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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Magnetic field in materials with non-constant magnetic susceptibility

I'm quite lost what $B$ and $H$ is. It seams to me that most of the texts I read do quite poor job in explaining them properly. They are explained only in cases when magnetic susceptibility is ...
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250 views

Electromagnetic current for interaction with Dirac spinors

The covariant form of the Dirac equation is given by $$(i\gamma^{\mu}\partial_{\mu} - M) \Psi(x) = 0 $$ Einstein's summation is implied here, $x=(x^0,x^1,x^2,x^3)^T$. I am simply looking for the ...
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121 views

Locations of destructive interference for two spherical waves

I have looked at this, but it did not help with locations. Really this just comes down to mathematical manipulation, which for some reason I fail to see. Here is my paraphrased setup: Consider two ...
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2answers
165 views

Magnetism due to relativity?

So I have been reading in some books that magnetism does not have to be assumed a priori, but can be obtained from the electric field + special relativity. And I have seen how this leads to the common ...
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1answer
720 views

Biot-Savart Law from linear to volume current distribution

Biot-Savart law for a linear current distribution is: $\displaystyle \vec{B}=\frac{\mu I}{4\pi}\int\frac{\vec{dl}\times \vec{r}}{r^{3}}$. In the book that my professor uses says that if we have ...
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4answers
642 views

More about the right hand rule?

We started learning about electromagnetism in physics class, and the Right Hand Rule comes in handy as seems easy to use, but I'm curious as to how it actually works. I guess it's more of a math ...
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1answer
389 views

What are the limits of validity for the magnetic field of a solenoid?

1) The field outside a solenoid is approximated to be zero, because of opposites points "cancelling out". Does this approximation of the field being almost zero become worse as the diameter of the ...
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2answers
189 views

Why does a solenoid's field look like this?

My book gives the above diagram but doesn't provide an explanation why the field looks like that. It simply says that the fields mostly cancel leaving the field above. Could someone walk me through ...
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182 views

How accurately can we measure human electromagnetic fields?

How accurately can our current technological tools measure the human bio-electromagnetic field emitted by a person? Or, to put it differently, does each person have a different electromagnetic field ...
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343 views

Can the $\vec H$-field have non-zero divergence? Does an $\vec H$-field monopole exist?

We know that, $\vec \nabla \cdot \vec B=0$ but $\vec \nabla \cdot \vec H\neq 0$, if $\vec \nabla \cdot \vec M \neq 0$. Does it mean that, in those cases $\vec H$-field has poles although $\vec ...
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632 views

Frequency of rotating coil

Given a coil initially in the x-y plane, rotating at angular frequency $ \omega $ about the x-axis in a magnetic field in the z-direction. This uniform time varying magnetic field is given by $B_z ...
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208 views

What is the energy distribution of light if it has an infinite length?

What is the energy distribution of light if it has an infinite length? I have read in one of the answers here on phys.SE that light has actually an infinite length. But then what is the energy ...
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329 views

Geodesic for Electromagnetic forces

Considering the fact that electrons tend to take the maximum conductance path to flow from A to B. This is justified by saying that $\vec{E}$ is larger in conductors. But once similarly it was thought ...
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585 views

AC Electromagnets

Could someone help explain the uses of AC electromagnets. Wherever I look it says that DC electromagnets create stronger magnetic fields. I understand why AC electromagnets could be used in ...
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3answers
2k views

Work done by Lorentz Force in case of motional emf

In the classical example of the slidewire generator where the rod slides on a U-shaped conductor in a magnetic field, we get a charge separation due to the Lorentz force. The way the induced emf is ...
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1answer
116 views

Is it possible to Vectorialize Quantum Field Theories?

If I take the rules for classical electrodynamics in the covariant formulation (the closest to QFT), I have a tensor that describes the field, $F_{\mu\nu}$. Now we know that we can take some of the ...
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2answers
173 views

Classical electrodynamics formulated in terms of forces

The Newton's law of universal gravitation is described in terms of a force, which is produced by an action at a distance. It also can be described using the concept of a field, and that would be an ...
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1answer
2k views

Deriving expression for motional emf

I'm having a trouble deriving the expression for emf caused by the Lorentz forces in a moving conductor. Consider the following classical example of a slidewire generator which consists of U-shaped ...
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1answer
96 views

Is the sum of the amplitudes of an electromagnetic wave always 1?

