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8

Modulo constants, this cross product is called the Poynting vector, $$ \mathbf S=\frac1{\mu_0}\mathbf E\times\mathbf B. $$ It represents the flow of energy in the electromagnetic field, so that the energy density $u=\tfrac12\varepsilon_0\mathbf E^2+\tfrac1{2\mu_0}\mathbf B^2$ obeys, in free space, the continuity equation $$ \frac{\partial u}{\partial ...


4

Short vision: The most fundamental is the fact that we get same physics in all inertial frames. In this light, the most fundamental quantity in classical electrodynamics is Charge,$^1$ measured and defined as: $Q=\epsilon_0\oint_S\vec {E}\cdot d\vec {a}$. Magnetic force is the consequence of charge invariance under Lorentz transformation and principles of ...


4

You have picked a very striking picture to illustrate your question, although the northern lights do not always have such a sharp lower border to them. However, let me advance a plausible explanation. The green northern lights are formed high up ($\geq 100$ km) in the Earth's atmosphere, largely by photons at 557.7 nm emitted from excited oxygen atoms. This ...


3

In both electrostatics and electrodynamics, the electric charge is defined as the most fundamental quantity. That's what people tend to say, but don't forget that electromagnetic waves propagate regardless of charge. Displacement current is not the motion of charged particles. Check out Taming Light at the Nanoscale: "Look around, and you will probably ...


2

Mechanically, we can store it as potential energy Force at a distance $x$ from a point magnet is given by: $F=\frac{k}{x^3}$ where $k$ is some constant. Energy is force over a distance, we will move outward, not take some other path around the plane. This allows us to assume the magnets are infinitely thin and facing each other, To simplify the equations: ...


2

The rule is called Lenz's Law. You already appear to know how to determine the direction of the magnetic field due to a current in a loop, which is part of the answer. What Lenz's Law tells us is that the direction of the induced current in the loop is such that it "opposes the change in the flux". Here's a picture I grabbed from ...


2

You are having some misconceptions Wire(more pricisely axle) is not rotated between magnetic field in a turbine generator.Wire(more pricisely axle) is used to rotate an coil (present between magnetic fields) present in generator. Magnetic field itself can not force electrons in a conductor to move untill it is at rest. We need an moving conductor so that a ...


2

First of all, the expression for the magnetic length that you give is wrong: there is a square root missing: $l_B=\sqrt{\frac{\hbar c}{eB}}$. Secondly, to understand the meaning, you don't really need to think about lattices or phases of the electron wavefunction as the previous answers would have it. Instead, begin by thinking about a motion of a classical ...


2

A capacitor, as you pointed out, its a device capable of storing electrostatic energy. The energy is stored in the electric field formed by the capacitor, usually between the plates. As you said, you can put capacitors in series, and in parallel, forming an equivalent circuit with an equivalent overall capacitance. The stored electrostatic energy can be ...


2

Actually, in a large solar flare particle energies can get up to 1 GeV, but the top energy of some particles is not really the issue. The issue is the flux of these high energy particles. A 10 MeV proton or electron pretty much rips through most spacecraft bodies, thus, their electronics are effectively exposed to particles at these energies. The often ...


1

Here is the misunderstanding: Now, if the magnetic force is greater than mg, the wire moves up. Now magnetic force is up and displacement is up too which means that work done by magnetic force should be positive. The statement that a magnetic field does no work is of a static magnetic field. You are positing a changing magnetic field by the word ...


1

To start with the law of increasing entropy applies to isolated systems. The system you describe is isolated if one considers the total entropy of both the paramagnetic material and the permanent magnet, including any radiation. The order introduced in the paramagnetic material is balanced by a disorder in the permanent magnet plus any radiation from ...


1

Magnetic field lines in and around a solenoid do not cancel out. This can be easily tested using a plotting compass. If the solenoid is long ( length $l > 10\, d$ greater than 10 times diameter) then the strength inside can be constant and given by $$B = \mu_r\mu_0\cdot \frac{n}{l}\cdot I$$ where n is number of turns per unit length and I the current ...


1

Indeed, an infinitely long and thin wire with a current $I$ has a magnetic field given by (in SI units): $$B = \frac{\mu_0 I}{ 2\pi r}$$ Now suppose your wire has a finite radius. Ampère's law shows that as long as cylindrical symmetry is mantained, the field depends only on the current and not on the detailed properties such as the wire's radius or the ...


1

The poles do have some determinable features. If you're on earth, the north end of a magnet will point towards the North Pole. The south end of a magnet will point towards the South Pole. By noting that the sun rises in the east and sets in the west, you can determine the north and south poles of earth. Thus, if you make an appropriate compass, you can ...


1

So you have that $\vec{B} = \frac{a}{r^2}\begin{bmatrix}0 & z & -y\end{bmatrix}$ thus the magnitude is $B = \frac{a}{r^2}\sqrt{z^2+(-y)^2},$ where $a$ is unknown. Can you write that as a function of $r?$ Can you investigate what happens as $r$ goes to zero? Are magnetic fields continuous in empty space (a vacuum)? If so, try the next five: What ...


1

The magnitude of the B-field is $a/r$ and circulates around the axis. By symmetry, you understand that the magnitude is zero on-axis. But if $a$ is anything but zero, your expression gives an infinite B-field magnitude. Therefore $a$ must be zero and therefore the B-field is also zero everywhere else inside the pipe. The result also follows from Ampere's ...


1

Is it the threat of having to eat five servings of fruits and vegetables a day? When the magnetic field deflects charged particles the energy is deflected and this means less radiation and less ionizing radiation from he particles that get deflected. A solar electron, proton, or alpha particle with 10keV would be capable of ionizing molecules and atoms. ...


1

RIC involves magnetic fields oscillating at a high frequency. The system won't pick up any other frequency. A constant-in-time (DC) magnetic field magnetic field has no direct effect because 0 Hz is the wrong frequency, and it has no indirect effect by the superposition principle. I guess it's possible that there may be a magnetic material in the RIC ...


1

The Maxwell equation says $$\operatorname{curl} \vec E = - {\partial \vec B \over \partial t},$$where $\vec B$ is the magnetic field and $\vec E$ is the induced electric field.That may appear, to an elementary student, to be a bunch of gobbledygook, but it means "the electric field curls clockwise around a change in magnetic field;" normally the + ...


1

I think the main idea that you are missing is that the induced current is caused by the change in the magnetic "flux" (which is not the same as the magnetic field). Without resorting to any calculus (which is needed for the real definition of flux) the flux is like the magnetic field times the cross-sectional area that it "goes through" inside your ...


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I write this because it is too long for a comment Situation You are putting $k$ watts (=joules/second) of kinetic energy into a body. We will show the acceleration decreases with time. $$E=\frac{1}{2}mv^2$$ so $$v=\sqrt{\frac{2E}{m}}$$ so $$\frac{dv}{dt}=\frac{m}{\sqrt{\frac{2E}m}}\cdot\frac{de}{dt}$$ (I can't be bothered to tidy this up - remember I'm ...



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