The four fundamental fundamental equations of electromagnetism.

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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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32 views

Compatibility between solutions of explicit Maxwell equations vs. wave equation?

When trying to solve for the allowed propagation frequencies in a cylindrical waveguide, I approached the problem by solving the wave equation for all three components of $\bar{E}$, and subsequently ...
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Is my simulation result for unpolarized light correct?

This is a follow-up of this question. After that, I picked up some knowledge of FDTD (an algorithm for solving Maxwell's equations) and simulated following scene: Pic 1 As the picture shows, a ...
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2answers
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Mistake in Briefer History of Time by Stephen Hawking [closed]

I was reading A Briefer History of Time by Stephen Hawking and Mlodinow. I found something silly. On page 36 at the bottom, it says the following : If, say, the sun suddenly disappeared, Maxwell's ...
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688 views

Why is the divergence of a magnetic field equal to zero?

We know due to Maxwell's equations that: $$\vec{\nabla} \cdot \vec{B}=0$$ But if we get far from the magnetic field, shouldn't it be weaker? Shouldn't the divergence of the field be positive? If ...
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35 views

Deduce magnetic field based on electric field

I'm learning Maxwell's electromagnetic equations and i can't wrap my head around this problem: Given the volume $x\in [0,1], y\in [0,1], z\in [0,1]$, electric field $\vec E(x,y,z,t)$ and material ...
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Maximum $B/E$ when $(|\delta E|/|\delta t|) \to +\infty$ (Maxwell's Equations) [closed]

Is there a maximum for $|B|/|E|$ changes in Maxwell's Equations, like if we have $(|\Delta E|/|\Delta t|) \to +\infty$ then how will be the $|\Delta B|/|\Delta E|$ or the resulting $|B|/|E|$?
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295 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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0answers
86 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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0answers
48 views

Sommerfeld radiation conditions for an electromagnetic field

There is some confusion in the definition of Sommerfeld radiation conditions for an electromagnetic field, which are related to the asymptotic behaviour of the field for a distance $r \to \infty$ ...
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2answers
51 views

Condition for the magnetic field

Let $B$ be the magnetic field. If $$\nabla \times B = 0$$ and of course $$\nabla \cdot B= 0$$ Can we conclude that $B=0$? For a general field it is wrong because every constant vector will ...
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188 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, ...
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37 views

General wave equation derived from Maxwell's equation

I need to derive the general wave equation from Maxwell's equation without using the divergence therom (because I haven't read multivariable calc yet!). My physics book gives one but I don't fully ...
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2answers
635 views

What could magnetic monopoles do that electrically charged particles can't?

I understand the significance to physics, but what can a magnetic monopole be used for assuming we could free them from spin ice and put them to work? What would be a magnetic version of electricity? ...
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8answers
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Do Maxwell's Equations overdetermine the electric and magnetic fields?

Maxwell's equations specify two vector and two scalar (differential) equations. That implies 8 components in the equations. But between vector fields $\vec{E}=(E_x,E_y,E_z)$ and ...
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2answers
52 views

Maxwell-Faraday Equation and Electric Fields

I have a question regarding, as the title says, this equation: $\nabla \times \textbf{E}=-\frac{\partial \textbf{B}}{\partial{t}}$ So, the above equation says that the curl of an electric field is ...
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9answers
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Can Maxwell's equations be derived from Coulomb's Law and Special Relativity?

As an exercise I sat down and derived the magnetic field produced by moving charges for a few contrived situations. I started out with Coulomb's Law and Special Relativity. For example, I derived the ...
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3answers
802 views

Which form of Maxwell's equations is fundamental, in integral form or differential form?

I am not sure which form of Maxwell's equations is fundamental, integral form or differential form. Imagine an ideal infinitely long solenoid. When a current is changing in time, can we detect ...
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2answers
86 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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2answers
140 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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1answer
51 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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2answers
120 views

Integration constants in Maxwell's equations (ambiguousness?)

In classical electrodynamics, if the electric field (or magnetic field, either of the two) is fully known (for simplicity: in a vacuum with $\rho = 0, \vec{j} = 0$), is it possible to unambiguously ...
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0answers
55 views

How to do this index notation differentiation?

I am studying classical Maxwell fields and I am stuck on this differentiating part. How can I derive the result given below ? $$\dfrac{\partial}{\partial(\partial A_{\mu}/\partial x_{\nu})} ...
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1answer
449 views

How can KVL & KCL be derived from Maxwell equations?

How can KVL (Kirchhoff's Voltage Law) & KCL (Kirchhoff's Current law) be derived from Maxwell equations in lumped circuits?(Lumped network : if $d$is the largest dimension of the network and ...
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1answer
107 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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3answers
149 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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792 views

Deriving the Poynting Theorem

I am trying to derive the Poynting theorem. So far, I've only been able to narrow down which equations I think I'll need to do so. These are the equations: Maxwell's Equations: $$ \nabla\times{\bf E} ...
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88 views

How to show with Maxwells Equations that nonaccelerating charges dont radiate? [closed]

How to show with Maxwells Equations that nonaccelerating charges don't radiate?
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33 views

Measurement of speed of static electric field propagation?

