New answers tagged

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This is much more simple than you imagine. Yes of course you use Newton II to get the acceleration and the Lorentz force as the right hand side. However, the key here is the statement that the charge moves with $v \ll c$. For an electromagnetic wave in vacuum then $B = E/c$. Thus is we look at the two terms in the Lorentz force, the first will have a ...


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You should remember one thing : electromagnetic field is just a spatial representation of how electric charges interact with each other, and by "interact" I actually mean "exchange some energy". Electrostatic and magnetostatic energies Lets imagine that we want to build "from scratch" a given charge distribution $\rho(\textbf{x})$. That means that we ...


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Is there an electric field around the poles of the battery before the circuit is attached, and is there still, after the circuit is connected? Yes. However adding the connecting wires is likely to change the distribution of the field. And why is the field equally strong everywhere in the wire, no matter the shape? Usually we design our circuits ...


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Do you know of below formula Use $B = \frac{\mu°}{4π} I(sin\alpha + \sin\beta)$ Click to know more on Bio-savart law for finite wire


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the concept of generating electricity from magnetism is that a moving magnetic field produces an magnetic motive force gives rise to the electro motive force to the electrons of the wire which is being induced and hence results in production of electric current. But really don't you think this is a childish concept the whole process is about absorption and ...


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The Kondo effect is a phenomenon that occurs when we have a magnetic impurity located in one place of a non-magnetic metal. The magnetic impurity has an residual spin due your electronic configuration. The electrons of the conduction band would interact with this electron via exchange interaction. We can see in equation 10 of the wiki page that the ...


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You have to think in terms of potential . Consider the first plate, say $A$. It can be charged to a maximum value $+Q$ since any further increase in charge will cause a leakage of charge due to the increase in potential. You can imagine that. The potential of a charge distribution decreases slowly than the electric field with distance. So we need no leakage ...


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The magnetic force acting on a charged particle doesn't affect the particle's energy. Otherwise magnetic forces cannot do work. It's because the magnetic force equation is given by $$\vec{F}=q\vec{v}\times\vec{B}$$ where $q$ is the charge, $\vec{v}$ is the velocity and $\vec{B}$ is the magnetic flux density. So, it is clear that by virtue of the ...


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One would expect that a positively charged sphere could hold a different amount of charge than a negatively charged one, one reason being that the tunneling probability for electrons to escape would tend to be different than for ions. There may be other effects as well that could cause a difference. If I were to venture a guess I would suppose that more ...


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If you're thinking about stable orbiting systems the big difference between gravity and the magnetic force is that magnetic monopoles do not exist. The simplest source of a magnetic field is the magnetic dipole. By contrast gravitational monopoles exist but gravitational dipoles do not. The Sun and the Earth are both (approximately) gravitational monopoles, ...


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The other answers are not strictly true, as "whiteness" is a neurological perception. We can perceive a neutral color when the red, green, and blue retinal cones have roughly equal stimulation, but that color is only "white" when it exceeds some magnitude. Otherwise it's what we call 'gray.' Further, in very dim conditions, only the retinal rods respond, ...


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Kindly follow the following link.https://en.wikipedia.org/wiki/Jean-Baptiste_Biot and plese go to the heading "Work". It says that the law was discovered experimentally in in the year 1820 i.e. 45 years before the Maxwell equations were published. The general formulation to the Biot-Savart law was given by P. Laplace. The expression of the Biot-Savart Law ...


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I think in the previous answer the focus has been too much on the method of using a determinant to calculate the cross product. But the question seems to be asking why one needs to calculate the given matrix determinant. You are given a magnetic field which is assumed constant and homogenuous, so we write down $$\overrightarrow{B}(\overrightarrow{x},t) = ...


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White light is made of visible photons of many colors (frequencies). Our eyes mix the different frequency and interpret it as white. Photons come in all frequencies and through evolution our eyes have evolved to register visible photons from red to violet. Blue photons are higher frequency than red photons. White light is not a photon but a mix of photons


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No, each color in the spectrum has a characteristic frequency. Every light source has a so called spectrum of frequencies. The relative intensity of these frequencies determines what color you see (or not). For example, the sun looks yellow because it's peak intensity is in the yellow wavelength. White light comes from a source consisting of a very broad ...


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In the equation provided for $r$, there is a mistake. The equation is got by equating the centripetal force acting on the charge with the magnetic force on the charge since the circular motion is provided by the magnetic field. So, $$r=\frac{mv}{qB}$$ the $v$ is the velocity of charge, not the voltage. To calculate the velocity, you are provided with ...


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There are two different values represented by $v$ in this problem: lowercase $v$ is the velocity of the electron uppercase $V$ is the voltage that accelerates the electron In both the force equation $F=qvB$ and the radius equation $r = mv/qB$, $v$ refers to the velocity of the electron. I believe this is where your mistake was, since you said that the ...