It's been a while, and I'm trying to verify my understanding. I remember reasoning (but never being taught) that the sum of the (normalized) electric and magnetic waves in a single electromagnetic ...
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170 views

Is there a differential equation that can represent a circuit with an arbitrary voltage source connected acrorss an antenna?

An RLC circuit with a voltage source can be characterized by the differential equation: $$ LC\;\ddot{I}\left(t\right) + RC\; \dot{I}\left(t\right) + I\left(t\right)-C \;\dot{V}\left(t\right) = 0 $$ ...
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273 views

What happens from the point when we apply potential difference across an inductor?

I am in a serious doubt about it. Consider a battery of emf E and we connect it to an inductor. Initially the switch is open, now we close the switch. My question is: What mechanism happens just ...
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3answers
346 views

Is there energy stored when iron is magnetized?

When a piece of iron is magnetized, and the domains are aligned, Is there energy stored? If so, how much energy is stored? If there is an attraction between that same iron and the source of the ...
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1answer
487 views

Information content of the electrostatic Maxwell equations vs Coulomb's Law vs Poisson's Equation

In electrostatics, we have Maxwell's equations: $\nabla \cdot E = \rho$ $\nabla \times E = 0$ These four equations (the second line standing for three equations) can also be written in terms of the ...
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309 views

Moving the plates of a charged capacitor to calculate energy density - where's the flaw in my argument?

For a charged air-dielectric capacitor, let the plates be parallel to the $xy$ plane, with the top carrying a positive charge $+Q$, the bottom a charge $-Q$. The force on an infinitesimal charge ...
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1answer
672 views

Time reversal and the solutions to Maxwell equations

The standard Lienard-Wiechert potentials describe the electromagnetic field at a point $P$ at time $t$ due to an arbitrarily moving charge $q$ at the retarded time $t-r/c$. An electromagnetic ...
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221 views

Magnetic moment and other invariants of Lorentz System

It's a standard fact that the quantity $\mu = v_{\perp}^{2}/B$ is approximately conserved in the system $d_{t}\mathbf{v} = \gamma (\mathbf{v}\times\mathbf{B})$. The paper Magnetic Moment to Second ...
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1answer
435 views

How to introduce the electromagnetic field in Quantum Field Theory?

There are many ways to introduce the electromagnrtic field in Quantum Field Theory(QFT), such as canonical quantization method which introduces the creation and annihilation oprators by treating the ...
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3answers
289 views

Energy conserved… or not? Confused!

I am confused. Could someone kindly explain what's going on in this question? A particle of mass $m$ and charge $e$ moves in the $x,y-$ plane. There is a constant magnetic field $B$ that points in ...
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1answer
424 views

Capacitance of a conducting disk

I'm reading this(PDF) derivation of the capacitance of a thin conducting disk. The surface charge density of such a disk can be shown to be: $\sigma(r) = \frac{Q}{4\pi a\sqrt{a^2 - r^2}}$ (in ...
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1answer
1k views

The gauge-invariance of the probability current

It is simple to show that under the gauge transformation $$\begin{cases}\vec A\to\vec A+\nabla\chi\\ \phi\to\phi-\frac{\partial \chi}{\partial t}\\ \psi\to \psi ...
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1answer
164 views

Uniqueness and existence of polygonal orbits through a spherical shell

Say we have a spherical wire mesh raised to a negative voltage. Then let's say we release a proton from near the surface, and away from the surface, at some angle and speed. Also, imagine that the ...
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1answer
3k views

Polarizability and the Clausius-Mossotti Relation

There seems to be a fairly large inconsistency in various textbooks (and some assorted papers that I went through) about how to define the Clausius-Mossotti relationship (also called the ...
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1answer
501 views

What breaks the symmetry between the electromagnetic and weak nuclear force?

