The four fundamental fundamental equations of electromagnetism.

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Inhomogeneous Maxwell's equations in CGS units

What is the basis or the way of writing the given inhomogeneous Maxwell's Equations in CGS units: $$\nabla.E=\frac{\rho}{\epsilon_0}$$ $$\nabla\times B=\mu_0J+\mu_0\epsilon_0\frac{\partial E}{\partial ...
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Time-harmonic Maxwell's equations

My question is about the time-harmonic or frequency domain (differential) form of Maxwell's equations. If one solves these and obtain the complex vector field $E$, are the real and imaginary parts ...
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Is magnetic reconnection reconcilable with magnetic field lines neither starting nor ending?

According to Maxwell's equations, magnetic fields are divergence-free: $\nabla \cdot \mathbf{B} = 0$. If I understand this correctly, this means that magnetic field lines do not start or end. How can ...
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Maxwell's equation; electromagnetism [on hold]

I'm just curious about this, but I want to know about Maxwell's equation? What its use? Please define it in a simple way.
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1answer
61 views

Why do high voltage transmission line workers need a Faraday cage suit?

In this video the high voltage transmission line workers are wearing a Faraday cage suit. Why is this needed? Without the Faraday cage, the resistance of the human would be very high compared to the ...
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35 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 $E$. ...
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49 views

$E$-field from changing current in straight wire

A very long insulated wire oriented along the $z$ axis of a cylindrical coordinate system is carrying current that is defined by the following function: $$I(t) =Io + k⋅t$$ (current increases linearly ...
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Spectroscopy from a classical light wave or photon only?

In chemistry we mostly regard light/electromagnetic radiation as a beam of particles or photons. This is a very useful model to explain molecular excitations and ionisations from quantum interactions. ...
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1answer
38 views

Apparent discrepancy between Lagrange field equation and Maxwell equation [closed]

I am deriving Maxwell's equations from a Lagrange field equation and have come across something I can not figure out no matter how hard I try. The problem is in the signs. If we take the Lagrange ...
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Where do Maxwell's equations come from?

I recently started learning the basic forms (integrals) of the Maxwell's equations, and everything that is related to electromagnetism seems to be derived from these fundamental equations. Now my ...
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1answer
50 views

Books on Faraday, Maxwell

Can you recommend a/some good book(s) on Faraday for the lay person? In particular, in relation to his 'Experimental Researches in Electricity'. Also, any books explaining how Maxwell explained ...
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Bobbin with $I=I_{0}\sin(\Omega t)$

If I have an infinite bobbin with $I=I_{0}\sin(\Omega t), \mu$ and $n=N/L$ using Ampère and supposing that $d\vec{D}/dt=\vec{0}$ I have found that $$\vec{B}=n\mu I_{0}\sin(\Omega t)\vec{e_{z}}$$ But ...
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Would magnetic charge (i.e., magnetic monopoles) be Lorentz invariant if it existed?

Would magnetic charge (i.e., magnetic monopoles) be Lorentz invariant if it existed? It is clear that Maxwell's equations in themselves permit magnetic charges but what would their relativistic ...
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Boundary conditions for vector wave equations

Assume the time-harmonic case of Maxwell's equations, one can obtain the following vector wave equations: $$ ...
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Calculating current on power line from induced voltage on nearby loop

The question I'm having trouble with is: A small circular loop of 5mm radius is placed 1 meter away from a 60Hz power line. The voltage induced on this loop is measured at 0.6 microvolts. What is the ...
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2answers
274 views

Are photon energies conserved in general relativity?

As I understand it, both Maxwell's wave equation and the null geodesics of general relativity are scale invariant. Thus an electromagnetic wave can be shifted along a null geodesic without changing ...
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Why wouldn't any Emission Theory work?

http://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/origins_pathway/#Emission Here, at the Emission theories of light, I loved the discussed theory. There seems to be a contradiction right ...
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172 views

Solution of simple problems using only Maxwell equations in differential form

Solve simple electrostatic or magnetostatic problems using only Maxwell equations. For example: In every book there is an excercise to find a magnetic field outside a thin wire of radius $a$ with ...
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37 views

Constant charge density and magnetic field

Suppose we have an arbitrary number of point charges in a vacuum, described by a constant charge density $\rho$. Can they be the sources of a magnetic field $\mathbf{B}$? My intuition is that they ...
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37 views

How to apply voltage source in FEM when solve Maxwell equation?

