative equals zero). So there is no need to repeat the proof of Poynting's theorem in the narrow sense of ...
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Electric potential vs electromagnetic potential questions

Q1: You got confused by using total electric field, whose integral can't uniquely define electric potential, because it depends on the path. Electric potential (also in AC circuits with very high ...
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Does zero free current entail zero $\vec H$?

For example, if only permanent magnets exist, the free current ($\bf{J}_{\text{free}}$) is zero, but both $\bf{B}$ and $\bf{H}$ are not zero.
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Is it true that the Poynting theorem $P=E\times H$ is quite valid for DC circuits?

Yes, Poynting's theorem $$-\frac{\partial u}{\partial t}= \vec{\nabla}\cdot\vec{S}+\vec{J}\cdot\vec{E}$$ or, equivalently, in integral form $$-\frac{\partial}{\partial t}\int_V u\ dV= \oint_{\...
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Does zero free current entail zero $\vec H$?

Yes, I agree with your argument. Don’t forget $\vec H$ and $\mathrm d\vec l$ are vectors! $\vec H\cdot\mathrm d\vec l$ is a "dot product", so the $\oint$ sum the same direction of $\vec H\...
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Wavelength and penetration by EM radiation

This summary, particularly the chart below, illuminatingly addresses your question: Interaction of radiation with matter P.S. posted as an Answer rather than a comment to preserve the above chart in ...
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Boundary conditions on current carrying wire

It is easier to answer if you have a sketch of the problem you want to solve. I think that good results can be obtained only by setting the outer space section large enough and giving no boundary ...
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2 votes

Why possibility for X-ray to excite inner electrons higher than outer electrons?

I was wondering this myself! I found part of the answer and thought I'd share it here for others. Yes, what the original poster had in mind is correct. The inner core electrons have a much higher ...
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Why do two magnets faceing eachother with opposite poles but offset horizontally repel?

Something to remember is the magnets are not really trying to attract or repel, they are trying to get their fields to align. The photo shows this field. If the magnets are stacked vertically north ...
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1 vote

Is there any role of permittivity of medium in finding electrostatic force between two charges in that medium in CGS system?

It's $1/4\pi\varepsilon_0$ that is equals to 1 in cgs units. That leaves $\varepsilon_r$ unchanged, so the force is still reduced by a factor $\varepsilon_r$ in a medium other than the void.
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2 votes
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What is the current density of a circular current?

If you compute the integral $\int_A\vec j \cdot \mathrm d\vec S$ where $A$ is a surface oriented in the $\hat\phi$ direction as illustrated below, then you would obtain $$\int _A \big(\delta(r-R)\...
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What is the current density of a circular current?

I think the flaw here is that you're equating a current density to a current. The line density of the current in the loop would be expressed as: $$\lambda = \frac{I}{2\pi R}$$ So that you can ...
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1 vote

Are scalar and vector potentials solutions to Maxwell's equations?

Are scalar and vector potentials $\phi = 0$, $\vec{A} = A_0 \cos (kx-\omega t) \hat{e}_z$ solutions to Maxwell's equations? They could be. It depends on what the source terms ($\rho$ and $\vec J$) ...
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Do electric fences such as those typically used to fence cattle generate magnetic fields?

Thank you Niels, your answer along with some more searching as to what the equations might be and thus the parameters I need to fill these equations allowed me to "simulate" a range of ...
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1 vote

Fake Perpetual Motion Device using an Electromagnet

Another way that this might work is that an electromagnet is turned on when the ball passes through the hole in the platform. This electromagnet would accelerate the ball faster than gravity towards ...
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Magnet falling through tube

Let me see if I can explain this without equations. To simplify things a little let's consider identical magnets falling through identically sized pipes of aluminum and copper in a vacuum. The only ...
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1 vote
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Plate with positive potential and Gouy-Chapman model

In order to know with any certainty which direction the particles will move in let's break down some of the additional clarifications to this problem: Charged particles will only accelerate in a non-...
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Why Hund's first rule neglect one of the spin triplet states?

