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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582 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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5answers
18k 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 ...
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3answers
2k 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} + ...
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3answers
906 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. ...
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3answers
809 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 ...
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2answers
618 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
971 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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2answers
287 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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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 ...
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4answers
10k views

Why is the conductor an equipotential surface in electrostatics?

Since the electric field inside a conductor is zero that means the potential is constant inside a conductor, which means the "inside" of a conductor is an equal potential region. Why do books also ...
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1answer
385 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
5k 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
767 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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3answers
520 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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5answers
11k 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, ...
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7answers
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Can magnetic fields be redirected and focused at one point?

I know that magnetic fields can be redirected, but... given a situation where you have static magnetic field over a large area, and you want to quickly change the magnetic field strength. Is it ...
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7answers
1k 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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4answers
3k 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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3answers
5k 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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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
2k views

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 ...
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3answers
9k views

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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5answers
153 views

Can a Coronal Mass Ejection (CME) cause a blackout on Earth and why?

Can a Coronal Mass Ejection (CME) cause a blackout on Earth and why is it so what's the relation between electro magnetic radiations and electrical and electronic appliance.what exactly does it do to ...
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2answers
935 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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2answers
5k 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
5k views

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 ...
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3answers
546 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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2answers
381 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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3answers
1k 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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1answer
169 views

Electrons and Magnetism

Electron at rest generates Electric field. Electron moving without acceleration produces electric and magnetic field. Electron moving with acceleration produces electromagnetic waves. Please explain ...
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3answers
558 views

Protons and Electrons Occupying the Same Space

When it comes to atoms electrons can't fall into the nucleus, which besides the off hand uncertainty explanation, I'm not sure which force prevents them from falling into the nucleus. I thought I ...
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2answers
6k 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 ...
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6answers
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Are metals more heavy due to the Earth's magnetic field?

Non-metal objects are attracted to the Earth due to gravity. So the weight of non-metal objects can be only dependent on their mass. On the other hand metals can be attracted to the Earth's magnetic ...
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5answers
3k views

What causes the permittivity and permeability of vacuum?

When light travels through a material, it gets "slowed down" (at least its net speed decreases). The atoms in the material "disturb" the light in some way which causes it to make stops on its path. ...
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3answers
6k views

Is it safe to use any wireless device during a lightning storm?

I need "educated" reasons whether it is safe to use any wireless device during a lightning storm. Most people said don't use it but they cannot explain why.
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3answers
180 views

What would it take to cause lightning to jump between the Moon and the Earth?

This question comes from @Floris' speculation at the end of his excellent answer about what it would take to kill everyone on the Earth with electricity. Doing all this in 1/10th of a second ...
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4answers
906 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 ...
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4answers
678 views

Least-action classical electrodynamics without potentials

Is it possible to formulate classical electrodynamics (in the sense of deriving Maxwell's equations) from a least-action principle, without the use of potentials? That is, is there a lagrangian which ...
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2answers
2k views

Effective aperture of isotropic antenna

I have always taken for granted that 'the aperture of a loss-less isotropic antenna is $\dfrac {\lambda^2} {4\pi}$'. On a whim, I tried to look up how this expression was derived, but so far I have ...
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4answers
5k 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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1answer
183 views

Experiments looking for monopoles

Background: (skip it if you know it) In the easiest formulation of classical electromagnetism magnetic monopoles do not exist. In fact, the Maxwell's equation $\nabla \cdot \vec{B}=0$ implies (using ...
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2answers
942 views

Does a nonzero Poynting vector mean that there is propagation of energy?

I don't know how this "paradox" can be solved. I'm given the following system: A permanent magnet with a magnetic field given by ($\hat{a}$ are unit vectors in the x and y directions) ...
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2answers
104 views

Could some astronomical objects have superconducting properties?

The colder it is, the more efficient the superconductivity process works. And as we know, if there is no star nearby, space gets pretty cold. I do appreciate that many condensed, burnt out, stars ...
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1answer
3k views

Magnetic field strength in a solenoid

I'm pretty new to physics. I've been conducting some experiments with electromagnets. My practical results don't match up with the theory. The magnetic field in a solenoid of length $L$ around an ...
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0answers
620 views

Is Electromagnetic Mass Possible?

If the sinusoidal electric component of a light wave were off-set to one side of the magnetic component and then the smaller "lobe" were to cancel out with much of the larger side, then where would ...
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3answers
1k views

Is it possible/correct to describe electromagnetism using curved space(-time)? [duplicate]

Comparing the simples form of the forces of both phenomena: the law of Newton for gravitation $V\propto \frac{1}{r}$, and the Coulomb law for electrostatics $V\propto \frac{1}{r}$, one might think ...
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0answers
103 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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1answer
328 views

Is every electromagnetic radiation considered “light”?

Somebody mentioned on Freenode chatroom for physics that All Electromagnetic Radiation are delivered in form of Photons not just light. Is it true? Does that mean if we get a THF electrical ...
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1answer
152 views

Does there exist electric field around all the substances?

A system of two equal and opposite charges separated by a certain distance is called an electric dipole. Electric dipole moment ($p$) is defined as the product of either charge ($q$) and the ...
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1answer
820 views

Two electron beams exert different forces on each other depending on frame of reference?

I am sure there is a simple explanation for my confusion, but I am a little puzzled: We are dealing with two parallel electron cannons that each produces a straight beam of electrons. They are placed ...