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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Trouble with the Lorentz law of force: Incompatibility with special relativity and momentum conservation?

In Physical Review Letters, there was a paper recently published: Masud Mansuripur, Trouble with the Lorentz Law of Force: Incompatibility with Special Relativity and Momentum Conservation, Phys. ...
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2answers
1k views

How does one show using QED that same/opposite electric charges repel/attract each other, respectively?

Why do same charges repel each other and opposite charges attract each other (please explain the phenomenon using real laws of nature (QED) not with the approximation model)?
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3answers
6k views

Faraday's law - does the induced current's magnetic field affect the change in flux?

I've had this conceptual problem with Faraday's law and inductance for a while now. Take the example of a simple current loop with increasing area in a constant field (as in this answer). So ...
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2answers
2k views

Why are EM waves transverse?

I was reading Griffiths' Introduction to Electrodynamics, specifically the section on plane waves. I can see that if we want a transverse wave traveling in the $z$ direction that we are only going to ...
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6answers
4k views

How do EM waves propagate?

I have read about this and what I surmise is that when charged particles such as electrons accelerate they produce time-varying electric fields. These E-fields produce H-fields and the process goes ...
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2answers
597 views

Is there any idea why the electric charges of electron and muon are equal?

Is there any idea explaining why the electric charges of electron and muon are equal? Edit: The total charge of a particle is proportional to the integral of its own electric field flow through the ...
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4answers
948 views

Faraday's paradox

I have studied that Faraday's law of induction and motional emf are two different lines of thinking but are essentially same. But then, how can Faraday's paradox be explained by Faraday's law of ...
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3answers
633 views

Do objects have energy because of their charge?

My gut feeling tells me things should have energy because of their charge, like they have energy because of their mass. Is this possible? Has it been shown? If not then what is missing to make such ...
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3answers
1k views

Shine a light into a superconductor

A type-I superconductor can expel almost all magnetic flux (below some critical value $H_c$) from its interior when superconducting. Light as we know is an electromagnetic wave. So what would happen ...
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249 views

What symmetry is associated with conservation of Lipkin's zilch?

The 'zilch' of an electromagnetic field is the tensor $$ Z^{\mu}_{\ \ \ \nu\rho}=^*\!\!F^{\mu\lambda}F_{\lambda\nu,\rho}-F^{\mu\lambda}\,{}^*\!F_{\lambda\nu,\rho} \tag1 $$ given in terms of the ...
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7answers
2k views

Why aren't there compression waves in electromagnetic fields?

I just started learning about optics, and in the book I'm reading they explain how the electrical field caused by a single charged particle could be described by a series of field lines, and compare ...
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1answer
295 views

How do higher-order optical chiralities look like?

The optical chirality of the electromagnetic field is a conserved quantity, analogous to the energy density, linear momentum density, and angular momentum density, which describes how chiral the EM ...
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4answers
1k views

Why doesn't more light bounce off of things in the manner of sound?

If I'm sitting in the den with my door slightly cracked, I can hear my wife washing dishes in the kitchen down the hall. But why can't I also 'see' images of her washing dishes if, say, I looked up on ...
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2answers
1k views

If you run an electric current through a wire loop, do the accelerated charges radiate?

Does an accelerated charge always radiate? For example the current electrons in an electric circuit when moving through a turn they are accelerated, do they radiate because of that acceleration? If ...
9
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1answer
750 views

Recovering all of Maxwell's equations from the variational principle

Whether you can get the first couple of Maxwell equations from a variational principle? In the second volume of the Landau theoretical physics said that it is impossible.
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4answers
5k views

Radio antennas that are much shorter than the wavelength

From my limited experience with ham radio when I was a kid, I expect transmitting and receiving antennas to have lengths that are on the same order of magnitude as the wavelength, and in fact I recall ...
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2answers
4k views

Is it possible to kill a human with a powerful magnet?

I'm asking in terms of physics. Can powerful magnetic induction rearrange spins of my body in such way I will die? How? Or maybe it can rip all iron from me, which would make my blood cells useless? ...
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5answers
3k views

Relativity and Current in Wire

If an observer is stationary relative to a current-carrying wire in which electrons are moving, why does the observer measure the density of moving electrons to be the same as the density of electrons ...
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2answers
784 views

Is there a Hamiltonian for the (classical) electromagnetic field? If so, how can it be derived from the Lagrangian?

