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One argument: conservation of linear momentum. Something has to take the difference in linear momentum.


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The other way of phrasing your question: if I have a surface of uniform charge density, and the field inside is zero everywhere, does it follow that the surface is a sphere? The answer is "yes". Imagine we have a non spherical surface. We know that it is possible to have zero field inside any conductor regardless of shape. But we also know that the charge ...


4

Many materials contain microscopic paramagnetic moments which are free to randomly orient themselves in zero magnetic field. If you apply a magnetic field, then the magnetic moments are able to lower their energy by entering a lower entropy state where they are magnetized. In such a material the entropy tends to decrease as magnetic field increase, at least ...


1

No, it does not imply that the surface is spherical and charged uniformly. Imagine a charged conducting shell of arbitrary shape. (An ellipsoid is a simple example.) Gauss' Law tells us that the charges in the conductor fly to the outside surface of the conductor, and the distribution of charges is such that the E-field inside is zero. But for a ...


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I might elaborate upon Sofia's excellent answer in two respects. Not all changing EM fields are wave like. Maxwell's equations have lots of solutions involving changing E and M fields. These can be broken down into two components, the "near field" and the "far field". The difference is that the far field components have a classical wave solution, and hence ...


1

I am trying here to answer your comment "I guess, if fields are undergoing a wave-like change in one frame of reference, they must undergo the same kind of change in any other frame of reference." It's a legitimate remark and I would formulate it even more clearly: in a frame of reference where the charge is at rest it doesn't emit e.m. waves. But it can't ...


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If there are no charges inside the cylinder, then the potential obeys Laplace's Equation: $$\nabla^2V = 0$$ In cylindrical coordinates, that's $$\left(\frac{\partial^2}{\partial r^2} + \frac 1 r \frac{\partial}{\partial r} + \frac{1}{r^2} \frac{\partial^2}{\partial \phi^2} + \frac{\partial^2}{\partial z^2}\right) V = 0$$ Based on your notation, it seems ...


1

Maxwell's Equations are usually written as: $$\vec{\nabla}\cdot\vec{E}=\rho/\epsilon_0,$$ $$\vec{\nabla}\cdot\vec{B}=0,$$ $$\vec{\nabla}\times \vec{E}=-\frac{\partial \vec{B}}{\partial t},$$ $$\vec{\nabla}\times \vec{B}=\mu_0\left(\vec{J}+\epsilon_0\frac{\partial \vec{E}}{\partial t}\right).$$ But the last two might be written more clearly as ...


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Its about Travel Time and Carrier Particles Particles with electric charge give off a field. That field is made of something; virtual photons, the messenger particle for the EM force. Charged particles give off so many and in such random directions that it basically acts like a continuous thing, a field. Individual photons must travel whatever distance to ...


-1

In the full quantum field theory treatment, photons are the quanta of the electric field. So electric field lines travel at the speed of light because their carriers travel at the speed of light. In Maxwell's equations, the speed of light and the propagation of the fields are linked, but not in such an obvious way. First, you can solve Maxwell's equations ...


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As I said in my comment I suggest you to use the Gauss theorem and the fact that inside each metal the field is zero. The picture shows the three metal plates (black), two of them connected to the ground for realizing potential zero. The closed surfaces (light-grey) pass through the metals, and I consider their vertical sides of surface equal to the unity. I ...


3

The cathode is where electrons are taken out of the metal and accelerated towards the screen. So the actual source of the electron rays is the cathode, the anode is simply for accelerating the electrons and to get them away from the cathode.


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The standard classical description due to retarded Lienard-Wiechert potentials does not describe this reaction force back on the source particle. There is force back on the first particle, but it occurs after a delay necessary for the retarded field of the second particle to get back to the first particle. This delay is due to the choice of retarded ...


3

Quantum mechanics and classical E&M have created a whole bunch of fruit. In no particular order: Light is an electromagnetic wave. This means that we are routinely making light with LEDs and the like. It's pretty cool that you can design better antennas, or waveguides, or what have you. While we're at it, knowing why Stefan-Boltzmann radiation goes ...


2

The problem here arises because the 4-current in the OP is assumed to be a 1-form, and after many years of accumulated rust on the subject I completely forgot that this is, strictly speaking, not the right geometrical object that can describe current density. Indeed, being a density, it must be a 3-form, and therefore the correct geometrical object is $$J = ...


2

A very simple example of electromagnetism in curved spacetime is the observed bending of light due to gravitational fields. Usually this is presented as the statement that "photons follow null geodesics." This statement can be derived in a geometric optics approximation to Maxwell's equations in curved spacetime (i.e. it is not just an additional postulate ...


0

If you have a thin circuit with a total resistance $R$, and place it in an external (changing) $\vec{B}$ field, then there is flux through the ring. First, there is flux $\Phi_1$ from the external, changing $\vec{B}$ field. Since that $\vec{B}$ field is changing, there is an emf due to that. Second, the current from the ring itself produces it's own ...


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The question of what causes what is a good one. It's best to think of fields as changing in time due to the spatial configurations of the fields. An example is: $$ \frac{\partial \vec{B}}{\partial t}=-\vec{\nabla}\times \vec{E}.$$ The instantaneous values of $\vec{E}$ not only exert forces on charges (to contribute to their acceleration) but also ...


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Classical electrodynamics is certainly studied in curved spacetimes to understand real phenomena. What better place for gravity and electromagnetism to work together than the ionized, magnetized plasma surrounding an accreting black hole? In particular, we observe quasars with extremely powerful relativistic jets. Quasars are the supermassive black holes at ...


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When you change the flux through a circuit, there are two reasons the flux changes: 1) First, the $\vec{B}$ field in a surface instantaneously spanned by the circuit (at that moment) is changing, in which case there is an electric field in that surface with a circulation $\oint \vec{E}\cdot d\vec{\ell}$ s around the loop that equals $\int -\frac{\partial ...


0

At a fixed time $t$, the wire is the line $(0,vt,z)$ where $z$ can be any value and $s$ can be your instantaneous distance to this line. Specifically, we can consider $\vec{A}(x,y,z,t)=-\frac{\mu_0I}{2\pi}\ln s\hat{z}$ where $s$ is nothing more than a shorthand for $\sqrt{x^2+(y-vt)^2}$. Thus, taking the quasistatic approximation, $$\vec{E} = ...



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