# Maxwel's equations Definition and 12 Discussions

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1. ### I Why must a pure force depend on the four-velocity?

Disclaimer: Please read in the following formulas ##E/c^2## instead of ##m##, because W. Rindler used relativistic mass, what might be confusing with today's usage of the term "mass". I am reading the chapter "38. The formal structure of Maxwell's theory" in Wolfgang Rinder's book "Introduction...
2. ### I Understanding the critic of this author for conventional S field

I joined an article by Davis and Onoochin. I have troubles to understanding his critic of the conventional field momentum interpretation (sec. 3). More precisely, while I am able to check that eq. (23) is true, and that the field is of the order ##1/r^5##, I don't understand in which way this...
3. ### Where I can find similar examples to this kind of question? "given the electric field. E = (-3 / x*e0)i, find the charge density."

I'm preparing for exam but it seems I can't find problems similar to this on the internet. Here I will apply Gauss's law on the electric field vector to get the charge density. but the problem is that I can't find similar examples on the internet that uses direct vectors on Maxwell's equations...
4. ### Deriving electric and vector potential

1- Write down the complete MAXWELL equations in differential form and the material equations. 2- An infinitely extensive area is homogeneously filled with a material with a location-dependent permittivity. There are charges in the area. Give the Maxwell equations and material equations of...
5. ### Cases when Ampere's circuital law fails to hold

Well, I guess that is pretty much my question.
6. ### Can the displacement current be equal to and opposite in sign to the conduction current so the total current will be zero?

If so, what will I measure in the Ampermeter, the zero total current or the value of the conduction current? I was thinking of the following example- a circuit consist of a current source, an Ampermeter, a switch, and a semiconductor. The semiconductor can have both conduction and displacement...
7. ### Constructing an equation for the induced EMF in terms of the radius of the circular loop

In order to calculate for the curl of the induced electric field for a loop moving in a uniform magnetic field, and using the cylindrical coordinate system for a curl, it's my understanding that since the B field is in the 𝑧̂ direction, then so is the partial time derivative of B, and therefore...
8. ### Propagation of EM waves

Homework Statement Use Maxwell's equations to elaborate an coherent explication of why electromagnetic waves propagate independently of the source that produces them. Homework Equations Maxwell's equations in vacuum: ##\nabla * E=0## ##\nabla * B=0## ##\nabla \times E = -\frac{\partial...
9. ### I How was the value of the permittivity of free space determined?

The permittivity of free space, ε0, is usually given without any derivation or historical context as to how it was experimentally determined. Could you explain to me how the value of ε0 was first determined experimentally or provide a resource that gives such a derivation? Thanks!
10. ### Electromagnetic Waves — Given E, find B....

Homework Statement A plane electromagnetic wave travels upward. At t = 0, x = 0, its electric field has the value E = 5 V/m and points eastward. What is the wave's magnetic field at t = 0, x = 0? Homework Equations B=B init. sin(kx-wt) E=E inti. sin(kx-wt) E=cB The Attempt at a Solution I am...
11. ### Slowly oscillating surface current on a solenoid

Homework Statement From an original surface current ##\vec{K}=K\hat{\phi}## on a finite solenoid, I got ##\vec{B}=\mu_{0}Kf(z)\hat{k}##, for ##r<R##. Assuming that ##\vec{K}## now slowly oscillates in time such as: ##\vec{K(t)}=K_{0}\cos\left(\omega t\right)\hat{\phi}##, so that I still can use...
12. ### How was Newtonian relativity ruled out in EM propagation?

What I've read on the Michelson/Morley experiment explains that it made the idea of the luminiferous aether seem less likely, but I don't think I've ever seen an explanation of why everyone didn't just assume that light follows normal Newtonian relativity. What I mean is this: according to...