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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How to Extend Relaxation Methods for 2D Laplace Equation given in Jackson E&M to 3D?

In Jackson (3 ed) chapter 1.13 an outline is given for using relaxation to solve laplace equation in 2D. The general procedure in 3D involves minimizing the quantity $$I[\Psi]=\frac{1}{2}\int_V ...
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2answers
160 views

Argument for symmetry of potential

Consider the following electrostatic charge configuration of a spherically symmetric, perfect conductor with total charge $Q = 2q$, where $q > 0$. A point charge $q$ is placed at the position ...
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1answer
116 views

Does the transmission axis matter for sending polarized light through polarized glass?

If I have polarized light and I send through only one polarized glass plane, does the transmission axis matter, or will the intensity be halved no matter what.
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114 views

Why is $D$ a $2$-form and $E$ a $1$-form?

Usually in electrostatics we start by introducing the vector field $\mathbf{E}$ representing the electric field due to some charge distribution. Later when we study fields in materials we consider the ...
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1answer
307 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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336 views

If electromagnetic waves have magnetic fields, why beam of flashlight is not disrupted by a Magnet?

Wikipedia article about Electromagnetic Radiation says "As an electromagnetic wave, it has both electric and magnetic field components". And this discussion also confirms Light is EM wave. Since we ...
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133 views

What is the intepretation of the electromagnetic tensor?

Let $A$ be the four-potential, then we know that we can form the electromagnetic tensor as $F=dA$. This is usually done as a way to have a better writing of Maxwell's equations. So, to simplify the ...
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128 views

Currents and magnetic fields produce forces that affect things they're not touching?

I was doing this past paper and am a little confused by question 5) part c)ii) I correctly calculated that the force acting on the rod due to the magnetic field is 0.016N but I can't see how ...
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89 views

Debye Hückel Theory valid for ions?

I am wondering about the following: Is Debye Hückel Theory only used if you look at how an external "strong" field(like a potential by a sphere that has a charge that is 1000times higher than the ...
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2answers
80 views

Alternative symmetries for the Maxwell Lagrangian?

I'm wondering about how to show that $A_a\rightarrow A_a+\alpha\partial_0A_a$, with $\alpha$ infinitesimal, is an infinitesimal symmetry of $\mathcal L=-\frac14F_{ab}F^{ab}$. \begin{equation} ...
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43 views

EMF & Magnetic force at the same time?

A conductor is placed in a magnetic field, current starts to flow, and the wire experiences the Lorentz force of $x$ Newtons. However, what confuses me is that $x$ is a value that is calculated from ...
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713 views

Why is the Hodge dual so essential?

It seems unnatural to me that it is so often worthwhile to replace physical objects with their Hodge duals. For instance, if the magnetic field is properly thought of as a 2-form and the electric ...
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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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1answer
54 views

Charging a capacitor

Below is an excerpt from a physics textbook: One common way to charge a capacitor is to connect these two wires to opposite terminals of a battery. Once the charges $Q$ and $-Q$ are established on ...
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2answers
2k views

Is it possible to get energy from electrical wire using induction?

Pardon me if this is a stupid question but my physics courses are from a long long time ago and I was a teenager back then. ;) Electricity in a wire generates electromagnetism, right? Would it be ...
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1answer
486 views

Ampère's Law for an infinitely long straight wire

In order to find the magnetic field generate by an infinitely long straight wire of radius R, I have to use local Ampère's Law : $\boxed{ \oint_L B\cdot dl = \mu_0 \sum_j I_j}$ If $r > R$ then $ ...
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1k 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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363 views
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209 views

Huggins Displacement Theory and Retrocausality

I was looking at the Wikipedia entries on Time Travel and the Grandfather paradox and noticed a paragraph on the so-called Huggins Displacement Theory. I haven't been able to find the source although ...
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114 views

how do I calculate the B field (strength and direction) on a point charge due to a permanent magnet

I am trying to create a simple 2D Simulation of magnetic fields similar to this; showing the field lines or the effect of permanent magnets. I keep coming across equations like this: ...
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601 views

Explosively Pumped Flux Compression Generator = EMP strong enough to destroy my phone from a mile away?

