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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“Reality” of EM waves vs. wavefunction of individual photons - why not treat the wave function as equally “Real”?

In thinking how to ask this question (somewhat) succinctly, I keep coming back to a Microwave Oven. A Microwave Oven has a grid of holes over the window specifically designed to be smaller in ...
14
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7answers
11k views

What does it take to understand Maxwell's equations?

Assume I want to learn math and physics enough to reach a level where I understand Maxwell's equations (The terms and reasoning in the equations I.e. why they "work"). What would I have to learn in ...
13
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3answers
3k views

Maxwell in multiple dimensions: What happens to curl?

I read this answer a while ago, and while thinking about $\nabla$, I realized something. Since the cross product can be written as a determinant, in higher dimensions we require extra vector inputs. ...
9
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3answers
2k views

Are Classical Field Theory and Quantum Mechanics of a single particle (nonrelativistic or “classical”) limits of Quantum Field Theory?

Recently I talked about QFT with another physicist and mentioned that the Quantum Field Theory of a fermion is a quantisation of its one-particle quantum mechanical theory. He denied this and ...
36
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4answers
4k views

How wrong are the classical Maxwell's equations (as compared to QED)?

Now, I don't really mean to say that Maxwell's equations are wrong. I know Maxwell's equations are very accurate when it comes to predicting physical phenomena, but going through high school and now ...
11
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1answer
536 views

Formulation of Transformation optics using a Material Manifold

Dear Community, recently, Transformation optics celebrates some sort of scientific revival due to its (possible) applications for cloaking, see e.g. Broadband Invisibility by Non-Euclidean Cloaking ...
12
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2answers
844 views

Is there a strong force analog to magnetic fields?

In special relativity, magnetism can be re-interpreted as an aspect of how electric charges interact when viewed from different inertial frames. Color charge is more complex than electric charge, but ...
5
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1answer
494 views

How do you go from quantum electrodynamics to Maxwell's equations?

I've read and heard that quantum electrodynamics is more fundamental than maxwells equations. How do you go from quantum electrodynamics to Maxwell's equations?
27
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6answers
3k views

Is a suit that hides a soldier's heat signature fundamentally possible?

I recently played "Crysis", a game where the protagonist wears a suit that allows the player to hide both himself and his heat signature. Then I watched Iron Man 3, where a kid suggests that Tony ...
13
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4answers
2k views

Fundamental invariants of the electromagnetic field

It is a standard exercise in relativistic electrodynamics to show that the electromagnetic field tensor $F_{\mu\nu}$, whose components equal the electric $E^i=cF^{i0}$ and magnetic ...
3
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1answer
10k views

Physical meaning of Maxwell's equations and origin of EM waves

Is it possible to describe the physical meaning of Maxwell's equations and show how they lead to electromagnetic wave, with little involvement of mathematics ?
1
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5answers
801 views

Can you depict the electron's electromagnetic field?

I've had a number of discussions with individuals about electromagnetism. A recurring issue concerns the distinction between field and force, and seems to be associated with the lack of unification in ...
23
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5answers
2k views

Why do we deal only with large scale magnetic fields in astrophysics, and not electric fields?

In astrophysics there is a lot going on about strong, large scale magnetic fields: in stars (prominences), magnetic dynamos, compact accretors collimating jets, etc. There's even a special ...
23
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6answers
17k views

What non-metal is attracted by a magnet?

Are there any non-metal objects that are attracted by magnets?
12
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5answers
1k views

Making symmetry between E and B fields manifest in Lagrangian

Maxwell's equations are nearly symmetric between $E$ and $B$. If we add magnetic monopoles, or of course if we restrict ourselves to the sourceless case, then this symmetry is exact. This is not ...
11
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6answers
8k views

What is canonical momentum?

What does the canonical momentum $\textbf{p}=m\textbf{v}+e\textbf{A}$ mean? Is it just momentum accounting for electromagnetic effects?
10
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3answers
6k views

Can superconducting magnets fly (or repel the earth's core)?

If a superconducting magnet and appropriate power supply had just enough $I\cdot s$ (current $\cdot$ length) so that when it was perpendicular to the earth's magnetic field, the force of the ...
8
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4answers
1k views

Influence of charged particle's own electric field on itself

I read this in my textbook: A charged particle or object is not affected by its own electric field. Since I find this completely unintuitive and my mind is yelling "wrong! wrong! how could a particle ...
6
votes
1answer
282 views

E&M and geometry - a historical perspective

Recently, I was contemplating the beautiful formulation of electromagnetism (specifically Maxwell's equations) in terms of differential forms: $$F=\mathrm{d} A\implies \mathrm{d}F=0 ...
10
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4answers
521 views

Electromagnetic field and continuous and differentiable vector fields

We have notions of derivative for a continuous and differentiable vector fields. The operations like curl,divergence etc. have well defined precise notions for these fields. We know electrostatic and ...
10
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5answers
26k views

Why is current a scalar quantity?

Current has both magnitude and direction. As per the definition of vector defined in encyclopedia, current should be a vector quantity. But, we know that current is a scalar quantity. What is the ...
10
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2answers
752 views

Forcing quadrupole moments to vanish for a neutral system

For a system of electric charges $q_i$, at positions $\mathbf{r}_i$, with a nonzero net charge $Q=\sum_i q_i$, one can define a "centre of charge" in the obvious way as $$ ...
7
votes
2answers
356 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 ...
7
votes
2answers
1k 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 ...
5
votes
2answers
578 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 ...
3
votes
4answers
824 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 ...
3
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3answers
590 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 ...
14
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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 ...
11
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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 ...
10
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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 ...
10
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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
votes
1answer
686 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.
9
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3answers
3k views

Maxwells Equation from Electromagnetic Lagrangian

In Heaviside-Lorentz units the Maxwell's equations are: $$\nabla \cdot \vec{E} = \rho $$ $$ \nabla \times \vec{B} - \frac{\partial \vec{E}}{\partial t} = \vec{J}$$ $$ \nabla \times \vec{E} + ...
8
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5answers
2k 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 ...
8
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3answers
946 views

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. ...
7
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3answers
1k views

Why should Conservative forces have their curl equal to zero?(intuition)

There are several conditions that must be met in order for a force to be conservative. One of them is that the curl of that force must be equal to zero? What is the physical intuition behind this? If ...
7
votes
2answers
663 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 ...
7
votes
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)?
7
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3answers
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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 ...
6
votes
2answers
334 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 ...
6
votes
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 ...
5
votes
1answer
250 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 ...
4
votes
1answer
438 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 ...
3
votes
4answers
6k 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 ...
2
votes
3answers
957 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 ...
2
votes
1answer
831 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 ...
14
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6answers
14k views

Where do magnets get the energy to repel?

If I separate two magnets whose opposite poles are facing, I am adding energy. If I let go of the magnets, then presumably the energy that I added is used to move the magnets together again. However, ...
10
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1answer
1k views

Can a free particle absorb/emit photons?

As simple as in the title.. I would like to know also some mathematics about it!
8
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5answers
6k 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 ...
8
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5answers
774 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 ...