I know the electromagnetic force is mediated by a photon and the weak nuclear force is mediated by two massive bosons. Are there any other insights into why the masses are so different?
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1answer
121 views

Question about Classical Transport Theory

With a distribution function of the form $f=f_{0} + \vec{v} \cdot \vec{g}$, one can obtain the current density. My question is about $\vec{g}$; we assume a general solution to $\vec{g}$ of the form ...
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2answers
513 views

The direction of the Lorentz Force

We have a square loop (I believe it's called) in a uniform magnetic field between the 2 poles of a permanent magnetic field (green is N, red is S). P is connected to the positive pole of a voltage ...
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1answer
612 views

Passing through the earth's magnetic field

When a projectile such as a jet plane passed through the earth's magnetic field, does an electric current get generated in the projectile? I don't sense it when I fly commercially. Why not?
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1answer
5k views

Optical constants of noble metals: the Drude model for microwave modelling

I have a question regarding the optical constants of noble metals. According to Johnson and Christy's paper Optical Constants of Noble Metals (Phys. Rev. B 6, 4370–4379 (1972), ...
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2answers
14k views

How do you find the magnetic field corresponding to an electric field?

If we are given the electric field $\vec E$ how can I find the corresponding magnetic field? I think I can use Maxwell's equations? In particular, $\nabla\times \vec E= -{\partial \vec B\over \partial ...
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2answers
981 views

Divergence of non conservative electric field

I'm looking for the proof that the 1st Maxwell equation is valid also on non conservative electric field. When we are talking about a electrostatic field, the equation is ok. We can apply the Gauss ...
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2answers
239 views

The earth's magnetic field

This might sound like a silly question. Is it possible for the earth's magnetic field to actually destroy or harm earth? (implosion, crushing etc.)
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1answer
1k views

Does a microwave resonantly excite the rotational levels when cooking?

Wikipedia states there is no resonance absorption, but says at the same time that the molecules are oscillating like dipoles, which is kind of the same if you are exciting the rotational levels ? The ...
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3answers
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formula for transparency of very thin film of metal

Is there formula that gives transparency of very thin film of given metal (tens of nanometers) to the visible light/light of given wavelength ? Which properties of metals are needed for the formula ? ...
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2answers
318 views

Understanding Dynamic light scattering

I'd like to understand the physics of dynamic light scattering experiment. In particular I want to understand the basic relation between relaxation time $\tau_q$ and the diffusion coefficient $D$: ...
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1answer
434 views

Unknown isotope

Problem description: The most common isotope of a single nucleus stripped of its electrons is accelerated through a potential difference of 1225V and fired horizontally into a B-field directed ...
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1answer
287 views

Electric field Fourier decomposition

I have the following decomposition for the electric component of light: $$\renewcommand{\vec}[1]{\mathbf{#1}}\vec{E}(\vec r)=\frac1{4\pi^2} \iint_\Omega \vec A(k_x, k_y) \mathrm{e}^{i \vec{k} \cdot ...
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1answer
164 views

Can you safely draw sparks from the nose of an electrified boy?

From Purcell's Electricity and Magnetism A spectacular conclusion of one of the popular exhibitions of the time was likely to be the electrification of a boy suspended by many silk threads ...
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1answer
1k views

Given charge distribution find electric field

Given a charge distribution $\rho(\vec{r})$ where $\vec{r}$ is the position vector and that $\rho$ is a function of only $|x|$, Why is it that the corresponding electric field $E$ is necessarily of ...
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4answers
5k views

Why does current alternate in an AC generator?

I understand how generators work, but I can't for the life of me conceptualize why the current in an AC generator reverses every 180 degrees!!! I understand that, using the right hand rule, it can be ...
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1answer
195 views

Scattering off a random magnetic field?

Here is another old exam question I'm wondering about: A proton moving in the $-x$ direction encounters a region of space with a magnetic field that randomizes the direction of the particle. The ...
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3answers
3k views

How to make a small tokamak?

$\require{mhchem}$I made a fusor once, like the easy science project: deuterium-deuterium ones, but they're really inefficient. I was wondering if it would be possible to make a small tokamak; not one ...