Explosively Pumped Flux Compression Generator detonated a mile away or so, what damage would be done to my phone, and other electronics? I would imagine it would be similar to a CD in the microwave ...
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1answer
160 views

Polarization vector and bound charge

Why is it that the bound charge is $Q_b = - \oint_S{\mathbf{P} \cdot d\mathbf{S}}$? In particular, why is there a negative sign? Hayt's book on electromagnetism describes this as the "net increase in ...
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3answers
131 views

Ferromagnets and magnets tend to align in the center. Why is that?

When you bring a large iron plate and a magnet, the magnet attracts the iron plate and it tends to slide itself to the center. When I place it on the edge, it always aligns at the center why is that?
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1answer
177 views

Current Carrying Coil - Torque [closed]

i'm stuck on how to answer the last part of this question and would really appreciate some pointers. A rectangular coil (sides $a = 15 \, \mathrm{cm}$ and $b = 20 \, \mathrm{cm}$, $m= 15 \, ...
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627 views

Is there a fourth component to the electric field and magnetic field?

The Question If the three vector electric and magnetic fields come from the four component four-potential, then is there a fourth component to the electric and magnetic field? Related Question I ...
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131 views

Can the two electromagnetic field tensors be combined into a more general tensor?

Given the electromagnetic field tensor $$\begin{align} F_{\mu\nu} = \begin{pmatrix} 0 & -E_{x} & -E_{y} & -E_{z} \\ E_{x} & 0 & B_{z} & -B_{y} \\ E_{y} & -B_{z} & 0 ...
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2answers
310 views

What is the physical significance of the Dipole Transformation of Maxwell's Equations?

The Question Given Maxwell's equations of the form \begin{align} \bar{\nabla}\times \bar{B} = \dfrac{4\pi}{c} \bar{J} + \partial_0 \bar{E} \\ \bar{\nabla}\times \bar{E} = -\partial_0 \bar{B} \\ ...
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32 views

Magnetic field of a wire with over 1000 amperes? [duplicate]

Does a large thick wire that has over 1000 amperes of current flowing through it generate powerful magnetic fields? What formula is best here to predict $B$?
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2answers
371 views

What are the 'oscillators' in the Drude Lorentz model?

Jackson's Electrodynamics defines the Drude-Lorentz model as a set of harmonic oscillators (running over indices $j$ below), which, if you write out the equations of motion and rearrange a little, ...
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1answer
392 views

Maxwell's equations of Electromagnetism in 2+1 spacetime dimensions

What would be different in the theory of electromagnetism if instead of considering the equations of Maxwell in 3+1 spacetime dimensions, one would consider 2+1 spacetime dimensions?
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1answer
139 views

Show that charge conservation $\partial_\mu J^\mu = 0$ implies global U(1) invariance?

The $U(1)$ global gauge symmetry of electromagnetism implies - via Noethers theorem - that electric charge is conserved. Actually, it implies a continuity equation: $$ \psi \rightarrow ...
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1answer
121 views

Why gauge invariance for electromagnetic fields?

What is the physical constraint that gauge invariance is a required condition for electromagnetic fields? What would happen if the electromagnetic fields were not gauge invariant?
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2answers
117 views

Is a magnetic field affected by the presence of air?

Does air affect a magnetic field's ability to attract ferromagnets? If a magnetic field and a ferromagnet were placed in a vacuum would there be a better performance?
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1answer
647 views

Can I Demagnetize a ferromagnet with a hammer?

If an iron is exposed to an external magnetic field, the iron's domains are all aligned with that ext-B . If I strike it with a hammer, will it be demagnetized? Comparing it with heat, I know the Tc ...
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3answers
896 views

Why do both plates of a capacitor have the same charge?

