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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Solving the equation of relativistic motion

How does one solve the tensor differential equation for the relativistic motion of a partilcle of charge $e$ and mass $m$, with 4-momentum $p^a$ and electromagnetic field tensor $F_{ab}$ of a constant ...
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4answers
5k views

North and south of magnetic field

The current I is flowing upward in the wire in this figure. The direction of the magnetic filed due to the current can be determined by the right hand rule. Can we determine the north and the south ...
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1answer
664 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
131 views

Magnetic Field and the Speed of Light

Is it just a historical choice that both magnetic field and the Lorentz force equation include the speed of light? I figure that whoever wrote up the equations (in cgs!) could have put both factors ...
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1answer
331 views

Uncertainty-principle and the Maxwell formalism of electromagnetic waves

An electromagnetic wave (like a propagating photon) is known to carry it's electric and magnetic field-vectors perpendicular and each depending on the differential change of the other thus "creating" ...
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1answer
167 views

CGS Units for Magnetism

Why does the formula for magnetic field force include the speed of light in the denominator in cgs units? Where does the extra $c$ go in SI units?
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1answer
531 views

inductance value of a single turn thin circular coil

the question may seem simple but I haven't found any fitting formula yet. The problem is the following: consider a single-turn, circular coil made of reasonably thin wire (diameter of the wire much ...
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3answers
1k views

There must be free positive charges, moving oppositely to electrons for the wire with current to stay neutral

All popular expositions (e.g. these ones) of relativistic electromagnetism claim univocally that electrons in motion become more dense due to the speed. They teach that Lorentz contraction of charges ...
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0answers
33 views

Small charged sphere's motion in earth's magnetosphere?

Suppose that a spherical metal sphere with mass $m=10^{-16}kgr$ radius $R=10μm$ charge $Q=10^{-9}C$ travels with $v=c/3$ and is trapped in the earth's magnetosphere at a distance around $r = 1000km$. ...
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2answers
177 views

Vector potential

I have difficulty understanding the following vector calculus example. Text can be found here. It is the 5th Q&A -- starting with equation (31.1035).It concerns finding the vector potential of a ...
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2answers
252 views

EM Fields in a Rotating Frame of Reference

I'm struggling on my approach to the problem of figuring out E and B fields in a non-relativistic way for a rotating frame of reference in the x-y plane around the z-axis. I am attempting to do this ...
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1answer
141 views

Non reciprocal light propagation

In search for some explanation in why magneto-optical materials (like the one used in the Faraday rotator and, consequently, in the "optical diode") act in such a "strange" way, I saw that this kind ...
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1answer
62 views

Phasor representation of voltage in frequency domain

In a text on application of electromagnetism in transmission line, there introduces a phasor for the voltage (in frequency domain) $$\tilde{V}(x) = V^+e^{-i\beta x} + V^-e^{i\beta x.}$$ Here $V^+$ ...
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2answers
618 views

Physical explanation for why total internal reflection occurs

I have been trying to understand total internal reflection (and have read several posts on this site already). Mathematically, I feel that I understand how the evanescent wave decays exponentially as ...
2
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1answer
3k views

Where is the amplitude of electromagnetic waves in the equation of energy of e/m waves? [duplicate]

Does the amplitude of the photon oscillations always stay constant and if it is not - what are the physical differences between the photon with higher amplitude in comparison to the one with the less ...
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0answers
955 views

Could Space Travel be achieved using a very strong magnetic field to warp space?

An Alcubierre Warp Drive could theoretically achieve faster than light space travel but requires exotic matter or negative energy to compress space in front of the spaceship and expand space behind ...
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3answers
225 views

Microscopic picture of an inductor

I have a good understanding of how inductors behave in electrical circuits, and a somewhat rough-and-ready understanding of how this behaviour arises from Maxwell's equations. However, what I don't ...
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1answer
121 views

EM Waves Energy Loss

Where does the energy go when two photons interfere destructively at a point on a screen in Young's double slit experiment ?
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1answer
255 views

Induced Current, Dipole Falling Under Gravity Towards Circular Loop [closed]

Suppose a magnetic dipole $\mathbf{m} = m \hat{z}$ is falling towards a circular loop of radius $b$ under gravity. Assuming the dipole always stays along the $z$-axis of the loop, determine the ...
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5answers
1k views

Relativistic origin of magnetic field

There is an explanation in the Wikipedia. Unfortunately the article is quite verbose and doesn't clearly explain why both positive and negative charges vary density even if only one is moving. It is ...
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5answers
679 views

Relativistic charge density in a closed loop

When charges of conductance are at rest, there is an average distance between them. The relativistic origin of magnetic field says that distances between electrons shrink when they are set into a ...
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2answers
177 views

What materials focus EM radiation in the 2.4GHz range

If glass and similar materials refract visible light effectively, what materials would be best for focusing lower frequencies of EM radiation, if any? If not, what other methods exist for focusing ...
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1answer
708 views

Importance of Ampere's Law

Consider a hollow cylinder carrying a current $I$ and a wire outside the cylinder carrying a current $I'$. Let's say the cylinder is symmetrical with even current distribution etc.. so the ...
3
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1answer
142 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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3answers
3k views

What does it mean for electric current to be a scalar?

