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Ohm and Fourier's law with Seebeck effect - derivation?

Check Landau & Lifshitz volumes 8 "Electrodynamics of Continuous Media" chapter III ("constant current"), paragraph named "Thermoelectric Phenomena" for the origin of ...
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Does direct current exist in an infinite straight thin wire?

Mathematically, the electromagnetic energy per unit length is divergent for an infinite wire supporting a finite electromagnetic field. The characteristic impedance is infinite. Thus, in principle, ...
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Does direct current exist in an infinite straight thin wire?

The integral on the LHS is not zero. Use Stokes theorem, and realize that because $|{\bf H}|\sim 1/r$, the boundary contribution is independent of the distance from the wire.
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What should be the direction of moving electron in magnetic field?

The picture in your book contains an error. The magnetic field has to go into the other direction. Otherwise the electric and magnetic force cannot cancel each other and thus the experimental setup ...
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Can ionized air be used as a conductive medium for eddy brakes?

Your question is a good one, and has been a subject of research for a number of years in the field of magnetohydrodynamics, or MHD (convenient search term). This is a frightfully complicated field ...
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What is electric potential really a measure of?

Electric potential is defined by the amount of work energy required to move a unit of electric charge from a reference point to a specific point in an electric field.
7 votes
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Can we choose the Coulomb gauge if we're in a gauge where the gradient of the scalar potential is zero?

You're asking whether we can impose both $\phi = 0$ and $\nabla \cdot \mathbf{A} = 0$ simultaneously. This will not be possible in any situation where $\rho \neq 0$, since if both conditions on the ...
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What should be the direction of moving electron in magnetic field?

If you use the conventional current direction you have to use your right hand. The left hand is used, if you take the first finger in direction of the moving electron. So your text should not just say ...
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1 vote
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What exactly does it mean by gauge-invariant "operators"?

The whole point of the quantization of gauge theories is that we don't really want a realization of the gauge symmetry in the quantum theory because the gauge symmetry is unphysical (see also this ...
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Does a constant magnetic field induce an emf in space irrespective of what is inside the space?

It matters not what the material of the rod is. If the rod was a metal there would be a migration of the free/mobile electrons and in an insulator the motion of the rod through the magnetic field ...
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Magnetic field lines permeability in vacuum

I think the problem you're having is that you're thinking of the field as a thing that travels through space, when it's nothing of the sort. The field is a property that exists everywhere, always. ...
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Does the quantum mechanical wave function work as a charge distribution?

Schrödinger initially believed that the wave function is related to actual charge distribution density, rather than to probability density. Some objections were raised to such interpretation. One of ...
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2 votes

Does the quantum mechanical wave function work as a charge distribution?

The charge distribution is related to the probability of the electron being in a given location. That is, the amplitude-squared of the wave fucnction, $\bar{\psi} \psi $. Under some circumstances ...
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Is it correct using Larmor Formula for identifying a non-inertial reference frame?

In principle, Larmor's formula for the radiated energy: $$ \frac{\text{d}E}{\text{d}t} = \frac{q^2 a^2}{6 \pi \varepsilon_0 c^3} $$ provides a method for an inertial observer to detect relative ...
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Understanding the role played by moving charge in electric field and why charges reside on surface only in current flowing conductor too

First think of a neutral wire - a metal with diameter r and conductivity $\sigma$ and is very long. One end of the wire is grounded, and at the other end of the wire there is a switch that can connect ...
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1 vote
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Relative permeability: why does $\mu_{air} = \mu_0$?

Ferromagnetic materials can have large $\mu$. But for paramagnetic and diamagnetic materials, a typical permeability is $ \mu_r = \frac{\mu}{\mu_0} ≈ 1 \pm 10^{-5} $. I don’t know of a good ...
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Can we just consider thermionic emission as a kind of thermoelectricity?

Feel free to call things what you wish. Just make sure you define your terms clearly in your publications, or people will be mighty confused.
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What produces the electromagnetic fields in the light wave when photons are chargeless?

