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You've asked a complex question and I really don't know if I'm getting it. One thing you asked gives me an idea of how to answer your overall question. You asked: What are the intuitive properties of charges and currents that lead one to write down Maxwell's equations? Strictly speaking about Maxwell's Equations, I don't think there is anything at all ...


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I think the way you posed your question implies a weird concept of physics. As I understand it, your question is "why do we expect the axioms we write down to yield physically reasonable results?" The point is, similar as in math, those axioms are usually not just written down randomly, following by their implications being explored. To the contrary, we ...


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There is no absolute justification for physical laws. In fact it is best to drop the term law. With Isaac Newton's De motu corporum, book 1 of the PhilosophiƦ Naturalis Principia Mathematica, the concept of physical laws emerged. Newton's laws were seen in the 18th and 19th century as close to what Moses brought down from Mount Sinai. This idea carried to ...


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Rather than saying the physical laws are based just on experiments I would say they are based on the Scientific Method. There are steps that must be checked: Observation - We observe some unexplained phenomena. At this stage one does a lot of experiment and if all of them gives the same result we can state an experimental fact. For instance: Water cannot ...


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The previous answers and comments inspired to me what follow: maybe this is the simplest (and so the best) way to see why $\frac{d}{dt} \int_S \mathbf{B} \cdot d \mathbf{a}$ vanishes when the loop contracts indefinitely. I can simply consider a small surface that doesn't vary in time, but it is essential take into account the possibility that the magnetic ...


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You're right that a function can be "small" at a point but have a "large" derivative at that point. But maybe the confusion is that you're imagining the surface $S$ shrinking in time, so that it's only "small" at one instant. But the surface doesn't shrink in time - you're taking the limit where it's "small" at all times. And if a function is always small,...


3

For any given electric field $\mathbf{E}(\mathbf{r},t)$, and assuming no constraints on the magnetic field, there is always a set of charges and currents (both possibly time-dependent) that produce that electric field. What's more, while the charges required are uniquely determined, the currents are not. Here's the construction: Let $\rho(\mathbf{r},t) = ...


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Maxwell's equations only give a unique electric field subject to a set of boundary conditions and an initial condition for the field.


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First of all, the tangential component of ${\bf E}$ (i.e. the component parallel to the interface) is always continuous across interfaces, so $E_z$ must be continuous at $r = R$, which fixes $C = 1/R$. There is no physical configuration of sources that could produce any other value for $C$. ${\bf E}$ does not depend on time, so ${\bf \nabla \times E} = -\...


6

The problem is that you calculated the curl wrong; you missed a delta function arising from the discontinuity. We can write $E_z$ as $$ E_z = \ln(Cr) \Theta(R-r)$$ and, using that $\Theta'(x) = \delta(x)$, we get that $$\nabla \times \mathbf{E} = -\frac{1}{r} \Theta(R-r) \hat{\phi} - \ln(CR)\delta(r-R)\hat{\phi}$$ so when giving $\nabla \cdot \mathbf{E}$...


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1) Electric flux lines model helps us to understand the behavior of an electric field much simply and it's pretty easy to visualize it. The definition of electric flux is the number of filed lines passing a given area normal to it. The field lines show the direction and magnitude of electric force at some point. The density of field lines at some region of ...


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Electric flux is a useful mathematical concept which gives us a measure of how much the field flows through an area which is positioned within the field. Consider a surface of area A which is perpendicular to an electric field E. The flux is given by EA. The larger the electric field, the more the field 'flows' and therefore the larger the flux. Similarly if ...


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Why 2 distributed lines is represented with series inductor and resistor along with parallel capacitor and resistor? What is the motivation for that? Current through the wires is associated with (let's not discuss which causes which) a magnetic field, and we can represent that with an inductor. Potential difference between the conductors of the line is ...


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We can do $\small0=i$ in the single form equation$$\epsilon^{ijk}\partial_j F_{0k} + \epsilon^{ijk}\partial_0 F_{jk} + \epsilon^{ijk}\partial_i F_{jk} =0$$ and because $\epsilon^{ijk}$ permutes we can write $$\epsilon^{jik}\partial_j F_{ik} + \epsilon^{ijk}\partial_i F_{jk} + \epsilon^{kij}\partial_k F_{ij} =0$$ From this we can divide out $\epsilon^{ijk}$...


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I think your question is about the perception of colour - ie how your brain responds to the mixture of light which stimulates the retina. This cannot be explained by the superposition of waves using Maxwell's equations. It is more a matter of physiology (biology) than physics [1]. Colour is not a property of the physical world. It is our subjective ...


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The light waves propagate directly and the flux of photons reduces at a rate of 1/r^2 from the canopy top. This means that fewer of the photons reach your retina or CCD of a camera while in orbit. It seems to be a more uniform color of green simply because that is the majority wavelength being reflected by the plants. As knzhou pointed out, light is ...



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