After reading the reasons for considering electric current as a scalar quantity, I was confused at a point which read "The magnitude and direction of current does not depend upon the direction of the ...
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3answers
4k 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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1answer
94 views

Is it possible for a charged, fast-moving object to slow down and enter geo-stationary orbit?

I've had a wild idea which I can not discuss at length in this forum, but it comes down to the following problem: A sphere of radius R=~10μm and mass m=~10-16Kgr is travelling towards the earth at v ...
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2answers
456 views

Attraction and repulsion of Magnetic materials [duplicate]

Why are diamagnetic materials repelled when placed in magnetic field and why are paramagnetic materials attracted when placed in magnetic field?
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1answer
35 views

Work due to introducing a dieletric in a capacitor

I have a doubt about a couple of exercises tha asks to find the work done on introducing a dieletric between the plates of a capacitor. Yes, this question is in the general case, how do we procede? I ...
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2answers
349 views

Forces as One-Forms and Magnetism

Well, some time ago I've asked here if we should consider representing forces by one-forms. Indeed the idea as, we work with a manifold $M$ and we represent a force by some one-form $F \in ...
10
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1answer
442 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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1answer
151 views

Induced voltage by a rotating ring

Two concentric rings dielectrics and uniformly charged are suspended on the same floor. The outer ring has a radius R and mass M, while the other has radius r << R and mass M. The outer ring ...
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1answer
180 views

Magnets and speed of light

I am in no way a physicist but I do have a fascination with physics. My question is if magnets are being explored / studied as a potential source to achieve the speed of light and if that is even ...
2
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1answer
295 views

What limits the maximum sustainable surface charge density of a sphere in space?

Suppose I charge a sphere and leave it in vacuum for 10 years. After that time, I want its surface charge density to be in the order of 10^5C/m^2. Would that be possible? Would it depend on the ...
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1answer
836 views

measuring electromagnetic induction

There is a famous law which says that a potential difference is produced across a conductor when it is exposed to a varying MF. But, how do you measure it to prove? It is quite practical. ...
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1answer
201 views

Understanding drift velocities in currents

I have a doubt about the understanding of drift velocities in a current. My problem is that the textbook speaks very loosely about this. It's like: "well, if we apply a field $E$ then the charges will ...
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2answers
962 views

Cancel out Earth's Magnetic field

Is there any tools except helmholtz coil to cancel out earth's magnetic field to calibrate magnetometers in practice.
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1answer
807 views

Back motor effect of loaded generators?

The back motor effect (see Counter-electromotive force) is the counter torque which opposes the rotational motion of the coils in a generator when the generator is under load. The back motor effect ...
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1answer
204 views

Negative emf in AC generator

At a certain instant in AC generator, when the normal of the plane (rectangular coil) makes an angle of 270 degrees with with the magnetic induction B, the value of emf is: $E = -NAB\omega$ My ...
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2answers
1k views

Difference between electrostatic and magnetic field [closed]

In this, F (the force set by the field) is perpendicular to the speed of the particle. In which case does F change the absolute value of V? Why or why not?
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1answer
2k views

The electric field of a conductive sphere containing a charge - grounded vs not grounded

Let's suppose we have a sphere but unlike theoretical ones it'll have some thickness say $\Delta r$ and inner radius $R$. What I was wondering about is how will it behave if we place some charge $q$ ...
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1answer
116 views

Electromagnetic field to cool a substance?

I saw somewhere that an electromagnetic field would cause a substance to let off thermal energy, ultimately resulting in the substance to cool really quickly. If this is possible, does the strength ...
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1answer
1k views

Equivalence between a charged rotating cylinder and a solenoid

Suppose we have a cylindrical shell of radius $r$ with surface charge density $\sigma$. Then we start rotating the cylinder at an angular speed $\Omega$. You can show that in this case the surface ...
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2answers
789 views

Eddy currents: Explanation of the force slowing down a moving metal plate

Suppose a solid metal plate moves trough a homogenous magnetic field $\vec{B}$ as shown in the following image. You will see that the plate will slow down (as long as not the entire plate is in the ...
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1answer
340 views

Why electric field outside the sphere that carries polarization is 0?

There is a sphere with radius $R$ that carries a polarization $$\vec P(\vec{r})=k\vec r$$ $\vec r$ is the vector from the center. I found electric field the outside generated by the sphere is $\vec ...
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7answers
9k views

Does a current carrying wire produce electric field outside?

In the modern texts of electromagnetism in the presence of stationary currents the electric field is assumed conservative $\nabla \times E =0 $. Using this we get $E_{||}^{out}=E_{||}^{in}$ which ...
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1answer
197 views

Energy stored in fields

How to intuitively think of energy stored in a magnetic/electric field? Kindly answer in a bit simple terms without referring to mathematics.
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2answers
215 views

Movement of the particle in a magnetic field

This is the numerical question. A particle having a mass of 0.05 mg carries a charge of $5\times10^{-6}C$. The particle is given an initial horizontal velocity of 5000 m/s, what is the magnitude ...
6
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2answers
256 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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0answers
22 views

Some basic questions about electric field & nucleus [duplicate]

I am not good in physics.You can say I am beginner in this field. I have some basic questions. I ju st want to know that [1] If there is repulsive force between same charges proton-proton then why ...