# All Questions

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### 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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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....
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 ...
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 ...
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 ...
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 ...
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 ...
1answer
327 views

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 ...
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 (...
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 ...