Could one measure the time delay between charging up an electrode and measuring the static electric field at some distance? For example I've looked up the specifications of an Electric Field Meter ...
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1answer
56 views

How to obtain Maxwell's Lagrangian from complex scalar fields?

I've looked in several books and they all show how to obtain electrical interactions by forcing local gauge invariance of any complex scalar field Lagrangian (like Klein-Gordon or Dirac). I manage to ...
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1answer
211 views

Physical meaning of Maxwell's equations and origin of EM waves

Is it possible to describe the physical meaning of Maxwell's equations and show how they lead to electromagnetic wave, with little involvement of mathematics ?
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2answers
5k views

How do you find the magnetic field corresponding to an electric field?

If we are given the electric field $\vec E$ how can I find the corresponding magnetic field? I think I can use Maxwell's equations? In particular, $\nabla\times \vec E= -{\partial \vec B\over \partial ...
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3answers
137 views

How to understand holography and hologram

I've spent some time reading wiki etc. What I get now is that apart from the normal light amplitude information, holograms also record the phase information of light. But this is so difficult for me ...
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2answers
586 views

Divergence of non conservative electric field

I'm looking for the proof that the 1st Maxwell equation is valid also on non conservative electric field. When we are talking about a electrostatic field, the equation is ok. We can apply the Gauss ...
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96 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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1answer
69 views

Assumptions when calculating $\vec{B}$ using Ampère's (circuital) law

When considering the same setup as in this question, i.e. a straight, infinitely long wire carrying the current $I$, Ampère's circuital law $$\oint_C \vec{B} \cdot \mathrm{d}\vec{r} = \mu_0 ...
2
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1answer
157 views

Why is there no (time derivative of charge density) in the $B$ field in Jefimenko's equations?

I was going through Griffiths chapter on potentials and fields just to brush up on a few old things. He gets to Jefimenko's equations by this general path: Maxwell's equations Introduce scalar and ...
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4answers
133 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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984 views

Is the induced electric field due to time varying magnetic flux always circular?

According to Faraday's law, changing magnetic flux induces an electric field. Is that electric field always circular?
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324 views

Does displacement current exist after the capacitor gets fully charged?

The displacement current is due to changing electric field. Since, after the capacitor gets fully charged there is no changing electric field there is no displacement current.(capacitor connected to a ...
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Where does the 3rd and the 4th Maxwell's equations lead us in the end?

Take the 3rd and the 4th equation from this table. The first tells us that an electric field can be generated by a magnetic field. The second, says that a magnetic field can be generated from an ...
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Are the Maxwell's equations enough to derive the law of Coulomb?

Are the 8 Maxwell's equations enough to derive the formula for the electromagnetic field created by a stationary point charge, which is the same as the law of Coulomb? If I am not mistaken, due to ...
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4answers
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Derivation of Maxwell's equations from field tensor lagrangian

I've started reading Peskin and Schroeder on my own time, and I'm a bit confused about how to obtain Maxwell's equations from the (source-free) lagrangian density $L = ...
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Do these steps demonstrate that acceleration of charged particle is proportional to current?

One formulation of Maxwell's Gauss Law for electric field is: $$\bigtriangledown E = 4 \pi k \rho $$ This can be worked into the Divergence Theorem as follows: $$\int\int_{A} F_\perp \:dA= 4\pi k ...
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Phasor form of Maxwell's Equations

I'm interested in the transformation from the standard Maxwell's equations to their phasor equivalents. From the literature, this means injecting: \begin{equation} E = Re(\boldsymbol{E}e^{j\omega ...
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77 views

Two spinor tensors and Maxwell's equations

Let's have two symmetric (by the indices) spinor tensors $F_{ab}, F_{\dot {a}\dot {b}}$ and conditions $$ F_{ab}, \partial^{\dot {a} a}F_{ab} = 0, \quad F_{\dot {a}\dot {b}}, \partial^{\dot ...
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Understanding the Ampere's Law

We want to study the magnetic field at point $P$. So, from the figure we take that: $\oint_{L_1} B\cdot dl=\mu_0 I_1$ $\oint_{L_2} B\cdot dl=\mu_0 I_2$ $\oint_{L_3} B\cdot dl=\mu_0 I_2$ The ...
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Is there a good experiment to demonstrate Gauss's Law for Magnetism?

I'm trying to come up with a simple experiment that can demonstrate the properties of Gauss's Law for Magnetism. I am aware that it is a mathematical representation of the fact that magnetic ...
3
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1answer
59 views

$D$ and $H$ in macroscopic Maxwell's equation: auxiliary or constitutive?

I'm not a physicist. I want to understand the macroscopic Maxwell's equations. But after reading Wikipedia and other Googled stuffs, I got very confused. In particular, $D$ and $H$ have two different ...
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2answers
141 views

Exterior (covariant) derivatives and electromagnetism

I'm porting Maxwell's equations to curved spacetime and am having trouble reconciling the tensor and forms treatments. I think the problem boils down to a misunderstanding on my part concerning the ...