The four fundamental fundamental equations of electromagnetism.

learn more… | top users | synonyms

1
vote
2answers
87 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 ...
1
vote
3answers
198 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 ...
1
vote
1answer
186 views

Maxwell's equations as the particular case of massive vector field equation

There was a discussion (please look to the comments on my answer) about getting Maxwell's equations for free spin-1 field by using massive spin-1 representation's equations. I'll start from the ...
1
vote
1answer
62 views

Is it necessary for EM fields to be dependent & co-exist in static conditions?

I was having a discussion today with one my colleagues in the lab about the independence and co-existence of EM fields.$$$$ My argument: In time-varying fields: EM fields are necessary dependent, ...
1
vote
1answer
53 views

Do the Maxwell equations yield the proper time of electromagnetic waves?

I apologize in advance for possible errors in my premises as I have no precise knowledge of Maxwell equations. Proposals for the correction or even abandon of my question are welcome. As Maxwell ...
1
vote
1answer
156 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?
1
vote
3answers
325 views

Magnetic B Field of Point Charge Not at Constant Velocity

I'm working on an N-body simulator for charged particles. I know that moving charged particles generate a magnetic field, and another moving charged particle could be effected by this magnetic field. ...
1
vote
1answer
258 views

Faraday's Law and magnetic monopoles

The magnetic monopoles does not exist which can be shown by $ \int {\vec{B} \cdot d\vec{A}} = 0 $. But in Faraday's Law of electromagnetic induction, we clearly show the EMF induced is the time rate ...
1
vote
2answers
672 views

Lorentz Invariance of Maxwell Equations

I am curious to see a simple demonstration of how special relativity leads to Lorentz Invariance of the Maxwell Equations. Differential form will suffice.
1
vote
1answer
81 views

Finding the magnetic vector potential by calculus of variations

Given the functional $$F[A]=\int_{\mathbb{R}^3}\{\frac{1}{2\mu(x)}|\nabla\times\vec{A}|^2-\vec{J}\cdot\vec{A}\}d^3x$$ with $\vec{A}$ is a candidate vector potential for the field ...
1
vote
2answers
102 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?
1
vote
1answer
109 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 ...
1
vote
2answers
155 views

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 ...
1
vote
1answer
269 views

Uncertainty-principle and the Maxwell formalism of electromagnetic waves

An electromagnetic wave (like a propagating photon) is known to carry it's electric and magnetic field-vectors perpendicular and each depending on the differential change of the other thus "creating" ...
1
vote
1answer
1k 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?
1
vote
2answers
429 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, ...
1
vote
1answer
257 views

Solution Maxwell's equations cylinder

I face some trouble solving Maxwell's equations inside a cylinder with perfect conductor boundaries (in 3D) ? We work with cylindrical coordinates $(r, \phi, z)$ and we make the assumption that fields ...
1
vote
1answer
133 views

Electric Potential at nano scale

I’ve a got a question; and I am hopeful that you can provide any information or direct me to a better resource. I'm not a physicist; so please correct me if I'm wrong. Scanning Probe Microscopy (SPM) ...
1
vote
1answer
91 views

Maxwell equations and Fourier decomposition

I'm currently working on maxwell equations and in order to lower the fields dimension, we perform a Fourier decomposition (according to $\theta$) due to the system symmetry. For any vector field ...
1
vote
1answer
123 views

Show that the plane of incidence is perpendicular to the surface of reflection

Is it possible to derive from the boundary conditions of the Maxwell equations for E and H, that the plane of incidence for an EM wave is perpendicular to the reflection surface? How? If not, what ...
1
vote
1answer
87 views

Idea of precursors of the electro-magnetic waves

The idea of the material Maxwell equation is almost clear. But I'm curious about the idea that except for material equation the pure Maxwell equation should work, but in harder sense: more currents ...
1
vote
1answer
151 views

Determine the flow and amplitude equation for thermal energy (with Del operator)

It is a question vector calculus and Maxwell's laws. I put it this way. Let's say, we are working in a $3$-Dimensional space ( e.g $x\cdot y\cdot z = 4\cdot3\cdot2$, a certain room/class of that size ...
1
vote
2answers
1k views

Conservation of Energy and the Poynting Theorem

Conservation of energy in an electrical circuit can be expressed by Ampere's law $$\nabla \times \textbf{B} = \mu_o \textbf{J} + \epsilon_o \mu_o \frac {\partial \textbf{E}} {\partial t}$$ when ...
1
vote
2answers
179 views

Should $E$ and $B$ change with Gravity?

