The four fundamental fundamental equations of electromagnetism.

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Are photon energies conserved in general relativity?

As I understand it, both Maxwell's wave equation and the null geodesics of general relativity are scale invariant. Thus an electromagnetic wave can be shifted along a null geodesic without changing ...
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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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Why wouldn't any Emission Theory work?

http://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/origins_pathway/#Emission Here, at the Emission theories of light, I loved the discussed theory. There seems to be a contradiction right ...
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193 views

Surely force on shell can't be balanced by field momentum?

Imagine a particle with charge $q$ at rest at the origin. It is surrounded by a concentric spherical insulating shell, also at rest, with charge $Q$ and radius $R$. At time $t=0$ I apply a constant ...
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Constant charge density and magnetic field

Suppose we have an arbitrary number of point charges in a vacuum, described by a constant charge density $\rho$. Can they be the sources of a magnetic field $\mathbf{B}$? My intuition is that they ...
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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 ...
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Displacement current - how to think of it

What is a good way to think of the displacement current? Maxwell imagined it as being movements in the aether, small changed of electric field producing magnetic field. I don't even understand that ...
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2answers
588 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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Force on Stationary Point Charge in Changing Magnetic Field [closed]

Consider a point charge (we will say a proton) a distance "d" perpendicular to a wire with a current I(t), which is increasing. According to Faraday's law, there is an induced electric field from the ...
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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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How to apply voltage source in FEM when solve Maxwell equation?

I need to solve the Maxwell equation of electric field by finite element method. In this function, the right hand side is the current density. However, in my problem, the voltage source with 1 MHz ...
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203 views

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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Reaction-at-a-distance: Do charged plates immediately repel each other?

Imagine that we have a pair of parallel plates, $A$ and $B$, separated by some distance as in Fig. $1$ above. At time $t_1$ we simultaneously charge both the plates. This could be done by ...
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1answer
49 views

Problem with the Ampere-Maxwell Law [closed]

We know that $$J=\sigma E$$ where $J=dI/dS$ is the current density, $\sigma$ the conductivity, and $E$ the electric field. So, if we put that into the Ampere-Maxwell law, then the law transforms ...
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2answers
397 views

Electric field from current without Maxwell's law of induction

A long, straight wire carries a current that decreases linearly with time. What is the direction of the induced electric field outside the wire? I would interpret this as follows: a current ...
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62 views

Isn't there a loop in maxwell's equations? [duplicate]

I am curious about the following case: Consider the electrical field in a particular point just changed for some reason. Then by the maxwell's equations, there will be magnetic field generated ...
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1answer
17 views

Local form of Ampere's law

How can I find the magnetic field created by an infinite straight wire of radius $R$ and current density $\vec{j}$ using only the local form of Ampere's law : $\vec{\nabla}\times \vec{B} = \mu_0 ...
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1answer
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What was the improvement that Maxwell did to the electromagnetic field equations and why?

What was the improvement that Maxwell did to the electromagnetic field equations and why? I understand that he combined the main equations so that you could get a wave equation for the vectors of ...
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1answer
63 views

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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1answer
193 views

What are the boundary conditions for EM waves normally incident on the interface between two dielectric media?

An EM wave, amplitude $E_0$, frequency $\omega_0$, is incident upon a material with relative permittivity (dielectric function) $$\varepsilon \left( z \right) = \left\{ \begin{gathered}{\varepsilon ...
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How are the Lorentz force, Maxwell's third law and Faraday's law of induction clasically related?

Faraday's law of induction can be used in any situation where the magnetic flux is changing through a closed conducting loop. While giving the correct answer, it seems to me that for the following ...
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48 views

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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Do We Need Maxwell's Equations Since They Fail to Account for An Experimental Fact at Least in One Occasion?

This question is an outgrowth of What is the difference between electric potential, potential difference (PD), voltage and electromotive force (EMF)? where @sb1 mentioned Faraday's law. However, ...
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Deriving Ampère's Circuital Law from Ampère's Force Law?

Ampère's force $d^2\vec{F_{21}}$ of current element $i_2d\vec{\ell_2}$ on $i_1d\vec{\ell_1}$ is$$d^2\vec{F_{21}}=-\frac{\mu_0}{4\pi}i_1i_2\frac{\hat{r}}{r^2}\left[2(d\vec{\ell_1}\cdot ...
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How do I show $e_r$ and its first- and second time derivative?

What does a charge q moving in a circular orbit with a constant velocity (a "rotating charge") and a stationary observer that measures the E field look like? And how do I show $e_r$ and its first- and ...
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74 views

How can electric field representation be obtained from Enge representation using Maxwell's equations?

Suppose we have a long electric capacitor. Let $L$ be its length ($z$ coordinate), $W$ its width ($y$ coordinate), and $D$ its full height (full aperture; $x$ coordinate). Let $L\gg W\gg D$. The ...
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Maxwell's equations invariant under all linear transformations?

