The four fundamental fundamental equations of electromagnetism.

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Electromagnetic inertia due to advanced radiation?

The scalar potential $\phi$ and vector potential $A$ at a distance $r$ from a charge $q$ are given approximately by $$\phi = \frac{q}{r}$$ $$\mathbf{A} = \frac{q\mathbf v}{r}$$ where the constants ...
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258 views

Magnetostatics of Current-Carrying wire

A question has been nagging at me about Faraday's Law as related to a wire with a constant current: If you have a circular loop of wire with some small resistivity, connected to a battery so that it ...
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Why must this boundary condition be met? (Electromagnetic wave at interface between two mediums)

My textbook says that The laws of Electromagnetic Theory (Section 3.1) lead to certain requirements that must be met by the fields, and they are referred to as the boundary conditions. ...
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57 views

Why is the magnetic field of a spherically symmetric current zero?

We now ask about the magnetic field produced by the currents in this situation. Suppose we draw some loop $\Gamma$ on a sphere of radius $r,$ as shown in Fig. 18–1. There is some current through ...
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Do the relations between E/B and D/H contain higher order multipole terms?

Jackson writes in section 1.4 (third edition) that \begin{align*} D_\alpha &= \epsilon_0 E_\alpha + \left(P_\alpha - \sum_\beta \frac{\partial Q'_{\alpha\beta}}{\partial x_\beta} + \ldots \right) ...
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Maxwell's equation in curved spacetime - how come? And experimental evidence?

I'm trying to understand the generalization of Maxwell's equations to curved spacetime. In FLAT (Minkowski) SPACETIME: If we define the "four-potential" as $$\ ...
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751 views

Maxwell equations and symmetry

Do the full inhomogeneous Maxwell equations obey parity (P) and time reversal (T) symmetry separately or only the full CPT symmetry? I believe the homogeneous Maxwell equations obey parity and time ...
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755 views

Neither Biot-savart nor Ampere Law can solve this problem?

I'm confused about the use of the Ampere's Law and the Biot-Savart Law due the inconvenience of each law. I want to calculate the magnetic field due to current carrying a circular loop over itself, ...
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Is Gauss' law valid for time-dependent electric fields?

The Maxwell's equation $\boldsymbol{\nabla}\cdot \textbf{E}(\textbf{r})=\frac{\rho(\textbf{r})}{\epsilon_0}$ is derived from the Gauss law in electrostatics (which is in turn derived from Coulomb's ...
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Where does the $\partial \vec{E}/\partial t$ term from Maxwell's equation go in Ampere's Law?

One of Maxwell's Equations (ME) is: $$\nabla\times\vec B = \mu_0\vec J+\epsilon_0\mu_0 \frac{\partial \vec E}{\partial t}.$$ While Ampere's Law (AL) is: $$\nabla\times\vec B = \mu_0\vec J.$$ ...
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Special Relativity: Transforming Maxwell's equations

I'm working through Einstein's original 1905 paper*, and I'm having trouble with the section on the transformation of Maxwell's equations from rest to moving frame. The paper proceeds as follows: ...
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Why is $\mu_0$ missing in EM formulas in Peskin and Schroeder?

In this post, $\hbar=c=1$ units are used throughout. It is well known that the action of classical electromagnetism is given by $$\mathcal S_{\text{Maxwell}} = \int ...
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461 views

Why ONLY Maxwell's equations are the basic equations of electromagnetism?

In electromagnetism we say that all the electromagnetic interactions are governed by the 4 golden rules of Maxwell. But I want to know: is this(to assume that there is no requirement of any other ...
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200 views

Question about units of mass, $M = (L^{3})(T^{-2})$?

In section 5 of the "Preliminary: On the measurement of quantities" chapter (page 3) in "A treatise on electricity and magnetism" Maxwell uses, total length, $s=mt^{2}/{2r^{2}}$to show that ...
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Does $E$ cause $B$ or does $B$ cause $E$ in Maxwell's equations?

