5

One answer to your why, is, because that is what Maxwell's equations say, and they model perfectly the data we have of classical electromagnetic interactions. Particularly the form : $$ \nabla\times E = -\frac{\partial B}{\partial t}, \;\;\text{Faraday's induction law} $$ The change in the electric field in space is affected by the change in the ...


5

Imagine that the secondary isn't connected to anything and isn't pulling any power. What keeps the primary current from being infinite? It's just a wire, connected across a voltage source, right? The answer is the inductance of the primary: It impedes the AC current from the AC voltage source. Even when the current in the secondary is zero, there's an ...


3

Imagine a current going through a resistor and generating heat. Does it matter which way the current goes? No, it doesn't; you get heat either way. So reversing the current many times a second, as AC, still generates heat. Sometimes people get tangled up because they somehow think that electrons are "used up" in electric circuits. But they're not. The ...


3

The two equations involving the divergence aren't dynamical (they have no time derivatives), and if they're satisfied initially, they're automatically satisfied at all later times. They tell us about the sources and sinks of the fields. The two equations involving the curl have time-derivative terms and a current term. The time-derivative terms describe ...


3

It's garbage. Just another perpetual motion/free energy scam.


3

Permanent magnets can't be explained in terms of Maxwell's Equations or Classical Physics in general. As most (if not all) of the phenomena that arrises due to microscopic behaviour, you need Quantum Physics to explain it properly. Permanent magnetism comes from spin. Spin is an intrinsic property of every particle, like mass. It is quantized, coming in ...


2

To answer your main questions: why can't I say If the flux is zero, Field lines are zero? The flux through a particular area is the difference of the number of magnetic field lines pointing one way through an area and the number of magnetic fields pointing the other way. If you have the same number of field lines pointing into and out of a particular ...


2

Starting from your equation (3) we have \begin{equation} \mu_0\mathcal{J}_\mu = \sum^4_{\mu=1}\frac{\partial F_{\mu\nu}}{\partial X_\nu} = -\sum^4_{\mu=1}\frac{\partial F_{\nu\mu}}{\partial X_\nu} \end{equation} therefore your equation (5) should read \begin{equation} \sum^4_{\mu=1}\frac{\partial F_{\nu\mu}}{\partial X_\nu} = - \mu_0\mathcal{J}_\mu \end{...


2

The fact that the material is magnetic means that it has a magnetization, which is a source of Magnetic Field. But another interesting thing happens. Because it is made out of matter, the magnet has a different permeability $\mu$ than of vacuum, which is an obstacle to the field permeating the material. This means the resulting magnetic field will be weaker ...


2

Adding a cosmological constant $\Lambda$ won't change Maxwell's equations (which are obtained when you vary the action with respect to the field $A_\mu$), but it will change the equations of motion in the gravity sector. See Supersymmetric, cold and lukewarm black holes in cosmological Einstein-Maxwell theory, for instance. Also this wikipedia article.


2

But when the interior of magnetic material is concerned how is the direction of B-Field justified experimentally. You don't need an extra justification, because magnetic material is nothing but a collection of charges, some of them being held in place by nonelectric forces, others moving. Since it's, deep down, just a collection of charges, the same laws (...


2

They’re not axioms: They’re experimental results. Coulomb, Faraday, etc did a lot of experimental work to observe and systematize the underlying phenomena. Maxwell then reformulated them (though not in the modern form) and added the displacement current term which itself was later confirmed experimentally. So the “why” historically comes down to “because ...


1

Use the right-hand rule: the thumb goes upwards with the conventional current of the wire. This means the magnetic field will be going counter-clockwise when viewed from the top. At the location of the charge, the magnetic field points out of the screen. Now, use Fleming's left-hand rule: The thumb will be the direction of the force which we want, the index ...


1

You are asking where the energy of a permanent magnet comes from. Now these objects are made of usually metals, that have electrons in them that are on this site cite two ways: loosely bound delocalized Now the magnetic energy of the magnet comes from the magnetic moments of their electrons. Ordinarily, the enormous number of electrons in a ...


1

But according to this in a DC circuit there should be no potential drop across the inductor(because di/dt would be 0) Correct, the voltages and currents in a DC circuit are constant (by definition) thus, inductors in a DC circuit have zero volts across. Were we only considering the instantaneous moment after the switch was pressed for the derivation ...


1

for very thin films of material, there is no "macroscopic" test technique to magnetically determine the film composition. This problem is easily solved if you have access to any of a number of vacuum methods of determining chemical compositions of thin films (secondary x-ray, auger spectroscopy, etc.) Most commercial labs containing an electron microscope of ...


1

A magnetic field produces current in a wire as it pushes electrons in a certain direction until the electrons compress and their electrostatic repulsion counters the magnetic driving force; equilibrium is reached, there is no current. A wire within a constant magnetic field will always reach an equilibrium state in which there is no current in the wire. ...


1

Maxwell's version of Faraday's law of induction is $$ \nabla\times {\bf E}= -\frac{\partial {\bf B}}{\partial t}. $$ Now apply $\nabla\times$ to both sides. Note that $$ \frac{\partial }{\partial t}(\nabla\times {\bf X})= \nabla\times\left( \frac{\partial {\bf X}}{\partial t}\right). $$


1

There are two basic equations for treating static magnetic fields in matter (In the following $\mathbf{J}=0$ is assumed). The first is $\mathrm{div}\mathbf{B}=0$ which essentially means that the magnetic flux density $ \mathbf{B}$ has no sources and $\mathbf{H}=\mathbf{B}-4\pi \mathbf{M}$ (here cgs-units are used) which defines $\mathbf{H}$ called magnetic ...


1

Since $\mathbf{v}$ is to the left and $\mathbf{B}$ is into the page, $\mathbf{v}\times\mathbf{B}$ is towards the bottom of the page. Thus, a mobile positive charge would flow clockwise (AEDCB) around the circuit and so the electric current is clockwise ('up' through the resistor). Recall that the direction of electric current is in the direction of positive ...


1

The closest I can find is attraction/repulsion of two parallel current carrying wires . There you go! You can model the permanent magnet as made up of lots of little current loops that each form the dipole element of an atom. (Why that’s a good model is a separate question). Together they act like a bigger loop. The field from that also induces a ...


1

This can not happen if only by energy conservation. The Maxwell equations may seem to indicate otherwise but electric and magnetic fields do not generate one another. They are mutually dependent quantities and it is this fact that is expressed in two of the four equations.


1

It is a textbook problem to get the magnetic field of a permanent magnet sphere that is perfectly uniform. It turns out it looks exactly like the field of a ideal dipole. The solution is a bit messy already, but if the magnet has a total magnetic moment of $\mathbf{m}$ and radius $a$, then the magnetic field for $r>a$ is: $$\mathbf{B}(r>a)=\frac{\...


1

I'll show to you "how this is the case", "how this works", but this needs time. This is a very interesting question and I'm sorry to see that books divide in two set: basic one that simply jump the problem (maybe mentioning it or reporting formula saying that calculations are boring, while they are exciting); and advanced ones, that obviously deal with a ...


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