Maxwell's equations in tensor notation read: \begin{align} \partial_\mu F^{\mu\nu} &= J^\nu \\ \partial_{[\lambda}F_{\mu\nu]} &= 0 \end{align} Consider doing a general coordinate ...
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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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53 views

How do I construct the Maxwell tensor $\bf{^*F}$ from Fadaray one $\bf{F}$ in a non-flat spacetime?

In the book Gravitation (Misner, Throne and Wheeler), it's said that to consider the line element of the flat space on the derivation of Maxwell tensor $\bf{^*F}$ from the Fadaray tensor $\bf{F}$ ...
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1answer
71 views

Invariance of Maxwell equations [closed]

Is there an easy way to show that the Maxwell equations $$ \partial_\alpha F_{\beta\gamma} + \partial_\gamma F_{\alpha\beta} + \partial_\beta F_{\gamma\alpha} = 0 $$ are invariant under a Lorentz ...
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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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What does it physically mean to take the curl of the curl of a field (wave equation derivation)?

What does it physically mean to take the curl of the curl of a field in the derivation of the electromagnetic wave equation from Maxwell's equations, as presented here, on Wikipedia? Why was it a ...
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How does a synchronous motor know to increase current when the mechanical load is increased?

Consider a very simple singe phase synchronous motor, such as the one shown in figure 1. This motor will not be self starting, but if an AC voltage is applied and the permanent magnet is given an ...
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4answers
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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 ...
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Aether/Ether in Electrodynamics?

From reading Maxwell's original papers on the formulation on the dynamics of electromagnetism, I saw that Maxwell kept mentioning aether in his paper. I know today in modern physics the Michelson ...
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Is Maxwell's field the wave function of the photon?

In his ArXiv paper What is Quantum Field Theory, and What Did We Think It Is? Weinberg states on page 2: In fact, it was quite soon after the Born–Heisenberg–Jordan paper of 1926 that the idea ...
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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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Maxwell's equations in curved spacetime

I know that we can write Maxwell's equations in the covariant form, and this covariant form can be considered as a generalization of these equations in curved spacetime if we replace ordinary ...
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Faraday's law in free space explaining away the constant vector?

Let's say that I have a plane electromagnetic wave travailing in free space, and I know the electric field part to be $\vec E$. If I am using Faraday's law to get the magnetic field part I will get ...
4
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Integral vs differential forms of Maxwell's equations

As stated in this post, the integral and differential Maxwell equations should be identical. However, in a text I was reading it states that The integral forms of Maxwell’s equations describe the ...
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Why does the electric field vanish at infinity?

When $r \rightarrow \infty$, $E \rightarrow 0$ for a point charge or set of charges or a finite charge distribution. While this seems obvious, I cannot find a reason why this is true when inspecting ...
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Knotted solutions of Maxwell's equations in flat vacuum - do they really exist?

The paper http://arxiv.org/abs/1502.01382 claims that such solutions exist and that a number of specialists know them since a long time. Is this paper correct? Jackson's text on electrodynamics does ...
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1answer
367 views

Information content of the electrostatic Maxwell equations vs Coulomb's Law vs Poisson's Equation

In electrostatics, we have Maxwell's equations: $\nabla \cdot E = \rho$ $\nabla \times E = 0$ These four equations (the second line standing for three equations) can also be written in terms of the ...
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1answer
31 views

Does displacement current occur in an inductor?

We have learned in school that displacement current comes about due to a change in electric field flux per time in a capacitor (Ampere-Maxwell Law). Does the same displacement current come about in an ...
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1answer
700 views

Proof of equality of the integral and differential form of Maxwell's equation

Just curious, can anyone show how the integral and differential form of Maxwell's equation is equivalent? (While it is conceptually obvious, I am thinking rigorous mathematical proof may be useful in ...
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Analytical solution to Maxwell's equations in 3D

I'm working on solving Maxwell's equation numerically and have implemented Yee's algorithm in Matlab. In order to check if the algorithm is implemented succesfully, I need an analytical solution to ...
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Would a rotating magnet emit photons?

If a magnet is rotating, around an axis perpendicular to the axis north-south axis of the magnet (which I assume to be cylindrical symmetrical), in space (so no-gravity/freefall or friction), should ...
8
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4answers
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Do the integral forms of Maxwell's Equations have limited applicability because of retardation?

In the usual bookwork treatment, it is easy to show that the differential and integral forms of Maxwell's equations are equivalent using Gauss's and Stokes's theorems. I have always thought that ...
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1answer
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How did special relativity change physicists views on the two prominent inverse square laws (ie Newton grav and Coulomb's law)?

On page 107 in Hartle's Gravity -- An introduction to Einstein's General Relativity, he says the following With the success of special relativity it became apparent that the Newtonian theory of ...
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Why magnetic monopole found in spin ice don't modify the Maxwell's Equations?

Magnetic monopole predicted by Dirac nearly a century ago was found in spin ice as quasi-particle(2). My question is Why magnetic monopole found in spin ice don't modify the Maxwell's Equations? (I ...