Hund's (1st) rule is based on the fact that if we fill the atomic orbitals with electrons, we can minimize the electron repulsion interaction energy by first maximizing |S| by putting electrons in ...
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Is there such a thing as infinitesimal electric field?

The word infinitesimal may be misleading due to its long history as a mathematical concept. However, it is just a synonym for a quantity that eventually goes to zero in modern mathematics. In ...
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INDUCTANCE depends on the number of turns in a solenoid. Is this the case with RELUCTANCE as well?

Reluctance is independent of the number of turns. Your confusion results from the fact that people use the word flux to refer to two closely related but different quantities. Recall that magnetic flux ...
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INDUCTANCE depends on the number of turns in a solenoid. Is this the case with RELUCTANCE as well?

The source of your confusion is that you are not considering the magnetic flux linked to the solenoid circuit rather you need to consider the magnetic flux linked with the material of the core of the ...
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3 votes
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Magnetic field lines are closed lines?

In general, it is not true that the magnetic field lines will form closed loops—although that it what happens in a lot of simple geometries. What is true instead is that the magnetic field lines ...
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How should I use the complex permittivity of a material?

Do I use the complex permittivity as is, and ultimately take the real/complex parts as needed? You can do that. The fields are also complex, and the physical part is often obtained by taking the real ...
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3 repelling parallel line charges

Firstly we need to understand that electric field has inertia. See this: https://www.physicsforums.com/threads/energy-density-in-an-e-field-does-it-contribute-to-inertial-mass.1015388/ Secondly we ...
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Surface charge on a current carrying conductor is impossible?

I think that unlike the answers stated above, there should be a different explanation. Consider a steadily flowing cathode ray. In a region around it, it will definitely create an electric field but ...
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Can the electric field have closed field lines?

In short: Does that mean that we can have closed field lines for the electric field, let's say for example, when we have moving magnets? Yes. If that's the case, can you have closed field lines in ...
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How to calculate the field distribution due to a current radiating in one direction?

In the case of an infinite perfectly conducting plane, you can use the image theorem. That is, since there is a perfectly conductive half space for $x<0$, the current density $\mathbf{J}(x',y',z')$ ...
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1 vote

Why is current density in a conductor of uniform cross sectional area constant at all points?

"Are there any fluctuations at all in reality?" In reality, there is Johnson-Nyquist noise: thermal current/voltage fluctuations in the conductor. This is routinely measurable with sensitive ...
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3 votes

Does the current inside a capacitor with dielectric becomes zero, if a DC (constant)voltage is applied?

Dielectrics have very low conductivity, so in many applications you can ignore the current flow through it You can model the real behaviour of an imperfect capacitor as an ideal capacitor ($I=C\frac{\...
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Why is current density in a conductor of uniform cross sectional area constant at all points?

A uniform current density $\vec{J}$ is just as much an abstraction as a uniform charge density $\rho$. Even if a "real" charge density $\rho$ is made up of a bunch of different point charges ...
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-1 votes

Are the field lines on a bar magnet diagram contour lines?

No. But not because magnetic field lines are not contour lines - they kind of are. In your case your 2d graphic is a 'slice' of a 3d case, so information is lost. If the magnet is a cylinder, then the ...
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Mutual gravitational acceleration (or deflection) of light beams as a function of the angle between them

The question was not posed well. A single angle isn't sufficient to define the configuration. Two line elements each defined by in position (3 variables) and orientation (2 variables) gives a total of ...
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Could an atom have a binary nuclei system?

Every nuclei is composed by some number of protons which are positively charged particles and thus repels each other apart. For gluing them together some number of additional neutral particles- ...
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1 vote

Apparent instantaneous EM propagation paradox in two concentric solenoids

If you think there's really a paradox, then in order to resolve it, you should ask yourself which assumptions are definitely true, so you can reconsider any remaining assumptions by process of ...
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-1 votes

Why is current density in a conductor of uniform cross sectional area constant at all points?