From the Maxwell's equations we get $$\frac{\partial E}{\partial x} = -\frac{\partial B}{\partial t}$$ and $$\frac{\partial B}{\partial x} = -\mu_0\epsilon_0\frac{\partial E}{\partial t}$$ ...
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572 views

Magnetic B Field of Point Charge Not at Constant Velocity

I'm working on an N-body simulator for charged particles. I know that moving charged particles generate a magnetic field, and another moving charged particle could be effected by this magnetic field. ...
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278 views

Why is the displacement current term needed in the Maxwell's equations?

Why did Maxwell believe that a displacement current term needed to be added to Ampere's circuital law? I have found loads of answers online about the plates acting as capacitors but i don't ...
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352 views

Why does $E=\nabla\phi$ follow from $\nabla\times E=0$?

I understand that using one of Maxwell's equations, $$\vec{\nabla} \times \vec{E}(\vec{x})=0,$$ it can be said that $$\vec{E}(\vec{x})=-\vec \nabla \phi(\vec{x}).$$ However, I can't find or ...
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Solution of simple problems using only Maxwell equations in differential form

Solve simple electrostatic or magnetostatic problems using only Maxwell equations. For example: In every book there is an excercise to find a magnetic field outside a thin wire of radius $a$ with ...
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818 views

How to use Ampere's Law for a semi-infinite wire with current?

Suppose that there is a semi-infinite wire which extends to infinity only in one direction. There are no other circuit elements at the other end(finite end) of the wire and the current does not loop. ...
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198 views

A James Clerk Maxwell Disproof

One of my favorite physicists to learn about was James Clerk Maxwell, for the fact that he unified the study of E&M in physics and he would often disprove theories that did not work as a ...
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Curl of an electromagnetic wave

I can't understand the concept of the curl of an electromagnetic wave. $$ \nabla \times E = -\frac{\partial \textbf{B}}{\partial t} $$ All of the examples I find show a current through a conductor, ...
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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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559 views

Invariance of Maxwell's Equations under inverting variables - Reference and use

Some months ago, an ArXiv paper mentioned in passing that Maxwell's Equations were invariant under reciprocating the variables, or at least this results in a dual set of Maxwell Equations. (Actually I ...
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308 views

Proof of Ampère's law from the Biot-Savart law for tridimensional current distributions

Let us assume the validity of the Biot-Savart law for a tridimensional distribution of current:$$\mathbf{B}(\mathbf{x})=\frac{\mu_0}{4\pi}\int_V ...
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108 views

How is Biot-Savart law verification of Maxwell's 4th equation for steady current?

Please provide some theoretical procedure which equates Biot-Savart law with the Maxwell's 4th equation for steady current, which is Ampere's law $$\quad \nabla\times{\bf B} = \mu_0{\bf J}.$$
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Where do Maxwell's equations come from?

I recently started learning the basic forms (integrals) of the Maxwell's equations, and everything that is related to electromagnetism seems to be derived from these fundamental equations. Now my ...
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314 views

parity invariance of Einstein, Maxwell and Dirac Lagrangians

How can we show that Einstein, Maxwell and Dirac Lagrangians are parity invariant?
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How is this classical “paradox” resolved in electromagnetism?

A magnet and a coil move relative to each other. In the frame of reference of the magnet, there is a magnetic field and consequently a force acting on the charges in the coil according to the Lorentz ...
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487 views

Electromagnetism duality theorem

Concerning Electromagnetism, textbooks often refer to the Duality Theorem. Sometimes it is presented like this: «Consider the Maxwell's Equations (with phasors) and a known field $\mathbf{E}_1$, ...
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1answer
205 views

How can electrons move along the conductive wire? ( seems to be a paradox )

Tangential components of the electric field across an interface between two media, with no impressed magnetic current densities along the boundary of the interface, are continuous. So: $ n \times (E_2 ...
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513 views

Electrodynamics and the Lagrangian density

Could anyone tell me what equations can I obtain from the Lagrangian density $${\cal L}(\phi,\,\,\phi_{,i},\,\,A_i, \dot A_i,\,\,A_{i,j})~=~\frac{1}{2}|\dot A+\nabla\phi|^2-\frac{1}{2}|\nabla \times ...
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Applying $\nabla\times\mathbf{B} = \mu_0\mathbf{J}$ in the presence of magnetic shielding

2012-06-13 - Revised question in experimental format (This is a thought experiment for which RF experts may have an immediate answer.) I'll assume (I could be wrong) the possibility of creating a ...
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307 views

Understanding Dynamic light scattering

I'd like to understand the physics of dynamic light scattering experiment. In particular I want to understand the basic relation between relaxation time $\tau_q$ and the diffusion coefficient $D$: ...
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1answer
115 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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Can Maxwell's Equations explain electromagnetic radiation emission in an atom?

