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Magnetic field of a uniformly moving charge paradox

The force between two charges has both an electric and magnetic component. The total force must be calculated using $${\bf F} = q({\bf E} + {\bf v}\times {\bf B})\ ,$$ where the E- and B-fields are ...
ProfRob's user avatar
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Magnetic field of a uniformly moving charge paradox

The magnetic lorentz force itself is not covariant under the change of coordinates, but the total force(general lorentz force) including the electric force=qE is covariant. This is one of the ...
guo xiao's user avatar
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Determinate the direction of the current of current-carrying wire by the right-hand rule

Each of the wires will generate its own magnetic field and you could calculate those magnetic fields individually, and use the right-hand rule to work out in which direction the magnetic fields ...
ProfRob's user avatar
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Determinate the direction of the current of current-carrying wire by the right-hand rule

Ampere's law: According to Ampere's law, the magnetic field line integral around a closed path is equal to the product of the magnetic permeability of that space and the total current through the ...
Qwerty's user avatar
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Why is Magnetism at the centre of a bar magnet zero?

The question is easy to answer if you realize that the magnetic field of a permanent magnet is caused by the alignment of the magnetic dipoles of electrons in the material. It is sufficient to ...
HolgerFiedler's user avatar
1 vote

Mathematical proof that bound currents do not result in accumulation of charge?

Divergence of polarization current $\partial_t \mathbf P$ does not vanish in general, so actually there can be accumulation of electric charge on a dielectric surface, or near a free charge inside the ...
Ján Lalinský's user avatar
-2 votes

Why is Sun's atmosphere hotter than its surface?

I think that the high gravity of the Sun imperceptibly shortens wavelengths which loads energy into them. This explains why the Sun's surface is cooler than its corona. When those waves reach a ...
Paul's user avatar
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Magnetic field of a solenoid with linear dielectric from a geometric series

I will attempt to answer my own question, but I am not quite convinced by this answer. An initial current $I_0$ produces a field $B_0=\mu_0 n I_0$, which leads to an initial magnetization of $M_0=\...
thedude's user avatar
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Mathematical proof that bound currents do not result in accumulation of charge?

This is a good question as too often such issues are dealt with by hand waving. Take a look at https://en.m.wikipedia.org/wiki/Covariant_formulation_of_classical_electromagnetism# (ignore reference 5, ...
my2cts's user avatar
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2 votes

Mathematical proof that bound currents do not result in accumulation of charge?

It feels to me like there might be some confusion between different surfaces here. I will not try to show tricks of how to prove bound currents do not lead to charge accumulation, and what happens ...
Cryo's user avatar
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Force between two current carrying conductors

what about L the length of the wires? what happens if I increase the length of wire A and keep the length of wire B the same as before? doesn't that mean that the force on A is now greater? Yes, the ...
The Photon's user avatar
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Force between two current carrying conductors

In the static case Newton's third law applies and whatever change in the forces acting on wire $A$ due to wire $B$ is experienced by the forces on wire $B$ due to wire $A$. Please also note that in ...
Farcher's user avatar
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What are the conditions under which these equations hold for dielectric and magnetic materials?

I've found the answer! My teacher didn't answer this question clearly so I asked this question a few days ago, but then the teaching assistant answered it. if $\frac{\vec{D}}{ε_0}$ represents the ...
smallerstar's user avatar
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What are the conditions under which these equations hold for dielectric and magnetic materials?

By definition: $$\textbf{D} = \epsilon_0 \textbf{E}_0 + \textbf{P} \ \ \ (1)$$ $$\textbf{B}_0 = \mu_0 ( \textbf{H} + \textbf{M}) \ \ \ (2)$$ these statements are always true no matter what materials ...
psychgiraffe's user avatar
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How strong would Earth's magnetic field be if it was ferromagnetic and didn't have the high temperature?

If the Earth's core were a ferromagnet, the magnetic field at the Earth's surface would be a couple of hundred times stronger than the magnetic field on Jupiter's surface, but at a radius ...
David Bailey's user avatar
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Ultracold magnetic traps for uranium enrichment

In principle yes: One can enrich elements with magnetic traps. Even other traps are in principle feasible to enrich elements (Magneto-optical traps). HOWEVER (this is a big however!) typically, ...
kai90's user avatar
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4 votes

How do Electric and magnetic fields generate each other (mathematically)?

It is commonly believed that a changing magnetic field generates a rotation of an electric field. This is not correct. A changing magnetic field and the rotation of an electric field are equivalent ...
my2cts's user avatar
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2 votes

The partition function of a particle in a magnetic field diverges. Why?

Making everything dimensionless so that $\hbar=1$: $$ H = \frac12(p-A)^2\\ A = \frac\omega2(-y,x) $$ with $\omega$ the cyclotron frequency, the usual theory of Landau level gives the spectrum of the ...
LPZ's user avatar
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2 votes

How do Electric and magnetic fields generate each other (mathematically)?

Towards the path of universal conservation of energy in an energetically isolated system, Lenz (1834) formulated his law as a principle avoiding self-amplification of magnetic systems: The fields of ...
Roland F's user avatar
1 vote
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Induced Electric field due to magnetic field in Faraday experiment

To start with question 3), the case where there is no coil but just a magnet that you move through empty space, as @user1245 asked in questionquestions/343447: is there a force opposing the motion? ...
Jos Bergervoet's user avatar
4 votes

How do Electric and magnetic fields generate each other (mathematically)?

From a spatial point of view, it very much looks like a changing electric field generates a changing magnetic field. And vice-versa. But this raises the problem of causality and locality. Its general ...
Mozibur Ullah's user avatar
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Does a single moving charge produce magnetic field in an empty universe?