How do we know that both plates of a capacitor have the same charge? You could argue conservation of charge, but I don't see how conservation of charge implies the charge on both plates is the same. ...
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1answer
175 views

Induced current and Ohm's law

I am trying to explain this problem: A circular conducting loop composed of N turns of wire has a radius of r and a total resistance of R. Perpendicular to the plane of the loop is a magnetic ...
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1answer
129 views

All possible electromagnetic Lorentz invariants that can be built into the electromagnetic Lagrangian?

Given the electromagnetic Lagrangian density $$ \mathcal{L}~=~-\frac{1}{4}F_{\mu\nu}F^{\mu\nu}~=~\frac{1}{2}(E^2-B^2) $$ is a Lorentz invariant, how many other electromagnetic invariants exists that ...
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1answer
56 views

Is it possible to incorporate the Lorenz gauge term into the electromagnetic fields?

I noticed that the Lorenz gauge term is represented by partial derivatives acting on the four-potential. Is it possible that the Lorenz gauge term could somehow be a similar object that belongs to the ...
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2answers
1k views

Is it possible to levitate a toy maglev train using only permanent magnets as long as the train stays in motion?

I am fascinated with magnets, and specifically the idea of magnetic levitation. I recently purchased a Levitron toy maglev train and have enjoyed finding the perfect sweet spot at which it levitates, ...
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0answers
79 views

What is $T_{\mu\nu}T_{\mu\nu}$ for the electromagnetic stress-energy tensor?

Given the electromagnetic stress-energy tensor components \begin{align} T_{\mu\nu} = \begin{pmatrix} u_{00} && s_{0 \nu} \\ s_{\mu 0} && \sigma_{\mu\nu} \end{pmatrix}_{\mu\nu} ...
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1answer
72 views

How does this particle behave in the magnetic field?

I have the above question and I have though about it every way and can't seem to find out. So what I have concluded (ignore the answers on the img) Is that the force is on the z axis because the ...
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0answers
223 views

Drift velocity of electrons in a superconducting loop

Do electrons travel at the Fermi velocity in a superconducting loop? For metals the Fermi velocity seems to be around $10^6$ m/s. So would electrons (in a Cooper pair) travel around the loop at this ...
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2answers
134 views

Visualising scalar and vector fields

As I have been studying electromagnetic theory, I have always been lead to confusion when trying to visualise the fields. Fortunately, the electric and magnetic fields are vector fields and also along ...
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1answer
115 views

What are “parity considerations” in deciding the form of the Hamiltonian?

In "introductory Quantum Optics", by Gerry and Knight, the Jeynes model is considered. In this model of electron-EM field interaction the electron is approximated by a two state system ($\lvert ...
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1answer
81 views

The question about quantization of free EM field

Let's have the free EM field theory with Coulomb gauge: $$ \partial^{2}A_{\mu} = 0, \quad A_{0} = 0, \quad (\nabla \cdot \mathbf A ) = 0. $$ One of the ways of quantizing the field is the following. ...
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1answer
140 views

What's an ideal wire?

I'm not talking about an ideal wire in a circuit (a wire with infinite conductance). I'm talking about an ideal wire in the case of the magnetic field of an infinite current carrying wire. What ...
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3answers
3k views

Prove EM Waves Are Transverse In Nature

Why we say that EM waves are transverse in nature? I have seen some proofs regarding my question but they all calculate flux through imaginary cube. Here is My REAL problem that I can't here imagine ...
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1answer
87 views

Step in a proof that $\textrm{div} \ \mathbf{B} = 0$ from Biot-Savart's law

Notation: The magnetic field $\mathbf{B}$ generated by a point charge $e$ moving with velocity $\mathbf{v}$ is given by Biot-Savart's law $$\mathbf{B} = \frac{\mu_0 e\ \mathbf{v} \wedge ...
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74 views

Field outside a solenoid?

Say you have a solenoid with diameter $d$ and length $L$. How can I show that as $d/L$ approaches 0, the field outside the solenoid is zero? I'm looking for a formal proof involving integration. ...
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43 views

Electric Field: distributed uniformly in one infinity tape of length [closed]

One charge density surface is distributed uniformly in one infinity tape of length with $2a$ width from distance $d$. Determine the Electric Field in the point perpendicular from the distance $d$ ...