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1) Universal covering groups are groups with the property of being simply connected. Each algebra has a unique covering group. The other groups, $\{G\}$, associated to the same algebra can be obtained from the covering group in the following way $$G=\frac{\tilde G}{Ker(\rho)},$$ where $Ker(\rho)$ is the kernel of the group homomorphism $\rho:\tilde ...


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Current is the amount charge that goes through a particular cross section area per unit of time. It does not matter whether the charge density is uniform or not for this current to be non-zero; the only thing that prevails is whether or not the charges are flowing. Observable features that a current is passing comprise for instance Joule heating of the wire ...


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It is, a priori, completely correct to add both primary and secondary constraints to the Hamiltonian density by Lagrange multipliers. What is not correct is how you determined the equations of motion: There is no "$F^{i0}$" in the Hamiltonian theory! It is called $\pi^i$ there and it is not dependent on $\partial_i A_0$, it is an independent canonical ...


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EM Waves are basically spinnings of photons. To create a EM Wave, you basically move some electrons in a directional way(think of an antenna). Electron is a charged particle as well as protons. Charged particles emit photons, and if you emit photons in an ordered way such as this: You are seeing a dipol antenna. When you apply negative voltage(intense ...


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The energy is carried in individual photons. A photon with twice the frequency has twice the energy. x-rays are made of photons with higher frequencies. The energy is transferred as kinetic energy as with the photoelectric effect. The energy of a photon is calculated as E=hf (Energy=Plank's constant x the frequency).


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I assume that it is a time varying "bent" , which is a gravitational wave. Only charges radiate electromagnetic waves. At the elementary particle level photons will be produced only during the interaction time of changing space, i.e. graviton-charged_particle interaction. Classically, accelerated and decelerated charges radiate, so a classical ...


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Only from charges. It's the quantum property that couples to photons. Gravity couples to anything, but there has to be some charge acccelerated to create photons. So gravity could accelerate it, but it also would depend on what is your frame of reference as to whether you'd see it. Another way to create photons from charges that normally don't exist is ...


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The electromagnetic radiation of gamma rays and X-rays is generated through accelerative processes involving atomic nuclei. The involved photons are the so called hard radiation and could destroy human tissue. The acceleration of electrons generates photons in the range of UV radiation, visible radiation and IR radiation. It is possible to send informations ...


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The key thing is that the surface have facets. That is, it has to have smooth flat parts that can reflect light like a mirror. If the surface is just amorphous then the scattering will tend to be too disorganized to see the polarization. I have seen polarized light coming off quite surprising surfaces. A manhole cover for example. It had been polished fairly ...


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In the classical theory of reflection (and refraction) of electromagnetic waves, there are equations which describe the reflection of light in two specific orientations. They are known as the Fresnel equations. However, the polarizations of light lie in a 2D vector space, so as long as you decompose any incoming wave of light into the two linearly ...


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Each of those spectral regions involve electromagnetic waves (photons) at a range of frequencies, and it is that which determines how they are generated, how they interact with matter (i.e. Particles with charge, one by one or in various groupings and configurations like atoms, molecules, bulk material composed of different molecules, different temperatures, ...


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(Others can correct me if I'm wrong, but...) I think the answer is no. Not even theoretically. Humans are basically diamagnetic, because they are mostly water. Therefore, if you got a large enough magnet, you could repel (or levitate) a person with it, but you could not possibly attract a person with it. Look up the Ignobel Prize for levitating a frog. ...


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As already mentioned, the action corresponds to massive electrondynamics, including external sources, in Minkowski spacetime. This is also known under the term Proca action. As you mention, the corresponding equations of motion can be found using Euler-Lagrange equation, that is $$0 = \frac{\partial \mathcal{L}}{\partial A_\mu} - \partial_\nu \frac{\partial ...


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by the Euler-Lagrange method you would simply get the following field equation: $(\square-\nu^2)A_\alpha=-\beta J_\alpha$, which is the Proca equation. You can read up about the Proca action online. I'm new to field theory, and someone should correct me if I am wrong.


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This is just the lagrangian for electromagnetism. The A is the vector potential and the expressions in parenthesis are the F tensor. You can read about it here


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The direction of the force acting on a charge q with velocity ${\bf v}$ moving in a magnetic field ${\bf B}$ is given as ${\bf F} = q {\bf v} \times {\bf B}$. In your question you have ${\bf v} = v {\bf i}$ and the electric field is (eventually) pointing in the direction ${\bf j}$. This means the direction of the magnetic field must be in the ${\bf k}$ ...


