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3

A compass has magnet to detect a magnetic field. It will not interact with electrostatic force, which is the only force interacting when the spoon is kept stationary. However, moving the spoon produces magnetic field of its own via Ampere's law. Another way to see this via lorentz force, where force acts only on a moving charge in the presence of magnetic ...


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What is an electromagnetic force? We have an electrical interaction between the electrical charges of the subatomic particles and a magnetic interaction between the magnetic dipoles of the subatomic particles. Furthermore, we have inductive processes in which two of three participants induce the third (electric drive with the Lorentz force, electric ...


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See the paper, "Magnetism, Radiation, and Relativity: Supplementary notes for a calculus-based introductory physics course" by Daniel V. Schroeder, Weber State University http://physics.weber.edu/schroeder/ dschroeder@cc.weber.edu for a clever and pleasing explanation of how special relativity can be used to explain the origin of forces between ...


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Could I explain to an apprentice how a motor and/or a generator works with arguments based solely on special relativity? No. You would also need electromagnetism. Maxwell’s equations are fully relativistic, but they are not usually considered to be part of special relativity.


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all of the mechanical energy given in system was gained by wood This is actually not correct. Remember the famous $E=mc^2$. As the battery powers the electromagnetic field energy is radiated away from the coil. As a result of losing the energy it also loses the mass. Thus, when it collides with the wood it will have less momentum and the wood will therefore ...


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Yeah, so, this is a reasonable confusion. In electromagnetism, the electric and magnetic fields are generated not just by charged particles existing, but also their motion through space. This means that there is a difference between a ring of charged particles standing still (electric field but no magnetic field) and that same ring spinning about its axis (...


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$\lambda$ here is the line charge density defined as $$\lambda=\frac{Q}{L} $$ Hence, it gives charge per unit length. Therefore, to get current for some infinitesimal length one must multiply by $dl$ and divide by $dt$, which is equivalent to $v$ in your case.


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You could use alternators with electromagnets, without a connection to the power grid by one of these means: Use solar panels to generate the current for the electromagnets. Use batteries to power the electromagnets, the batteries being charged using either solar panels and/or using a fraction of the power produced by the alternators. Instead of batteries,...


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This is how I would approach the problem knowing only basic Newtonian mechanics (and differential equations). I'll try to explain exactly when and why it becomes convenient to introduce the "small oscillations" approximation. As you say you have already proven, the ball is at rest when the gravitational force equals the Coulomb repulsion, and the ...


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The blank assertion that "photons are the force carrier of the electromagnetic force" is sort of true, but a bit misleading if you don't have the technical knowledge to unpack what it is trying to say. When the golf club pushes the ball, it is correct that the forces are largely electromagnetic. The situation also involves the Pauli exclusion ...


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Yes the electric field does contain energy. The energy density due to the electric field is given by $$u=\frac{\epsilon_0}{2}E^2$$ And the energy associated with the electric field is: $$U=\frac{\epsilon_0}{2}\int_\text{entire field}E^2dv$$ For point charge, if you compute this, close to the origin, our integral blows up. That simply tells us it would take ...


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Temperature is defined for a system in (at least local) thermal equilibrium. The electromagnetic field is present everywhere and, when in thermal equilibrium, has a blackbody spectrum. Thus, a body made of charged particles "vibrating" at temperature $T$, in the presence of an electromagnetic field at the same temperature $T$, will on average gain ...


1

Emf is not a force in the strict sense. Nor is it an electric potential, though it has the same dimensions. It is work per unit charge done in moving charge around a circuit. It is commonly confused with potential because it is often the potential difference that is doing the work, so they are often equal. For example, the potential difference across the ...


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The point is that if you, for example, have a charge at the center of a sphere, all field lines go straight out from the charge (or straight in, depending on whether the charge is positive or negative) and terminate there. So charges are sources and drains for these field lines. If there are no charges inside a closed surface, indeed all field lines entering ...


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A closed surface containing a charge will have flux lines that originate at the charge which pass through the surface. In fact the net flux through a closed surface is proportional to the net charge enclosed by that surface. This is Gauss's Law for Electric Fields (Usually listed as the first of Maxwell's Equation, which were given to us in their modern form ...


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Induced EMF is integral of induced electric field over some path. In the simplest case, it is the product of induced electric field and some length. This quantity can be understood as work of induced field per unit charge when it gets transported along specific path. Its unit is Joule per Coulomb which is Volt. It is a "force" not in the sense of ...


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You need to apply the Biot-Savart law to the problem. See Biot-Savart law (Wikipedia) Essentially, this involves taking the line integral of the current around the loop using \begin{equation} \mathbf{B}(\mathbf{r}) = \frac{\mu_0}{4\pi}\oint \frac{I~d\mathbf{l}\times\mathbf{r}'}{|\mathbf{r}'|^3}, \end{equation} where $\mu_0$ is the magnetic permeability, $d\...


