The classical theory of electric and magnetic fields, both in the static and dynamic case. Also covers general questions about magnets, electric attraction/repulsion etc. Distinct from electrical-engineering.

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Current Density Boundary Conditions and its Implications

According to Ohm's Law, one can say $ \overline{J} =\sigma \overline{E} $ if the field is in a conductor, and $ \overline{J} =0 $ if it's in empty space. Now if we take the surface of a conductor and ...
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72 views

Perpetual motion in electric dipole restricted to a circular path with a charge at the centre

This problem is from Griffith's Introduction to Electrodynamics (4th Ed.), Problem 4.31. A point charge $Q$ is "nailed down" on a table. Around it, at radius $R$, is a frictionless circular ...
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142 views

Force between two current carrying wires: the general case

Assume two straight current carrying parallel wires with currents ($I$ and $I'$) flowing in the same direction, at a distance $R$ from each other. From Ampère's law (and from Biot-Savart as well) it ...
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40 views

Why does this 'Quantum Pinned' superconductor allow easy repositioning

I'm confused by videos such as this (popular demonstration of 'Quantum Levitation'): https://www.youtube.com/watch?v=Ws6AAhTw7RA So my current understanding of superconductors is that when in the ...
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71 views

Motion of a charged particle in a “solid” charged sphere (accounting for radiation)

Consider a particle (point charge) with charge $q$ and mass $m$ that crosses into a uniformly charged sphere (with charge $Q$ and radius $R$). The trajectory of the particle is a diameter of the ...
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76 views

Calculating the magnetic permeability of a known plasma

I have a plasma, of which I know the composition, temperature, exact electron/ion/particle densities. How can I then calculate a theoretical permeability of the plasma. Is this even possible? I ...
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50 views

Time-dependent electric and magnetic field between two point charges

I would like to get expressions for the time-dependent electric and magnetic fields in the region around two moving point particles. I can't see how this is possible. Clearly you can't use Gauss' Law ...
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79 views

Phased non linear array antenna - First Sidelobe

I have a problem I cannot seem to solve and I REALLY need some help. It's about phased-array antennas whose dipoles are not equally spaced, not equally phased, not equally fed (amplitude). Let's ...
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182 views

Proof that electric and magnetic fields in a EM wave are perpendicular

Is there a general proof, that for electromagnetic waves the magnetic and electric fields are perpendicular? The only ones I can find only focus on plane waves.
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54 views

Physical significance of toroidal moments

The electric field of a toroidal dipole moment $\vec t$ is the same as the electric field of a electric dipole moment $\vec p$, except that it is scaled with the factor $ik$. The $i$ makes the ...
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95 views

What does the net force do with this droplet in magnetic field?

Consider a spherical droplet with radious $R_d$ which is coated with an immiscible ferrofluid with volume equal to $2v_f$. While the droplet is in rest on a surface, if I approach two magnets in ...
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28 views

Building huge magnetic field gradient

Looking at how MRI works, I came across the fact that the spatial resolution depends on the magnetic field gradient, this gradient being created by "gradient coils". I was not able to find what the ...
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57 views

What is “above” and what is “below” the surface of a sphere?

When studying Electromagnetism using D.J. Griffith's Introduction to Electrodynamics, the boundary conditions for the electric potential across a surface charge density are expressed using the normal ...
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100 views

Electric and magnetic field in a black hole

I have many questions about this topic: Does the electric field of a charged black hole look like this? I mean how can it have an electric field if nothing can escape from a black hole, and what is ...
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128 views

Stress Energy Tensor of EM Field

Stress energy tensor for electromagnetic field is given by $$T^{\mu\nu}=\frac1{4\pi}(F^{\mu\alpha}F^{\nu}{}_\alpha-\frac14 g^{\mu\nu} F_{\alpha\beta}F^{\alpha\beta}).$$ My textbook (unpublished ...
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61 views

Electrodynamics boundary conditions with complex $\epsilon$ and $\mu$

I wonder if the usual derivation for boundary conditions at an interface given in EMT textbooks hold for complex permittivity and/or permeability? Do the fields carry phase information themselves(i.e. ...
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149 views

Odd experiment results (electromagnetics)

Okay, a bit of background. So I'm working on a linear accelerator (you might know it as a Gauss rifle), and I had worked through the equations I thought I needed (Magnetic force, displacement, etc.) ...
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86 views

Induced emf in a circular conducting wheel

Consider a conducting wheel with $N \in \mathbb{N}$ spokes which is completely in a homogenous magnetic field $\vec{B}$ perpendicular to the wheel plane. ...
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29 views

Categorization of electromagnetic solitons?