I need to solve the Maxwell equation of electric field by finite element method. In this function, the right hand side is the current density. However, in my problem, the voltage source with 1 MHz ...
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1answer
58 views

Problem with the Ampere-Maxwell Law [closed]

We know that $$J=\sigma E$$ where $J=dI/dS$ is the current density, $\sigma$ the conductivity, and $E$ the electric field. So, if we put that into the Ampere-Maxwell law, then the law transforms ...
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62 views

Isn't there a loop in maxwell's equations? [duplicate]

I am curious about the following case: Consider the electrical field in a particular point just changed for some reason. Then by the maxwell's equations, there will be magnetic field generated ...
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20 views

Local form of Ampere's law

How can I find the magnetic field created by an infinite straight wire of radius $R$ and current density $\vec{j}$ using only the local form of Ampere's law : $\vec{\nabla}\times \vec{B} = \mu_0 ...
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How to use Ampere's Law for a semi-infinite wire with current?

Suppose that there is a semi-infinite wire which extends to infinity only in one direction. There are no other circuit elements at the other end(finite end) of the wire and the current does not loop. ...
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1answer
66 views

Can Maxwell's Equations explain electromagnetic radiation emission in an atom?

Can Maxwell's equations be used to explain the process of spontaneous emission when an electron drops from a higher energy level to a lower energy level? According the Maxwell equations, a changing ...
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What was the improvement that Maxwell did to the electromagnetic field equations and why?

What was the improvement that Maxwell did to the electromagnetic field equations and why? I understand that he combined the main equations so that you could get a wave equation for the vectors of ...
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Do the relations between E/B and D/H contain higher order multipole terms?

Jackson writes in section 1.4 (third edition) that \begin{align*} D_\alpha &= \epsilon_0 E_\alpha + \left(P_\alpha - \sum_\beta \frac{\partial Q'_{\alpha\beta}}{\partial x_\beta} + \ldots \right) ...
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How do I show $e_r$ and its first- and second time derivative?

What does a charge q moving in a circular orbit with a constant velocity (a "rotating charge") and a stationary observer that measures the E field look like? And how do I show $e_r$ and its first- and ...
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273 views

Maxwell's equations invariant under all linear transformations?

Maxwell's equations in tensor notation read: \begin{align} \partial_\mu F^{\mu\nu} &= J^\nu \\ \partial_{[\lambda}F_{\mu\nu]} &= 0 \end{align} Consider doing a general coordinate ...
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Maxwell's equation in curved spacetime - how come? And experimental evidence?

I'm trying to understand the generalization of Maxwell's equations to curved spacetime. In FLAT (Minkowski) SPACETIME: If we define the "four-potential" as $$\ ...
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How do I construct the Maxwell tensor $\bf{^*F}$ from Fadaray one $\bf{F}$ in a non-flat spacetime?

In the book Gravitation (Misner, Throne and Wheeler), it's said that to consider the line element of the flat space on the derivation of Maxwell tensor $\bf{^*F}$ from the Fadaray tensor $\bf{F}$ ...
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1answer
76 views

Invariance of Maxwell equations [closed]

Is there an easy way to show that the Maxwell equations $$ \partial_\alpha F_{\beta\gamma} + \partial_\gamma F_{\alpha\beta} + \partial_\beta F_{\gamma\alpha} = 0 $$ are invariant under a Lorentz ...
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Does a Static E-field Increase the Gauge Invariant Vector Potential Without Bound?