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It is not a force - it provides an electrical potential (voltage). Specifically, it has dimensions of potential energy divided by charge. One usually thinks of an EMF in terms of something like a battery that has a voltage between its terminals. The rate of change of a spatially varying voltage is the electric field. The actual force on a particle is its ...


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There are two main errors: Single particles don't have a temperature. Temperature is a statistical feature of bulk matter. Single particles don't emit EM radiation when they move. Instead their energy is quantised. Under Classical theories all atoms would quickly collapse as their electrons radiate all their energy away.


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Ferromagnetism is explained on a microscopic scale; Within the body of the magnet, the direction of the field lines is explained by the orientation of magnetic domains, and there is no theoretical reason why those could not be oriented to form a "twisted" path. But, outside of the body of the magnet, the direction of the field lines will be ...


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The Maxwell-Faraday equation in integral form states that $\displaystyle \oint_{\partial \Sigma} \mathbf{E} \cdot \mathrm{d}\boldsymbol{\ell} = - \frac{\mathrm{d}}{\mathrm{d}t} \iint_{\Sigma} \mathbf{B} \cdot \mathrm{d}\mathbf{S}$ On the left hand side of the equation the line integral is around a complete loop and this is called the emf. For the right ...


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Short answer: elementary particles, no. Composite particles, yes. A charged particle just moving without acceleration does not lose energy, but if it accelerates then the Larmor formula applies (in the non-relativistic case): $$P=\frac{\mu_0q^2}{6\pi c}a^2.$$ So the relevant question is, will a hot particle accelerate? If the particle is elementary even ...


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It is somewhat problematic to rigorously define $\partial_i\partial_j\frac{1}{r}$ in 3D distribution theory, cf. e.g. this Math.SE post. Nevertheless, due to the identity $$ \nabla^2\frac{1}{r}~=~-4\pi\delta^3(\vec{ r}),\tag{A}$$ it makes heuristic/physical sense to assign $$ \partial_i\partial_j\frac{1}{r}~=~-\frac{4\pi}{3}\delta_{ij}\delta^3(\vec{ r}) ~+~ ...


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By assuming the Lorenz gauge you also have restricted $\psi$ to obey $$\square \psi = 0 \,.$$ $\square = \partial_\mu\partial^\mu=\partial_t^2- \Delta$ up to a minus sign depending on your Minkowski metric convention. This solves your problem. By the way, I recommend to use covariant notation.


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They are cold and lonely, and other particles of the same charge find them repulsive ;) More seriously - cold/hot is the concept based on temperature, which is the measure of the average kinetic energy of the particles. As such, the temperature is not directly related to the charge of particles, although in some situations one may affect the other. One ...


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You can imagine that the sphere exists at infinity and the surface of it takes zero potential. Nextly, imagine the operation which bring the test charge from the top surface of the sphere at the infinity to the conductive sphere. After the operation, we get the 2 potentials, one of them is the reference potential(zero volt) and the other is the potential at ...


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To me, Maxwell's equations are synonymous with the work of god, so much so that I'll even take these equations as definitions for the fields. So, what I call the electric and magnetic fields are respectively the two vector fields $\mathbf{E}$ and $\mathbf{B}$ which (in the presence of charges and currents $\rho,\mathbf{J}$) satisfy $\nabla \cdot \mathbf{E}=\...


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How much easier would electromagnetism be to understand if the electron were given not only its intrinsic charge but also its intrinsic magnetic dipole. The discovery of an electrically charged particle - easily separated by a potential difference and easily stored by an insulator between the electric poles - has obscured the fact that subatomic particles ...


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Vacuum polarization in Born-Infeld theory In vacuum, the Maxwell field equations (which represent classical electrodynamics) are linear in the fields $\bf{E}$ and $\bf{B}$ but the Born-Infeld (BI) model of nonlinear electrodynamics breaks the linearity (linear superposition) of classical electrodynamics. As will be evident, this nonlinear feature in the ...


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You cannot create or destroy (net) charge, it must always be conserved. If the current flowing into some object is different than the current flowing out of the object, you will necessarily be accumulating charge on that object. This is possible, but typically won't happen in the cases you specifically mention. In circuit analysis you assume it never happens,...


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The material regains its magnetic properties. There are demonstrations of this in some science museums (sadly, I can't track down which have such an exhibit).


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There are different ways to control power input to an electric device. One is, indeed, to input stabilized voltage using a source with very small output resistance. Regardless of the load resistance (within engineering limits), the voltage on the output terminals of such a source will be constant. But sometimes it's useful to know how a device performs when ...


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In a medium there in general is dispersion, so that the group velocity depends on the frequency. Note that the phase velocity can even exceed $c$, namely when $n<1$ such as occurs for x-rays. A pulse of light contains many frequencies, each with their own amplitude and phase. These components all travel at their own velocity and with their own extinction. ...


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The current in a diode depends roughly exponentially on the voltage. So the only real difference from one to the other is the distribution of the measurement points. If you do a voltage sweep at equidistant points, you will be sampling the current in exponential intervals. If you sample in equal distances in current, you will be taking samples at logarithmic ...


