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18

I don't think that nobody seriously thinks that unification of electricity and magnetism never happened or that it is unimportant. You just have to look at the standard model, and you'll find a term in the lagrangian (in units with $\hbar = c = \varepsilon_0 = 1 $): $$\mathcal{L}_{EM} = -\frac{1}{4}F^{\mu\nu}F_{\mu\nu}$$See? No electric or magnetic fields, ...


6

This sketch might help ;) It is an interactive picture of a charged particle in a plane, with the electric field lines and projections of the magnetic field lines also drawn. Here is what I thought about while making this visualization. The original question had depictions of an electric field due to a static charge and a magnetic field due to a current. My ...


3

I know of another geometric interpretation of the electromagnetic field that is invariant under Lorentz transformations and more general transformations of coordinates. It is not well known and requires you to think of two-dimensional surfaces in four-dimensional spacetime. But it can be visualized (as easily as any visualization of spacetime), is coordinate ...


3

I personally struggle with visualizing the electron's electromagnetic field $F_{\mu\nu}$ at a stroke because there are too many variables involved: six interrelated quantities at each point in space. However, as Bosoneando points out, those six quantities are trivially related to the usual electric and magnetic fields by \begin{align} E_i &= -F_{0i} ...


2

You can certainly draw pictures which contain both the $\vec E$ and $\vec B$ field lines in different colors, and together they specify the electromagnetic field. The only problem is that, in this form, the vector fields themselves are not Lorentz-covariant so if you, say, assume that the electron's stationary E-field and zero B-field are the same in an ...


2

When a wave travels through a rope, the rope goes up and down, the position of all the 'rope-particles' changes, they oscillate and this makes up the wave. With light, it is indeed the electromagnetic field oscillating, but you shouldn't think of the arrows that represent that field in your first picture of light as 'extending into the rest of the space'. ...


2

Yes and no. Charges and currents curve the $U(1)$ gauge connection. We experience this curvature every day so we even have a special name for it: an electromagnetic field. Just like spacetime curvature is called gravity. However, the choice of the word 'curvature' is somewhat unintuitive here due to the fact that it is not our spacetime that gets curved. ...


2

As far as I understood from my so far cursory look into a living review article by Poisson, Pound and Vega on The Motion of Point Particles in Curved Spacetime, it's a bit messy. But I think if you manage to go through GR, this should be manageable, as well. It will probably help if you've dealt with Green's functions before and even better if you've seen ...


2

You have two questions, and they have different answers. First of all, let's be clear about what Gauss's law is in integral form: $$ \int \vec{E} \cdot \mathrm{d} \vec{A} = \frac{Q_\mathrm{encl}}{\epsilon_0} $$ In words: the total flux integrated over a closed surface is equal to the charge enclosed in that surface, divided by the permittivity of free ...


1

The rotation of the Earth's dipolar magnetic field produces an electric field in space. Because the electric field is zero in the rotating frame, it is equal to $$ \mathbf E=-(\omega\times \mathbf r)\times \mathbf B $$ in a fixed frame, where $\omega$ is the angular velocity of the Earth, $\mathbf r$ the radial distance and $\mathbf B$ the magnetic field. ...


1

Reducing eddy current does not change property of conductor or circuit Eddy currents (also called Foucault currents) are circular electric currents induced within conductors by a changing magnetic field in the conductor, due to Faraday's law of induction. Eddy currents flow in closed loops within conductors, in planes perpendicular to the magnetic field. so ...


1

Constantine, take a look at what Minkowski said in Space and Time: "In the description of the field caused by the electron itself, then it will appear that the division of the field into electric and magnetic forces is a relative one with respect to the time-axis assumed; the two forces considered together can most vividly be described by a certain analogy ...


1

The result given to you by your professor is OK. Special relativity allows you to solve the problem in any reference system, and then going back to the original reference system. So the easiest way to solve your problem is going to the reference frame where the two electrons are at rest. There you have only a electric field $$\vec{E}'(\vec{r}) = ...


1

When a motor moves it also acts as a generator and the current trough the windings is given by the difference of the external voltage and the induced voltage. When the motor stands still, though, the generated voltage is zero and the windings will draw the max. current they can based on their DC resistance. In other words, the faster the motor runs, the ...


1

Be careful because that formula is only valid for a very limited set of field geometries. It is always better to derive EMF from the change of magnetic flux. To answer your question, the induced voltage at zero current does not depend on the resistance of the conductor. As soon as a load is connected to it, the effective voltage measured on the conductor ...


1

According to Maxwell's equations $$ \textrm{curl}\,\textbf{E} = -\frac{\partial}{\partial t}\textbf{B} $$ therefore a variation of the magnetic field in time generates a non-zero curl for the electric field, whose solution, together with the other set $$ \textrm{div}\,\textbf{E} = \frac{\rho}{\epsilon_0} $$ describes the electric fields at any point ...


1

Suppose you shine a linearly polarized laser at the wall. Let's call the direction of laser propogation $\hat{z}$ and the direction of the electric field polarization $\hat{x}$. Then if you plot the $x$-component of the electric field vs. $z$, you will get a sine wave. The wavelength of the light is the wave length of the sine wave. So if one peak was at ...


1

The wavelength is not defined as the length after which the waves repeats itself: that is only a pictorial representation that works in one dimension for simple one component waves but it is not valid in general. Instead, given any solution of a wave equation represented as Fourier transform $$ \psi(\textbf{x},t)=\int ...



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