The gauge invariant formulation of Maxwell's Laws (7.13): Indicates that the transverse electric field is the time derivative of the transverse vector potential. This gauge invariant vector ...
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What does it physically mean to take the curl of the curl of a field (wave equation derivation)?

What does it physically mean to take the curl of the curl of a field in the derivation of the electromagnetic wave equation from Maxwell's equations, as presented here, on Wikipedia? Why was it a ...
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How does a synchronous motor know to increase current when the mechanical load is increased?

Consider a very simple singe phase synchronous motor, such as the one shown in figure 1. This motor will not be self starting, but if an AC voltage is applied and the permanent magnet is given an ...
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Aether/Ether in Electrodynamics?

From reading Maxwell's original papers on the formulation on the dynamics of electromagnetism, I saw that Maxwell kept mentioning aether in his paper. I know today in modern physics the Michelson ...
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Is Maxwell's field the wave function of the photon?

In his ArXiv paper What is Quantum Field Theory, and What Did We Think It Is? Weinberg states on page 2: In fact, it was quite soon after the Born–Heisenberg–Jordan paper of 1926 that the idea ...
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Faraday's law in free space explaining away the constant vector?

Let's say that I have a plane electromagnetic wave travailing in free space, and I know the electric field part to be $\vec E$. If I am using Faraday's law to get the magnetic field part I will get ...
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Integral vs differential forms of Maxwell's equations

As stated in this post, the integral and differential Maxwell equations should be identical. However, in a text I was reading it states that The integral forms of Maxwell’s equations describe the ...
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Why does the electric field vanish at infinity?

When $r \rightarrow \infty$, $E \rightarrow 0$ for a point charge or set of charges or a finite charge distribution. While this seems obvious, I cannot find a reason why this is true when inspecting ...
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How wrong are the classical Maxwell's equations (as compared to QED)?

Now, I don't really mean to say that Maxwell's equations are wrong. I know Maxwell's equations are very accurate when it comes to predicting physical phenomena, but going through high school and now ...
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Does displacement current occur in an inductor?

We have learned in school that displacement current comes about due to a change in electric field flux per time in a capacitor (Ampere-Maxwell Law). Does the same displacement current come about in an ...
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Analytical solution to Maxwell's equations in 3D

I'm working on solving Maxwell's equation numerically and have implemented Yee's algorithm in Matlab. In order to check if the algorithm is implemented succesfully, I need an analytical solution to ...
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1answer
94 views

How did special relativity change physicists views on the two prominent inverse square laws (ie Newton grav and Coulomb's law)?

On page 107 in Hartle's Gravity -- An introduction to Einstein's General Relativity, he says the following With the success of special relativity it became apparent that the Newtonian theory of ...
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Interpretation of the displacement current

From Maxwell's equations, why is the displacement current viewed as a source for a magnetic field? If the displacement current were moved to the other side of the equation it would like like a current ...
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59 views

Knotted solutions of Maxwell's equations in flat vacuum - do they really exist?

The paper http://arxiv.org/abs/1502.01382 claims that such solutions exist and that a number of specialists know them since a long time. Is this paper correct? Jackson's text on electrodynamics does ...
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Free charge density and current in an ohmic material

I have come across what seems a paradox -or at least an exotic conclusion- regarding current conduction in an ohmic material. It is well known that free charge density can only be zero on an ohmic ...
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Anyone know of a flow chart or list of common/useful consequences of Maxwell's equations?

I just recently started to appreciate the Maxwell equations. I had never really take the time to study them but I feel like I'm finally more familiar with them. I've noticed that it seems like a lot ...
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Can a charge moving in an open trajectory qualify as current?

It is sometimes said that a point charge is equivalent to an electric current. If it were a steady current, I should be able to find it from Ampere’s law or Biot-Savart’s law. Even if the current is ...
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Why does charge build up at the boundary surface of two media?

On a homework problem, we are asked to to use the first two Maxwell equations, $$\nabla\cdot \mathbf{B} = 0$$ $$\nabla \cdot \mathbf{D} = \rho$$ to show that along the boundary surface of two ...