1

Actually you are right, the most easy way is to (carefully) increase voltage. However, the problem is that above the threshold voltage the characteristic curve rises up very steeply. Meaning if you are not super carefully you can end up with very large currents that destroy your LED or laser diode. This is why usually LEDs and lasers schould be operated &...


1

For simplicity, let's consider a one-dimensional system without any scattering process. The Hamiltonian can be written as $\hat{{\mathcal H}} = \hat{{\mathcal H}_0} - eE\hat{x}~~(e < 0).$ Here, the electric field is assumed to be of magnitude $E~$ in the $x$ direction. The translation operator $\hat{T}$ satisfies $$ \hat{T} f(x) = f(x + a), $$ for any ...


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It is hard to know without properly defining all the terms in your question and possibly a sketch to go with. However, I should imagine it is due to Faraday's law of induction. The rate of change of magnetic flux in the electromagnetic braking system will then be proportional to the velocity of the carriage (I'm assuming this is an elevator question as you ...


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You also don't know how position changes over time and you need both, velocity and position, to plot your graph. The equation you wrote is differential equation and need to be solved first for function z(t), possibly by numerical methods. Once you know this, you can compute your derivatives you are interested in and plot them in a graph.


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$\hat{r}’$ is a unit vector with a magnitude of 1. As such, it is dimensionless. One way to see this is that we can create a unit vector out of any vector by dividing it by its own magnitude: $\hat{A} = \vec{A}/|\vec{A}|$. But $\vec{A}$ and $|\vec{A}|$ have the same units, and so $\hat{A}$ is dimensionless. Once you realize this, it is not hard to see ...


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Suppose an EM wave is emitted by some source in a step fashion. That is, ideally, prior to some time $t_0$ there is no emitted wave, and after that time there is an emitted wave with some constant non-zero amplitude. An initial wave will leave the emitter at the speed of light in a vacuum, even if the light is passing through matter. This initial "front&...


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How can an experiment built on the premise that light actually slows down in matter work, when light actually travels through the apparatus at the speed of light in a vacuum and only the phase-velocity of the superposed wave is lowered? Indeed. The correct functioning of the experiment is certainly good evidence supporting the premise upon which the ...


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I asked this question in regards to the theory(theory?) that the Great Pyramid at Giza was designed as such a device. In the "Queens Chamber" was found residue of zinc chloride/aluminum chloride and sulfuric acid that was poured in to the northern and southern shafts to mix there. The H2 gas produced in this reaction would rise through the quartz ...


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I don't have Feynman's lectures available, but I am not sure if you have interpreted him correctly. The fact that the speed of light is different in matter (and varies with wavelength) is the foundation for such profound effects as refraction and dispersion. Just take any prism and see the effects, and you'll know that the speed of light in matter is real.


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Tangentially... This might be a good time to get familiar with approximations in physics problems. It used to be, analytic expressions were the most desirable, and so people approximated special functions and unpleasant expressions with series expansions. The idea of a series expansion is converting an expression from one form (possibly a closed form) to one ...


2

The electrostatic force on the ball as a function of its height $y$ is $F(y)=kqQ/y^2$. For small $\delta$, the Taylor series says that $F(y_0+\delta)\approx F(y_0)+\delta F^\prime(y_0)$, where the prime indicates the derivative with respect to $y$. The net force is then $F(y_0+\delta)-mg = \delta F^\prime(y_0)$. Note that if the mass were instead attached to ...


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Thanks to @Duepietri, I've come to a conclusion. Taking into account that $D_{\mu}$ needs to be gauge invariant, the minimal coupling $$D_{\mu} = \partial_{\mu} + ieA_{\mu}$$ would give some remaining terms, of which we could compose an interaction: $$\mathcal{L}_{int} = -e\bar{\psi}\gamma^{\mu}A_{\mu}\psi -ieA_{\mu}\left[\left(\partial^{\mu}\phi^*\right)\...


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I prefer to think of a photon as an EM wave “packet” of finite size and with a discrete amount of energy. It can interfere with itself to produce a probability pattern which can be measured in centimeters. The intensity of the wave at any point determines the probability that all of the energy of the packet may be absorbed by some other entity (like an ...


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Well, you've missed a little thing. And here's what: The equation τ=Iα is valid as long as the point of reference you are using is itself the frame of reference, and lies on the body (even if the point is actually outside the body, we extend the body so that the whole new extended body rotates about the same ICOR) . Thus, the point about which you wish to ...


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This is more a question for history of science SE. It was Heinrich Hertz who demonstrated that electromagnetic disturbances travel at the speed of light, as predicted by Maxwell. This was considered proof of Maxwell's identification of light as an electromagnetic wave. Nowadays all relevant experiments confirm this and this identification is a as close to ...


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The phenomenon you're describing is the end result of millenias of observations. The theory has been developed since ancient culture. One might have observed small particles being attracted to certain substances having been rubbed against wool for example. Then there have been the prolonged use of the compass. Eventually electricity was coined, and someone ...


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