I've seen over the years several mentions of electromagnetic solitons that appear in the high-intensity regime (where vacuum polarization becomes important). Some of these are coupled with plasmas, ...
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81 views

Momentum of capacitor in a uniform magnetic field

We are observing ideal, charged, parallel plate capacitor placed in uniform magnetic field parallel to plates. Whole system is at rest and isolated (we have forces that hold plates separated, but net ...
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58 views

Strength of Magnet in Magnetic Bearings

While reading about magnetic bearings, one reads about passive/active magnetic bearings. By passive, one means no electric current is put into the bearing for attaining magnetic levitation/flux. In ...
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59 views

Does a conducting wire give off measurable radiation?

In the Drude model (semiclassical, but should still apply here I think), the conducting electrons are in a constant electric field, and, in between collisions with the lattice ions (that happen, on ...
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57 views

Momentum operator of a particle in an electromagnetic field

In quantum mechanics, to all observables correspond some self-adjoint operators. In the absence of an electromagnetic field the momentum operator is clearly $\vec{P}:=\frac{\hbar}{i}\vec{\nabla}$. ...
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123 views

Magnetic Force on a Ferromagenetic Material

I am currently working on a project involving solenoids, and I needed a force(Newtons, not a measure of magnetic field strength) equation. What I came up with after some digging around on the ...
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47 views

About memory effect in E&M when E and B field has dependence in the history of E and B fields

How should one define the memory effect in E&M formally? What is the physical way to visualize the memory effect? How should one understand it intuitively?
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94 views

Electrodynamics using exterior calculus

Can anyone suggest resource for full course of electrodynamics using exterior calculus?
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102 views

How to properly construct the electromagnetic tensor in curved space-time? (Part II)

In this question, I am testing what was previously discussed. I can't seem to get my results to match D'Inverno's electromagnetic tensor for a charged point (page 239 of his book - Introducing ...
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152 views

One question about derivation of Maxwell equations

I saw the following way of derivation of Maxwell equations: author starts from Lorentz transformations for the 3-vector of force, then he applies them for the Coulomb law, after that gets the Lorentz ...
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173 views

The anapole moment, derivation from Dirac current density

Basically I am looking for a way to expand the electromagnetic interaction energy $W = A_{\mu}j^{\mu}$ (both $A$ and $j$ obtained from the Dirac equation) similar to the classical expansion in ...
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110 views

Vector potential and gauge in electromagnetism

In a paper by Zimmerman [JOURNAL OF APPLIED PHYSICS 114, 044907 (2013)], it is stated that the Lorenz gauge in electromagnetism is the only gauge with real physical meaning. How do I reconcile this ...
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30 views

Magnetic fields and forces, Gravitation fields and forces

Is a current carrying wire affected by the magnetic field that it produces? In other words, will a current carrying wire be acted on by a magnetic force produces by its own magnetic fields? Is a mass ...
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67 views

What are the parameters for Pauli's repulsion pseudo-force?

