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Phoenix87 has already given a correct answer. Let us here just try to stress the main point: It's Gauss's law $$\Phi_E~=~ \frac{Q}{\varepsilon_0}.$$ In $d$ spatial dimensions, the electric field caused by a point charge $Q$ is therefore $$|\vec{E}(r)|~=~ \frac{Q}{\varepsilon_0 ~{\rm Vol}(S^{d-1})} ~\propto~ r^{1-d},$$ because the surface-volume of a ...

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The best interpretation I can see of this fact is related to Gauss' theorem. Poisson equation is of the form $$\nabla^2\phi = \rho,$$ but if you set $\mathbf F = \nabla\phi$, this is also an equation for the vector field $\mathbf F$, $$\nabla\cdot\mathbf F = \rho.$$ Let us consider a density distribution given by a total mass $Q$ centered at a single point, ...

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Gravity can attracts only matter made up of Atoms and why other matter such as; electrons, solar wind, light& heat rays don't respond for gravity at all ? Only atoms have got internal rotary systems where electron clouds are orbiting the nucleus at balance of the two forces 'centrifugal force' and 'Coulomb's attraction'. Gravity is due to a wave of high ...

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I recomended to study non-euclidan geometry from the book "Non-Euclidian Geometry" by Stefan Kulczycky (Transleted from Polish) - Pergamon Press Haim Reouven-Israel

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You are correct in the way that you use the center and radius. You are also mostly correct that $C=2f$, however this is only true when the size of the mirror is small, compared to the radius of the mirror. The relationship $C=2f$ holds best for small angular diameters. What you are noticing in your optical simulation is that when the angular diameter of ...

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No it is not an error, because the diagram looks at the maximum angle specifically (and that's where the equality holds). He is saying that inside an optical fiber, there is a ray that travels at the critical angle: this ray, when it comes out of the fiber, represents the maximum possible exit angle. As the refractive index mismatch between the fiber and ...

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The advantage of writing the metric in null or double null coordinates are that the surfaces along which u or v are constant is lightlike

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This is only a small part of the answer to your question, but group theory is widely used - point groups for individual molecules and space groups for crystals - used to help describe/make caclulations of electronic structure and vibrations

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The pictures you have above are great ways to visualize the deformation of space-time by a mass, but they can be misleading. A black hole, for example, is not just an extremely deep well, it's a point where the curvature grows infinite. If you were to try to imagine what this would look like in the above pictures, it would be like poking a hole in the ...

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This thread is a year old, but I felt the need to make this book known. The following book is perhaps what you seek: Special Relativity in General Frames: From Particles to Astrophysics. Eric Gourgoulhon. Springer (Graduate Texts in Physics), 2013. It is destined to be a classic text on the subject. It adopts a four-dimensional point of view from the ...

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The relative distances of the earth, sun and moon were determined by Aristarchus. See my summary here. By measuring the size of the earth (as e.g. Eratosthenes did) these can be turned into absolute distances. Once heliocentrism was introduced the planetary distances could be determined as follows: Distance from Venus (or Mercury) to the sun: continually ...

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