The classical Lagrangian for the electromagnetic field is $$\mathcal{L} = -\frac{1}{4\mu_0} F^{\mu \nu} F_{\mu \nu} - J^\mu A_\mu.$$ Is there also a Hamiltonian? If so, how to derive it? I know how ...
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683 views

Vector Potential for Magnetic field when the field is not in simply-connected region

According to Poincare's Lemma, if $U\subset \mathbb{R}^n$ is a star-shaped set and if $\omega$ is a $k$-form defined in $U$ that is closed, then $\omega$ is exact, meaning that there's some ...
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2answers
1k views

Decomposition of a vectorial field in free-curl and free-divergence fields

Is it always possible to do that decomposition? I'm asking it because Helmholtz theorem says a field on $\mathbb{R}^3$ that vanishes at infinity ($r\to \infty$) can be decomposed univocally into a ...
6
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2answers
516 views

Does a rotating disk develop a potential difference between the centre and rim?

This stems from thinking about the question If a perfect conductor where to move what happens to the electrons?. Suppose we have a rotating disk with no external magnetic field, so this is not a ...
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2answers
351 views

Faraday's law for a current loop being deformed

I'm working through Jackson's Classical Electrodynamics text (3rd version, chapter 5.15) about Faraday's law: Faraday's law is pretty familiar: $\int_c E \cdot dl = -\frac{d}{dt}(\int_s B \cdot n ...
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1answer
267 views

What is the action for an electromagnetic field if including magnetic charge

Recently, I try to write an action of an electromagnetic field with magnetic charge and quantize it. But it seems not as easy as it seems to be. Does anyone know anything or think of anything like ...
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1answer
461 views

Batteries and voltage?

The voltage of a battery gives you the difference in potential energy 1C of charge would have at the positive terminal vs the negative terminal. If I connect a wire to both terminals, the battery ...
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4answers
7k views

How does inductor store energy in the magnetic field?

I learnt from book that magnetic field does no work because the force is proportional to $\vec{v}\times\vec{B}$ where $\vec{v}$ is the particle velocity. That vector cross product is always at right ...
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3answers
1k views

How does a single charge produce magnetic field?

I have studied in Introduction to electrodynamics (Griffiths) that magnetic field is actually due to effects of relativity unequal Lorentz contraction of the positive charge and negative lines, a ...
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1answer
906 views

Retrieving Maxwell's equations from the minimum action principle

I'm currently working at the start of Alexei Tsvelik's book Quantum Field Theory in Condensed Matter Physics. I'm kinda stumped on a few essential steps. Starting with the action: $$S = \int dt \int ...
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2answers
1k views

An example which contradict to Newton's 3rd law?

Let a,b be two charged particles. $$\vec{r}_a(0)=\vec{0}$$ $$\vec{r}_b(0)=r\hat{j}$$ $$\vec{v}_a(t)=v_a \hat{i}$$ $$\vec{v}_b(t)=v_b\hat{j}$$ In which both $v_a$ and $v_b$ $<<c$. Then ...
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1answer
549 views

How the inverse square law in electrodynamics is related to photon mass?

I have read somewhere that one of the tests of the inverse square law is to assume nonzero mass for photon and then, by finding a maximum limit for it , determine a maximum possible error in ...
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5answers
7k views

What are electromagnetic fields made of?

I am trying to understand electromagnetic fields so I have two question related to them. What is a electromagnetic field made of? Is it made of photons / virtual photons? How about a static electric ...
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5answers
822 views

How would I go about detecting monopoles?

A question needed for a "solid" sci-fi author: How to detect a strong magnetic monopole? (yes, I know no such thing is to be found on Earth). Think of basic construction details, principles of ...
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4answers
1k views

How does charge work if photons are neutral?

How can an electron distinguish between another electron and a positron? They use photons as exchange particles and photons are neutral, so how does it know to repel or attract?
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2answers
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Why does electromagnetic induction actually occur?