Electric charges are not the only thing that can generate electric fields. Changing magnetic fields can also create electric fields. Also, changing electric fields creat changing magnetic fields. So ...
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3 votes
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The Maxwell equations in 4-dimensional notation for vacuum and covariant component of electromagnetic tensor

Not quite. Using $c=1$ we have $A_\mu= (\phi, -{\bf A})$ where ${\bf A}$ is the usual three vector vector potential. So you should have $A_\mu= (\phi, A_i)$ with the covariant component $A_i=-A^i$. ...
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How to show monopole term in magnetic vector potential is 0?

Here is a simple proof using a corollary of the Divergence Theorem. I'll assume $\nabla \times \textbf{B} = \mu_0 \textbf{J}$, meaning $\frac{\partial \textbf{E}}{\partial t} = 0$ (electrostatic ...
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Magnetic explosions on Sun

Magnetic fields in an ionized plasma have more complicated behaviors than magnetic fields in free space. A lone charged particle in free space will undergo “cyclotron motion” in the plane which is ...
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-1 votes

Magnetic explosions on Sun

https://www.nasa.gov/feature/goddard/2019/nasa-s-sdo-sees-new-kind-of-magnetic-explosion-on-sun and https://iopscience.iop.org/article/10.3847/1538-4357/ab4a0c when the voltage has exceeded the LEL ...
2 votes

What is rotation of magnetization?

One can think of a domain as a region where many atoms line up so that the magnetic field they produce add together to produce a resultant magnetic field. Imagine that magnetic field as being produced ...
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Circuit in a $B$-field question

The induced voltage will definitely not cancel in general. That is the entire point of magnetic induction. Unless you specify that the field is constant and the wires don't move, it is actually quite ...
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Circuit in a $B$-field question

The induce voltage is calculated by the change of magnetic flux, if neither the area nor B changes you have no induced voltage
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How electromagnetic train works?

Complete physics of levitating train is nicely animated and explained in this film: https://www.youtube.com/watch?v=XjwF-STGtfE There are various films on the Internet, but for me the description is ...
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How electromagnetic train works?

You are correct. Without an active feedback mechanism that senses the distance between the train and the track the two would stick together just like ordinary magnets. There is even a mathematical ...
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Inductor connected to an AC source

To formalize all the previous answers, model the switch by a step function: $$ H(t) =\begin{cases}0 & t< 0\\1 & t \geq 0\end{cases} $$ And use it to limit the power source to positive t. ...
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What is electric potential really a measure of?

I like to think of electric potential as "pressure". By Ohm's law, $$I = V/R$$ Here, $V$ is the potenial difference. The current carrying wire lets in more current, if the potential ...
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Is the magnetic field outside a solenoid almost null for AC current?

Bio-Savart does not apply to AC currents. It is a law of magnetostatics. For AC currents we have to use the full Maxwell equations or a retarded potential formula like Jefimenko's equations. In ...
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What is electric potential really a measure of?

It is a scalar function whose gradient gives the force a charge would experience were it placed at a point. It is a function which measures the change in energy if a charge were to be brought from ...
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What is electric potential really a measure of?

Electric potential is the ability of a system to perform work on a charge. There do not have to be other charges in the system itself.
1 vote
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Understanding why the current can be treated like below for magentic field calculation

The usual Biot-Savart law looks like Where we can set vector $\vec{e}=\vec{dl}/|\vec{dl}|$ in the current direction. So, if cross-sectional area of wire is S we can rewrite: $$\vec{B}(\vec{r})=\dfrac{...
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Inductor connected to an AC source

Both your equations are correct as they are for different situations with the equation the general one $i=\frac{V_0}{L\omega }(1-\cos\omega t) = \frac{V_0}{L\omega } - \frac{V_0}{L\omega }\cos\omega t$...
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Inductor connected to an AC source

it is printed in my textbook that the value of $c$ equals zero, This is incorrect. It should say that $c$ is the value that makes the current equal to zero at $t=0$. $$i(t=0) =-\frac{V_0}{L\omega }\...
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Inductor connected to an AC source

The typical textbook treatment of an inductor to which $V=V_0 \sin\ \omega t$ is applied 'shows' the current to be $I=I_0 \frac 1{L\omega} \sin\ (\omega t-\frac{\pi}2)=-I_0\frac 1{L\omega} \cos \omega ...
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What is capacitance, in general?