The average drift velocity is proportional to the electric field strength. For the potential difference between the two ends of a uniform wire to be independent of the radius, the electric field must ...
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Why is current density in a conductor of uniform cross sectional area constant at all points?

But, given that electrons flow at random, how can current density be the same everywhere? Electrons do not flow purely at random. There is a systematic part of their motion in addition to the random ...
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1 vote
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Why the Tokamak Fusion Reactors need to be so big if electromagnetism works better for small distances?

And so, wouldn't be more interesting to try and achieve nuclear fusion if the Tokamak space was tiny, but longer, like a really thin ring? Oh, if only we could! The problem is this: the plasma can be ...
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Circular motion of proton in special relativity

This is precisely what is seen in a relativistic particle accelerator. https://en.wikipedia.org/wiki/Cyclotron#Relativistic_considerations
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Circular motion of proton in special relativity

Your equations are correct. The square root comes from the relativistic equation for momentum: $p=mv\gamma=mv/\sqrt{1-v^2/c^2}$.
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1 vote

Apparent instantaneous EM propagation paradox in two concentric solenoids

If you are careful about all the delays, you will not find a paradox. For example, you strongly energize a long solenoid by applying a voltage to the ends of the wires. Perhaps you close a switch. ...
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1 vote
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Is the induced electric field in a current changing solenoid actually that what we call magnetic vector potential field?

The magnetic vector potential isn't the induced electric field. However, in the case that the net charge density $\rho = 0$ The induced electric field can be expressed purely in terms of the magnetic ...
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1 vote
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Could you magnetize and at the same time elactrostatically charge a piece of rusted iron?

When we say "a piece of iron" it usualy ment a piece of steel. Pure iron is very uncommon. Many varieties of steel can be magnetized (they are feromagnetic). The rust on the surface does not ...
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1 vote
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Series expansion of unitary operators in terms of other operators

The general principle at work here is made precise by Stone's theorem on one-parameter unitary groups. In short, if $U(\epsilon)$ is a strongly continuous$^\dagger$ family of unitary operators ...
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1 vote

Series expansion of unitary operators in terms of other operators

First of all, what is the meaning of $U(x_1, x_2)$? In classical physics, it would be a complex number with magnitude 1 such that the phase difference between $\psi(x_1)$ and $U(x_1, x_2) \psi(x_2)$ ...
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2 votes
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Can you magnetize iron by putting it in the air gap of a two parallel plates capacitor?

I think that you are referring to "the Maxwell term": the magnetic field that curls round a changing electric field. $$\nabla \times \mathbf B =\mu_0\epsilon_0 \frac{\partial \mathbf E}{\...
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Do Maxwell's equations still apply in fluids?

The "macroscopic formulation" of Maxwell's equations (linked by others in the comments) are often called "Maxwell's equations in matter" because they account for the fact that ...
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Wave Equation in 2D and 3D

The wave equation contains the second derivatives in respect to position. So, you have the Laplace operator applied to the function (your $\psi$ ) that expreses the displacement from equilibrium, in ...
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2 votes
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What is the signal velocity in a very thin enameled magnet wire?

In theory, for a straight wire in empty space, the TEM mode centered on the wire has only finite energy in the insulation, but infinite energy outside. The insulation thus has no effect on the wave ...
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How is surface charge induced on the surface of circuit wires when connected to a battery?

Before the battery is connected to a circuit, there must be no net charge anywhere inside or on the wire because otherwise there would be a different in electric potential and a current would flow. ...
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2 votes

Do electric fences such as those typically used to fence cattle generate magnetic fields?

An electric fence is powered by a supply circuit which produces a high-voltage output which is fed to the fence wire. The current accompanying the high voltage is limited by that circuit to a low ...
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