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Background Stars are composed of plasmas, which are an ionized gas that exhibit a collective behavior much like a fluid. There are two important aspects of plasmas to keep in mind. The first is that they act like very highly conductive metals in that the electrons can move very freely in order to cancel out any charge imbalance. The consequence is that ...


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Overall, a star stays more or less neutral. This is true for all stellar objects beside black holes. I am using a simple calculation that can be found in a footnote of https://arxiv.org/abs/1001.3294 on p. 11 chap. 2. Suppose the star has an overall charge of Z times the elementary charge, $Ze$, and we consider the Coulomb repulsion of a test particle, say ...


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Maxwell's equations, in their microscopic form as formulated by Lorentz, are the standard postulates of electrodynamics. From them all electromagnetic formulas and properties can be derived. The symmetry of these equations relative to spatial translation implies, as follows from Noether's theorem, the law of conservation of linear momentum of the charges ...


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The relation between the electric and magnetic field are theoretically described by Maxwell's equations (here in vaccuum and without external sources). In terms of the electric and magnetic fields $E(\overrightarrow{x},t),B(\overrightarrow{x},t)$ they read, as you have propably learned in the class you mention, $$\begin{align} \overrightarrow{\nabla} \cdot ...


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It comes about by assuming that the wavelength ($\sim k^{-1}$) is much larger than the typical atomic length scales ($r$).


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With electric and magnetic fields a charge can be set in motion. For example, one can accelerate the charge in circles or make it go up and down. Such an accelerated charge will produce EM waves. A way to think about it is that when the charge is in a fixed position it produces a field as given by Coulomb's law originating from the position of the charge. ...


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The principle of relativity says that there is no experiment that can determine absolute motion. So all observers, regardless of relative motion, need to agree on the outcome of any experiment. Because to the relativity of observers' measuring devices, they may not numerically agree on the measurements. By applying the laws of relativity they will be able ...


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A few comments before doing the calculation: In the CM frame, there is only an attractive force, while in the given frame, there is both an attractive and a repulsive force. This is no more mysterious than the fact that a vertical object in my frame can look tilted to somebody with rotated axes. Going from the CM frame to your frame mixes the electric ...


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Lorentz Transformations Suppose we call the lab frame the K-frame and a frame moving at velocity, $\mathbf{v}$, relative to the K-frame called the K'-frame. Then we can express the electromagnetic fields in the K'-frame in terms of the K-frame fields as: $$ \begin{align} \mathbf{E}' & = \gamma \left( \mathbf{E} + \boldsymbol{\beta} \times \mathbf{B} ...


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The observer moving with the CM will measure that the force of repulsion the electrons is given by $F=\frac{e^2}{4 \pi \epsilon_0 d^2}$ ($d$ is their separation), he can only make measurements in his reference frame (that is moving with speed $v$), and will not be able to be determine this speed.


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In my understanding, the free charge is any charged particle that is not being restrained in the boundary, while the bound charge is in the boundary.It does not matter whether the material you currently discuss is a dielectric or a conductor.


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In a sense, the two definitions you mention are the same. One of the postulates of special relativity is that the speed of light is the same in all reference frames, so the definition of "the coordinate transformation according to the postulates of special relativity" is the same definition as "the coordinate transformation under which the speed of light is ...


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Both questions have the same answer: The coordinate system is chosen such that $\theta = 0$ points to the top. So if $\theta_0 = 0$, then the circle is fully immersed in the magnetic field. The limits of integration will be just $0$ to $2\pi$. In the other extreme case, where the circle barely touches the magnetic field, one has $\theta_0 = \pi - \epsilon$ ...


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There are lots of ways of approaching special relativity. My own preferred approach is the invariance of the line element. Suppose you move a small distance in spacetime $(dt, dx, dy, dz)$ then the length of the line element $ds$ is defined by: $$ ds^2 = -c^2dt^2 + dx^2 + dy^2 + dz^2 \tag{1} $$ This equation is known as the metric equation and is derived ...


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I agree that this question may be a duplicate, but previous questions seemed to be focused on particular geometries and situations. Here's my two cents.. The Lorentz force is $J \times B$ You might combine Maxwell's equations (while neglecting the timescales for charges to move to conductor surfaces ($\frac{\partial \mathbf{E}}{\partial t}$)) to get the ...


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The formula for the solenoid or toroid assumes that the length of the solenoid is much greater than its radius, and that the pitch (distance between turns) is much smaller than the radius. These assumption do not hold for a single current loop.


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MRI signal is always complex and it is related with signal demodulation. The detected signal is multiplied by a sinusoid or cosinusoid with frequency equals to $\omega_0 +\delta \omega$, respectively leading to the real and imaginary channels. You can find the complete algebra at $Haacke,\ Magnetic\ resonance\ imaging$ chapter 7.3.3 Phase is really useful ...



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