In a general physical system we generally have through variables and across variables. We also have flow and effort variables. See Vibration and Shock Handbook - Silva. In an electrical network ...
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Current through a capacitor in AC Circuits

The pi/2 term comes about when converting angular measure from degree units to radian units, where 2(pi) radians equals 360 degrees. BTW here is a simple way to visualize current flow through a ...
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Loop of wire in changing magnetic field, open circuit vs. short vs. intermediate

I disagree with your analysis. Irrelevant of the circuit being closed or opened, there is always a voltage difference. The voltage difference between any two points is the opposite of the circulation ...
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1 vote

Classical Harmonic Oscillator in a Magnetic Field

This is a system of linear differential equations with constant coefficients, which can be solved by many approaches. Perhaps, it is worth pointing out that, since the order of the system is $4$, one ...
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1 vote

Classical Harmonic Oscillator in a Magnetic Field

To decouple your equations, you can perform the change of variable $$z=x+iy$$ so that $$m\ddot z=kz-ia\dot z$$ Solutions are exponential, $z=e^{rt}$ with $mr^2=k-iar$. Finally, $x$ and $y$ are given ...
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Having difficulty understanding what the significance of permittivity in free space is

What does ϵ0 mean in real life? It simply means that you are using SI units. In SI units Coulomb's law is $$F = \frac{1}{4 \pi \epsilon_0}\frac{q_1 q_2}{r^2}$$ but in Gaussian units Coulomb's law is $...
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Electric field due to charge within a sphere

Well Electric field will be the part you have plus simple culomb potential. The 1st part is for '0' solutions of poisson equation i.e charge density is zero part which will give you that part and ...
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Deducing the Heaviside-Feynman formulae from Jefimenko's equations

Too long for a comment, and I don't have time to work out the kinks for a complete answer just now: I've attempted to work through this by rewriting Jefimenko's equations as $$ \mathbf{E}(\mathbf{r},t)...
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Intuition of Faraday's law at a boundary

If they are not equal, then magnetic field at boundary should be infinite. Consider the following little rectangular loop $\Gamma$ which straddles the boundary. If $E_{y1} \ne E_{y2}$ then we have ...
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Is there any material available whose strength changes with an input stimulus, say current or magnetic field etc?

Electromagnetic locks might be a solution.
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Is there any material available whose strength changes with an input stimulus, say current or magnetic field etc?

There are polymeres, that change size or shape when stimulated by an electric field They are called Electroactive Polymers. Those materials are used (among others) to create artificial muscles. ...
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Is there any material available whose strength changes with an input stimulus, say current or magnetic field etc?

If strength means elasticity, I am going out on a long shot here: EuRu$_2$P$_2$ and EuPd$_2$Si$_2$ under go a valence transition at some combination of pressure and temperature, for EuRu$_2$P$_2$ (...
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Loop of wire in changing magnetic field, open circuit vs. short vs. intermediate

I'd use $$\mathscr E-L\frac{dI}{dt}=RI$$ In which $\mathscr E$ is the emf due to the changing external magnetic field, as given by the equation you have cited, $L$ is the inductance of the loop and $R$...
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Why is Earth's magnetic field not strong?

Sure, the magnetic field magnitude of Earth, which forms the magnetosphere, is small compared to say, a good bar magnet. However, the magnetic moment of Earth is on the order of $\sim 8 \times 10^{22}...

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