I have found the following formula for the repulsion potential due to the overlap of the electron clouds arising from Pauli's exclusion principle: $$V = A\exp(-r/\phi)$$ where r is the distance ...
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371 views

Electromagnetism - Proof of the Uniqueness theorem for an external problem

In the electromagnetic Uniqueness theorem, we consider a volume $V$ enclosed by a surface $S$. It is initially assumed that two different fields are valid solutions for the Maxwell's equations with ...
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250 views

Drift velocity of electrons in a superconducting loop

Do electrons travel at the Fermi velocity in a superconducting loop? For metals the Fermi velocity seems to be around $10^6$ m/s. So would electrons (in a Cooper pair) travel around the loop at this ...
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223 views

Huggins Displacement Theory and Retrocausality

I was looking at the Wikipedia entries on Time Travel and the Grandfather paradox and noticed a paragraph on the so-called Huggins Displacement Theory. I haven't been able to find the source although ...
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269 views

Absolute permittivity and permeability of free space

I'm reading about the propagation of EM waves in vacuum. We define the wave equation using two constants: $\epsilon_0$ and $\mu_0$. Of course they are absolute permittivity and absolute permeability ...
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445 views

Maxwell equations and symmetry

Do the full inhomogeneous Maxwell equations obey parity (P) and time reversal (T) symmetry separately or only the full CPT symmetry? I believe the homogeneous Maxwell equations obey parity and time ...
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1k views

Calculating the electro magnetic field strength needed to repel a permanent magnet

I have a design where a permanent magnet is placed on top of an electromagnet. When the electromagnet is powered off, the permanent magnet is attracted to the iron core of the electromagnet. When the ...
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106 views

Hidden momentum

I'm trying to learn about hidden momentum. After reading what I could find with a google search, I understand that it is equal to the momentum carried by radiation, calculated with the Poynting ...
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495 views

What is the minimum physical distance between two electrons?

If electrons repel, then it seems to me that energy is required to decrease the distance between two electrons. Since energy and mass are equivalent, adding energy to a system also adds some mass. ...
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490 views

Electromagnetic duality

A key aspect of modern physics is the mapping of theories or different descriptions of a theory into a one-to-one correspondence. As I am trying to further understand the electromagnetic field tensor, ...
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265 views

Help Understanding Equation for Characteristic Time of Induced Magnetic Field

I am reading this book, the part in particular about Eddy-current separation starting at Page 246, in it there is an equation for calculating the "characteristic time with which the induced magnetic ...
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260 views

Hall effect with similar positive and negative carriers?

The Hall effect includes the transverse (to the flow of current) electric field set up by the charges which accumulate on the edges, to counter the magnetic component of the Lorentz force acting on ...
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50 views

Is the electrical signal delivered to a load by a receiving antenna always $\propto \frac {\partial}{\partial t}$ of the $\vec{E}$ or $\vec{B}$ field?

A time-varying $B(t)$ field through a loop antenna induces a voltage proportional to $\dot{B}(t)$. A Hertzian dipole along a time-varying $E(t)$ field also induces a voltage across a load--while I ...
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70 views

Gravity and Larmor effect

I have a Q: Does "Equivalent Principle" and "Larmor effect" imply that the charged particle should radiate electromagnetic wave if it is at rest in uniform gravitational field (like it is at rest on ...
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504 views

Are the poles of a hollow electromagnet on the ring or in the center?

Question: Will this work as I've shown it here, more or less, or will the iron cylinder being hollow produce results not shown? Topic: I'm experimenting with magnetic fields and have been testing ...
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2k views

How to calculate magnetic pole strength?

I have 2 magnets. I need to know the force between them. In a previous Phys.SE question, conclusion was: we need to use a dipole-dipole interaction equation, which included m, which the magnetic ...
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40 views

How do we generalize limitations on the propagation speed of sinusoidal waves to limitations for transmitting any kind of information?

Our calculations on EM waves basically deal with harmonic waves and through such calculations and relations, we derive some relations and limitations for wave like phenomena. Of these relations are ...
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100 views

value of $\omega$ in nonlinear equation

In this article the authors wrote a nonlinear equation as $$-\frac{\partial^2 \phi}{\partial t^2}+ \nabla \phi= \phi+ \sum_{k=2}^\infty g_k \phi^k$$ They have scaled the time as, ...
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92 views

Consistency of equation with special relativity?

The following is the equation which, I want to know, if it is valid in relativistic domain. Consider two equal charges moving in same direction with velocity $v$ and charge $q$ at a separation of ...