A moving point charge always produces time dependent magnetic and electric fields according to the Maxwell equations and special relativity.
my2cts's user avatar
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Does a single moving charge produce magnetic field in an empty universe?

It is always interesting that people do not think about the fact that an electron is not only an electric charge and therefore has an electric field, but is also a magnetic dipole and therefore always ...
HolgerFiedler's user avatar
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How do Electric and magnetic fields generate each other (mathematically)?

Linked differential equations may reinforce one another leading to unbounded exponential growth - but they do not have to. For example, the linked equations $\displaystyle y = \frac {dx}{dt} \\ \...
gandalf61's user avatar
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1 vote

The partition function of a particle in a magnetic field diverges. Why?

I may have solved my issue (thanks to @By Symmetry for the hint). Indeed, the divergence appears to be related to the infinite area covered by the quantum system in 2D. We could consider the similar ...
Cham's user avatar
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1 vote

Deriving the Curl of the Magnetic Field, Role of the Nabla Operator

The BAC-CAB identity does not apply here as $\nabla$ is an operator and not a vector. The important lesson is that you cannot assume, in general, that vector identities hold for $\nabla$. The correct ...
Vincent Thacker's user avatar
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Confusion regarding magnetic moment

Imagine if you have two dipoles that are right next to each other pointing in opposite directions. Such a configuration has no dipole moment, and at long range the field is a "quadruple" ...
quantumwave's user avatar
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Does a single moving charge produce magnetic field in an empty universe?

According to our current understanding of electromagnetism, a single moving charge in an empty universe would not produce a static magnetic field in the reference frame where the charge is at rest. ...
Adonay Gandolffi's user avatar
3 votes
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Landau levels in symmetric gauge, what is the constraint on the quantum numbers?

I have looked at this problem in the context of the Weyl equation. Below is a word-for-word extract from my notes, so it is not exactly what you want, but the square of the Weyl operator is the ...
mike stone's user avatar
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Magnetic Field in the plane of a circular current carrying loop

So your argumentation using Amperes law and rotational symmetry does hold. But as mentioned in the comments you need to take care of the direction you are looking at. Your argumentation tells you, ...
Zaph's user avatar
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3 votes

Are all recursive interactions between electric and magnetic fields always orthogonal to each other?

There is not a causal relation between electric and magnetic fields. According to Jefimenko's Eqs (https://en.wikipedia.org/wiki/Jefimenko%27s_equations), $\vec E$ ($\vec B$) is caused by charge, and ...
JEB's user avatar
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Are all recursive interactions between electric and magnetic fields always orthogonal to each other?

Not necessarily. Consider a waveguide, the TM and TE modes it presents have $\mathbf{E}$ and $\mathbf{H}$ in general not orthogonal to each other. The functional form of the fields depends on the ...
agaminon's user avatar
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1 vote

Quantum angular momentum of a particle in an homogeneous magnetic field

Here I try to give some results that do not rely on the B field being uniform, or a particular choice of gauge. Starting from the definitions of the quantum operators $$ \vec{M} = \vec{r} \times \vec{\...
Bio's user avatar
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Quantum angular momentum of a particle in an homogeneous magnetic field

I think I got it! The commutator (10) is the quantum version of the classical time derivative of the angular momentum (classical expressions below): $$\tag{A} \vec{\mathrm{M}} = \vec{\mathrm{r}} \...
Cham's user avatar
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4 votes
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Potential difference in a ring

The cell's job is to create an electric field that makes the "free" electrons inside a metal move. You don't need a positive and negative end in the case you describe, because the electric ...
Wolphram jonny's user avatar
1 vote

Can the Dzhanibekov Effect celestial bodies, like Earth’s crust and/or core causing the flipping of magnetic poles?

As you note, Earth is spherical (and already spinning on an axis). So, the three moments of inertia required for the Dzhanibekov Effect are not very distinct. Without some massive additional force ...
Wookie's user avatar
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1 vote

Are there losses in an ideal transformer?

For an ideal transformer, the core is assumed to be linear with infinite permeability. As a result, the energy stored in the magnetic core $\int\frac{B^2}{2 \mu}d\tau $ is zero. There is therefore no ...
Vincent Fraticelli's user avatar
1 vote

Are there losses in an ideal transformer?

Let's consider an open secondary, so that you do not have the complication of a current flowing in it. The primary winding is connected to an oscillating voltage source and some sort of limiting ...
Peltio's user avatar
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3 votes

Are there losses in an ideal transformer?

An ideal transformer is by definition lossless. This is why it is called "ideal": the ideal model ignores all the real-life losses that transformers experience. These include resistive ...
niels nielsen's user avatar
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A "Classical" Explanation of The Meissner Effect?

Superconductivity does not produce the Meissner effect on a topology of a sphere just because of the fact, that the 2-sphere cannot carry arbitrary, continuous, non-singular vector fields. The ...
Roland F's user avatar
4 votes
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Why are the formulae for the electric flux density and the magnetic flux density fundamentally different?

Functionally, $\mathbf{E}$ and $\mathbf{B}$ are analagous because they both represent the total field, taking into account both free and bound sources. However, mathematically, we have $\mathbf{E}\sim\...
Vincent Thacker's user avatar
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What is the typical value of magnetic dipole of a magnet?

$10 \;\text{mT}$ was the value given by FSU's High Magnetic Field lab, though it depends on the size of the magnet and its composition. Source: https://nationalmaglab.org/about-the-maglab/around-the-...
basil's user avatar
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