Lets examine a typical GR metric: $$ds^2=g_{00}dt^2-g_{11}dx^2-g_{22}dy^2-g_{33}dz^2$$ The "d" going with ds has its correct meaning when the path is specified with respect to a one dimensional ...
1
vote
0answers
24 views

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 ...
1
vote
1answer
41 views

Uniformly charged sphere's electric field

I am facing this topic for the umpteenth time in my college career and, of course, every teacher has explained it in a different way. In this course, to find the expression of the electric field of a ...
1
vote
0answers
38 views

Electromagnetic fields in daily life [closed]

I have been reading up on electromagnetism lately, and to gain some intuition I wanted to know what effects electric and magnetic fields would have in daily life if they were generated "without any ...
1
vote
0answers
58 views

Were Maxwell's equations first formulated by McCullough?

Some years ago, I heard a talk about a an Irish or Scottish physicist named McCullough who had formulated Maxwell's equations several years before Maxwell. This fellow was recognized for his work, ...
1
vote
0answers
158 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 $r \to \infty$ ...
1
vote
0answers
141 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 ...
1
vote
1answer
176 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 ...
1
vote
1answer
240 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 ...
1
vote
0answers
49 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 ...
1
vote
0answers
62 views

Maximise magnetic force at one point while minimizing at another

Is it possible to have a magnet that attracts one object strongly, but not another object behind that first object? Given an (electro-) magnet M above two thin parallel steel sheets P1 and P2 in the ...
1
vote
0answers
94 views

Can universe be a closed manifold?

I had a question at MSE which gave a rise to another question. Maxwell equations can be written in form $$d\star F = J$$ Then by Stokes theorem we have $$ \int_U J = \int_U d \star F = ...
1
vote
2answers
77 views

What's so special about wave solutions of EM?

Maxwell's equations allow for wave solutions via oscillations between electric and magnetic field content. Couldn't we generate electric waves also if that solution didn't exists? Imagine there was ...
0
votes
2answers
253 views

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 ...
0
votes
3answers
871 views

Divergence equations (Maxwell)

Let $\mathbf{E}(r,t),\mathbf{B}(r,t)$ be two vector fields (in $\mathbb{R}^3$), s.t. they satisfy fot $t=0$ the equations: $\nabla \cdot \mathbf{B}(r,0)=0.$ $\nabla \cdot ...
0
votes
3answers
1k 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} ...
0
votes
1answer
50 views

Can someone show me how Green's function would apply for this simple case?

I'm reading up on some stuff on basic electrostatic here: http://hyperphysics.phy-astr.gsu.edu/hbase/electric/laplace.html Can someone use Green's function to show me the form of $V$? Update: I ...
0
votes
2answers
2k views

Lorentz and Galilean transformation

I read about Lorentz and Galilean transformation in a book of modern physics some days back, but couldn't clearly understand the difference between the two? Also it was stated there that maxwell's ...
0
votes
1answer
45 views

Maxwell calculations that predicted the generation of waves (further use for wireless telegraphs)

At this point in this documentary about the history of electricity: https://www.youtube.com/watch?v=oPnS2WO2_0k&t=4m40s the guy says the Maxwell calculations predicted the generation of certain ...
0
votes
1answer
35 views

Is the field generated by an electromagnet always proportional to its current?

Imagine that I use a long wire to create an electromagnet. Let's also assume that the current flowing along the wire is constant, and that the wire is winded on the vacuumm. Is the magnetic field ...
0
votes
3answers
548 views

Advanced Heaviside-Feynman formula implies electromagnetic inertia?

The Heaviside-Feynman formula (see Feynman Lectures vol I Ch.28, vol II Ch. 21) gives the electric and magnetic fields measured at an observation point $P$ due to an arbitrarily moving charge $q$ $$ ...
0
votes
2answers
830 views

Positive emf? What does positive emf mean?

Could someone please explain to me why we want to take the "magnitude" of the emf?
0
votes
1answer
299 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 ...
0
votes
1answer
35 views

Predicting Faraday's law, Changing Fields

Are there other equations that we can predict Faraday's law from? I know that each of Maxwell's equations are 'fundamental', but I feel like Gauss's law and Ampere's Law are very "nice", and for some ...
0
votes
1answer
36 views

Is $H_0^1$ something reasonable for the electric field for a perfect conductor?

I'm trying to pull over some concepts that were derived for Navier-Stokes like equations to Maxwell's equations for the perfect conductor. At a certain point, I am about to assume that the electric ...
0
votes
1answer
65 views

Application of Displacement Current

I'm reasonably happy with the derivation and results of displacement current, however, I'd like to be aware of a few practical applications of this idea. So far, the only one I'm aware of is when ...
0
votes
1answer
985 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 ...