Can Maxwell's equations be used to explain the process of spontaneous emission when an electron drops from a higher energy level to a lower energy level? According the Maxwell equations, a changing ...
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106 views

Magnetic field in materials with non-constant magnetic susceptibility

I'm quite lost what $B$ and $H$ is. It seams to me that most of the texts I read do quite poor job in explaining them properly. They are explained only in cases when magnetic susceptibility is ...
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824 views

Is there any relation between weak and strong fields, similar to electric and magnetic fields?

Is it possible to unify the strong, weak, electric and magnetic field just by Maxwellian type equations? (Maxwell by adding a small change - unified electric and magnetic field, then Einstein's ...
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463 views

why is advanced radiation absent?

the Lienard-Wiechert green functions have future and past null cones of radiation. Maxwell equations allow for a continuous range of mixtures between the retarded and advanced components, but we have ...
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660 views

Electron model under Maxwell's theory

I was not able to recall my memories, so: What is the formula that states the frequency of electrons revolving around nucleus is equal to the frequency of light (or photon) emitted (or radiated)? (I ...
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51 views

Do divergence and curl of Lorentz force have some physical meaning?

Time ago I started thinking about this: if we take the well known Lorentz Force expression, namely $$\mathbf{F} = q\left(\mathbf{E} + \mathbf{v}\times\mathbf{B}\right)$$ and we operate $\nabla\cdot ...
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Can a Set of “Maxwell's Equations” for Newtonian Gravitation be Derived from Newton's Force + Special Relativity?

When I learned about electromagnetism in my first year of undergraduate school, Maxwell's equations were derived roughly in the following way (see also here or in [1]): Gauss's law for a static ...
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Electric field from time varying charge density

Inside a cylinder of infinite length in $z$ axis, there is charge density $ ρ = cos(βz -ωt)$. I want to find the electric field and as far as i can understand we will get a radial component of $E$. ...
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Spectroscopy from a classical light wave or photon only?

In chemistry we mostly regard light/electromagnetic radiation as a beam of particles or photons. This is a very useful model to explain molecular excitations and ionisations from quantum interactions. ...
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56 views

Does a Static E-field Increase the Gauge Invariant Vector Potential Without Bound?

The gauge invariant formulation of Maxwell's Laws (7.13): Indicates that the transverse electric field is the time derivative of the transverse vector potential. This gauge invariant vector ...
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Maxwell's Equations, cast in terms of magnetic vector potential [closed]

Derive $$ \nabla \times \frac{1}{\mu_r} \nabla \times A + \mu_0 \sigma \frac{\partial A}{\partial t} + \mu_0 \frac{\partial}{\partial t} \left( \epsilon_0 \epsilon_r \frac{\partial A}{\partial t} - ...
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How to properly construct the electromagnetic tensor in curved space-time? (Part II)

In this question, I am testing what was previously discussed. I can't seem to get my results to match D'Inverno's electromagnetic tensor for a charged point (page 239 of his book - Introducing ...
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One question about derivation of Maxwell equations

I saw the following way of derivation of Maxwell equations: author starts from Lorentz transformations for the 3-vector of force, then he applies them for the Coulomb law, after that gets the Lorentz ...
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594 views

Electromagnetism - Proof of the Uniqueness theorem for an external problem

In the electromagnetic Uniqueness theorem, we consider a volume $V$ enclosed by a surface $S$. It is initially assumed that two different fields are valid solutions for the Maxwell's equations with ...
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634 views

Electromagnetic duality

A key aspect of modern physics is the mapping of theories or different descriptions of a theory into a one-to-one correspondence. As I am trying to further understand the electromagnetic field tensor, ...