In my book, it is written that "An emf is induced in a loop when the number of magnetic field lines that pass through the loop is changing" (Faraday's law) I understand that whenever there is a ...
6
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1answer
2k views

Degeneracy Pressure, What is it?

There has been numerous question, some violent even in physics@SE regarding PEP and EM forces. But what baffles me is what is degeneracy pressure? I know there are 4 fundamental forces- EM, gravity, ...
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2answers
9k views

What is the difference between Biot-Savart law and Ampere's law?

What is the difference between these laws? Which law is more useful? When to use Ampere's law and when to use Biot-Savart law?
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3answers
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What does this quote about the four dimensional divergence of an antisymmetric tensor mean?

In the beginning, God said that the four dimensional divergence of an antisymmetric second rank tensor equals zero and there was light. Can someone explain what is the meaning of this quote by ...
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4answers
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Confusion between Electric field and Magnetic field of a charged particle.

Consider a charged particle (electron or proton) at rest. It is surrounded by its own electric field. Now consider an electron moving with certain velocity (less than speed of light), Still is there ...
4
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3answers
558 views

How to understand “accelerating charge radiate” using intuition? [duplicate]

While I know that accelerating charges produces EM radiations (at least in lots of cases), most discussion about this matter only focuses on which kind of situation will emit EM radiations and which ...
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2answers
1k views

Which mathematical operation does the right hand rule for current come from?

I am currently wondering about this famous rule: Where does it come from mathematically that when you point with your thumb in the direction of the current, your curved fingers will point in the ...
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3answers
624 views

The magnetic field of a magnetic monopole

Let us define the magnetic field $$\vec{B} = g\frac{\vec{r}}{r^3}$$ for some constant $g$. How can we show that the divergence of this field correspond to the charge distribution of a single magnetic ...
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3answers
3k views

Why does light in a room not form constructive and destructive interference patterns?

This is something that I have wondered for a long time. How come when I walk around why do I not see random black spots where light has collided destructively and bright spots where it has collided ...
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3answers
145 views

Does waving a magnet around create light?

If I wave around a bar magnet, the magnetic field in the space around it changes. Is this enough to go through the whole speed of light derivation implying that the motion creates an electromagnetic ...
3
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2answers
113 views

What happens when a field turns on or off?

Short Setup I am curious about the the mechanics of fields, whether electromagnetic, gravitational, etc. So as a specific example in order to simplify (hopefully) how to ask this question, consider ...
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5answers
691 views

Why doesn't this perpetual motion machine work?

Imagine a non-magnetic tube bent into the shape of a triangle, with two sides forming downhill ramps, and the third side connecting the two ramps. Through this tube travels a metal ball, which is ...
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2answers
5k views

Electric field and electric potential of a point charge in 2D and 1D

in 3D, electric field of a piont charge is inversely proportional to the square of distance while the potential is inversely proportional to distance. We can derive it from Coulomb's law. however, I ...
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2answers
423 views

Does constraint for speed of Electric and magnetic fields violates Conservation of momentum or Newton's third law?

I'm just a beginner so bear with me. Consider two frames at rest wrt to each other separated by distance enough for light to take a minute or so. At a given instant we create two large dipoles by some ...
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1answer
147 views

Ampère's law from Biot-Savart law for linear currents with multivariate calculus

My book, W.E. Gettys's Physics, starts from the Biot-Savart law $d\mathbf{B}=\frac{\mu_0}{4\pi}\frac{Id\boldsymbol{\ell}\times\hat{\mathbf{r}}}{r^2}$, ...
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3answers
2k views

Exciting Surface Plasmon-Polaritons with Grating Coupling

I'm very new the topic of SPPs and have been trying to understand this particular method of exciting surface plasmons using a 1D periodic grating of grooves, with distance $a$ between each groove. If ...
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2answers
9k views

Derivation of the Biot-Savart Law [duplicate]

Can someone provide a derivation of the Biot-Savart law for electromagnetic induction? To be clear, $$ d\vec{B}~=~\frac{\mu_0}{4\pi}\frac{I d\vec{\ell}\times \vec{r}}{r^3}. $$ Is there a simple way ...