All Questions

Filter by
Sorted by
Tagged with
3
votes
2answers
121 views

Intuition of Maxwell's Equations [duplicate]

Is there an intuitive explanation for Maxwell's equations? I know they are axioms but is there a logical understanding of why instead of mathematical. Both forms don't explicate the scientific ...
0
votes
1answer
31 views

How does charge movement vary between insulators and conductors?

I've been reading A Student's Guide to Maxwell's Equations by Daniel Fleisch, and he states: in nonconducting materials (called "insulators" or "dielectrics"), charge does not move freely, but may ...
0
votes
1answer
183 views

Maxwell's equations UPML in FDTD with inhomogeneous media

I'm looking at matching the UPML (uniaxial perfectly matched layer) defined in Taflove&Hagness' Computational electrodynamics to an inhomogeneous media (inhomogeneous w.r.t. both $\varepsilon$ and ...
1
vote
3answers
111 views

Where am I going wrong in deriving Maxwell's first equation in differential form?

By denoting the source coordinates with prime, I get flux through a closed surface: $$\Phi= \displaystyle\oint_{A} \mathbf{E}(x,y,z) \cdot \mathbf{\hat{n}}\ dA =q (x',y',z')$$ And now using the ...
0
votes
3answers
123 views

Physical Interpretation of $\nabla \cdot \vec{E} = \frac{\rho}{\epsilon_0} $

The differential's form of Gauss' Law is $$\nabla \cdot \vec{E} = \frac{\rho}{\epsilon_0}. $$ This suggests that at every point in space, the the electric field $\vec{E}$ is determined by the charge ...
8
votes
2answers
1k views

If Ampere's law implies the Biot-Savart law, which implies Gauss's law for magnetism, does that mean Maxwell's equations are redundant?

Studying electromagnetism, I came across the following fact: Maxwell's third equation (divergence of magnetic field is zero) can be derived from the Biot-Savart Law. The Biot-Savart Law can be ...
1
vote
1answer
47 views

How is the third case obeying integral form of Maxwell's second equation?

Let $m$ denote pole strength. In the diagrams: (1) Sky blue: Closed Gaussian surface (2) Red: North pole of magnet (3) Green: South pole of magnet (4) Yellow: Part of magnet cutting Gaussian surface ...
1
vote
2answers
322 views

Why is the divergence of electric field equal to $\rho \over \epsilon_0$ in electrodynamics?

These two equations are true in electrostatics/magnetostatics: $$\nabla \cdot \vec{E}= {\rho \over \epsilon_0},$$ $$\nabla \cdot \vec{B}=0.$$ I have learned that they are also true in electrodynamics....
1
vote
1answer
119 views

Generalization of the Gauss' Law to a lorentz-covariant law in Paper of Kobe: Is it “guessed”?

In the Paper Generalization of Coulomb's law to Maxwell's equations using special relativity by Donald H. Kobe, he tries to derive Maxwell's equations by trying to find covariant laws between tensor ...
3
votes
1answer
177 views

Factor of 4 (or 2) in the gravitoelectromagnetic (GEM) Lorentz-force law. Which is correct? Why is it there?

I realize that the Gravitoelectromagnetic equations (GEM) are derived from the Einstein field equation (EFE) in the degenerate case of reasonably flat spacetime, which is the case for the propagation ...
0
votes
1answer
63 views

What does the charge density signify in the differential form of Gauss law?

Let us say that I have uniformly charged sphere of total charge Q and radius R. The electric field due to this charge distribution at r=R/2 is given by, $$E = \frac{kQ}{2R^2}\hat{r}$$(This was derived ...
2
votes
3answers
197 views

Why do we need a second equation for electric field in Maxwell's Equation?

Suppose we are dealing with electrostatics for this question. A physicist carries out experiments with static charges and determines that, the electric field $\vec { E } (\vec { r } )$ is a quantity ...
0
votes
1answer
174 views

Mathematically Proving Gauss's Law of Magnetism is Indeed Zero, Not working out

Gauss's Law of Magnetism shows us that the divergence of Magnetic field is $0$, $\bigtriangledown \cdot \vec{B}=0$ Then how do you derive that statement by showing the divergence of a magnetic field ...
0
votes
1answer
327 views

Is the curl of the gravitational field required to fully describe Newtonian gravity?

We are familiar with Newton's law of gravitation: $$\textbf{F} = \frac{-GMm}{r^2} \hat{\textbf{r}},\tag{1}$$ which leads to a gravitational field strength relation: $$\textbf{g} = \frac{-GM}{r^2} \...
3
votes
2answers
245 views

Why can we use the 2D projection of a 3D gaussian surface to calculate electric flux?

In order to calculate the electric flux passing through one side of a cone with no net charge enclosed, I originally thought you needed to take infinitesimal areas and dot the normal vector with the ...
1
vote
2answers
2k views

Trouble understanding Electric flux and gauss law

Well, i know that the electric flux is the number of field lines passing a certain area, but (1)what does that mean? I can't the concept itself. I know it have many applications, gauss law one of them,...
3
votes
1answer
3k views

Is Gauss law still true in dielectric material?

In vacuum we have $$\nabla \cdot \mathbf{E} = \frac {\rho}{\varepsilon_0}.$$ Can we still use this formula when there's dielectric material in space? Where $\rho$ is total charge density.
0
votes
0answers
109 views

Does Gauss flux theorem hold in relativity?

Does the Gauss flux theorem, stated in the classical electrostatics as $\iint{\vec{E}}\cdot{\vec{dS}}=q/\epsilon_0,$ hold in the case of relative motions. For instance if we observe a charged body ...
5
votes
5answers
2k views

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 ...
3
votes
1answer
297 views

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 $E$. ...
1
vote
1answer
309 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 ...
0
votes
1answer
449 views

Can Gauss' and Ampere's Laws be written in terms of the divergence of an energy four-vector?

In the first 20 minutes of this video, Susskind derives the continuity equation for charge conservation: $$\dot{\rho}+\nabla\cdot\vec{J}=0$$ (Where $\vec{J}=\frac{\partial\dot{q}^m}{\partial A^m} \:;...
16
votes
4answers
37k views

Divergence of a field and its interpretation

The divergence of an electric field due to a point charge (according to Coulomb's law) is zero. In literature the divergence of a field indicates presence/absence of a sink/source for the field. ...
1
vote
0answers
56 views

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 \...
7
votes
3answers
1k views

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
votes
2answers
1k 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 (...
1
vote
1answer
590 views

Gravimagnetic monopole and General relativity

Review and hystorical background: Gravitomagnetism (GM), refers to a set of formal analogies between Maxwell's field equations and an approximation, valid under certain conditions, to the Einstein ...