A law in Classical Electromagnetism and Newtonian Gravity.

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Proof of Gauss' Law [duplicate]

How would you prove Gauss' law for an asymmetrical closed surface? I can find it for symmetrical surface but couldn't for Asymmetrical surfaces.
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Do these steps demonstrate that acceleration of charged particle is proportional to current?

One formulation of Maxwell's Gauss Law for electric field is: $$\bigtriangledown E = 4 \pi k \rho $$ This can be worked into the Divergence Theorem as follows: $$\int\int_{A} F_\perp \:dA= 4\pi k ...
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Relation between Gauss' law and Coulomb's law

In Coulomb's law if the relation was as if electric field intensity was to vary inversely $1/r$ with distance rather than the inverse $1/r^2$ of square of distance, would the Gauss's law still be ...
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Is there a good experiment to demonstrate Gauss's Law for Magnetism?

I'm trying to come up with a simple experiment that can demonstrate the properties of Gauss's Law for Magnetism. I am aware that it is a mathematical representation of the fact that magnetic ...
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Electric flux for a rectangular surface? [closed]

I have the following homework problem: A line of charge $\lambda$ is located on the z-axis. Determine the electric flux for a rectangular surface with corners at coordinates: $(0, R, 0)$, ...
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If we change the radius of spherical surface does electric field or flux change?

Suppose a point charge is located at the center of a spherical surface. The electric field at the surface of the sphere and the total flux through the sphere are determined. 1).What happens ...
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Why is electric flux through any closed surface $q/\epsilon_0$?

Why is electric flux through any closed surface $q/\epsilon_0$? In schools we are only taught of its simplest case, i.e. flux through a sphere with charge centered at origin. And then it is ...
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Electric Field from Dielectric Shell

This is a question taken from a past E&M exam A thick spherical shell (inner radius $R_1$ and outer radius $R_2$) is made of a dielectric material with a "frozen in" polarization ...
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2 dimensional Coulomb's law equation

We can notice that in the Coulomb's law equation, $$\begin{equation}\tag{1}F=\frac{1}{4\pi\epsilon}\cdot\frac{q_1q_2}{r^2}\end{equation} $$ $4\pi r^2$ factor in the denominator expresses directly ...
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My conundrum with Gauss’ law in electrostatics

If I use Gauss’ law to calculate the electric field outside of a charged (conducting or insulating) sphere or a point charge, the fields are the same. However, as a test approaches a point charge, the ...
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Electric Field Between Two Parallel Infinite Plates of Positive Charge and a Gaussian Cylinder

Is the electric field between two positively charged parallel infinite plates one with a charge density twice the other effect the electric field on the outside of the plates? I am thinking no, ...
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Newtonian gravity equation in a 2 dimensional world [duplicate]

I am wondering if my line of thought is correct - and thus the resulting answer to the problem above would be correct. As we know the gravitational force (of two point masses) is given by $$F = ...
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Net flux calculation through a cube [closed]

Ans: Applying Gauss’s law the net flux can be calculated. And for option (B), I guess the flux will be 0. But not sure. Can anyone explain all the 3 options? For left and rignt face, EA = ...
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insulator based gauss law questions

My book is incredibly scarce on insulator based Gauss law questions. Conductors seem to handle themselves pretty simply. Here's a question I'm working on that isn't part of my book. where the radii ...
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Electric field outside a sphere with a cavity

I have a sphere of radius $2a$ centered at the origin and made of a nonconducting material that has a uniform volume charge density $\rho$. A spherical cavity of radius $a$ eccentric to the right side ...
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Physical interpretation of $\iiint (∇\cdot\vec E)\mbox{d} V$ [duplicate]

Can anybody explain the physical interpretation of Gauss's law $$\iiint (\nabla\cdot \vec E)~\mbox{d}V~=~\frac{Q}{\epsilon_0}? $$ Also, how is the differential form of Gauss's law obtained from ...
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Flux through side of a cube

I am looking at Griffiths introduction to Electrodynamics 3rd ED. Problem 2.10 asks for the flux of $E$ through the right face of the cube, when a charge $q$ is in the back left corner of the cube. ...
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Intuition behind defining divergence as flux divided by volume?

For a continuously differentiable vector field $F$ the divergence theorem can be used to give $$(\nabla\cdot F)(a) = \lim_{r\to 0} \frac{3}{4\pi r^3}\int_{|x-a|=r} F \cdot n dA$$ This should mean that ...
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Can someone give an intuitive way of understanding why Gauss's law holds?

Gauss' Law of electrostatics is an amazing law. It is extremely useful (as far as problems framed for it are concerned :D. I do not have a real world-problem solving experience of using Gauss' Law). ...
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Potential of arbitrary charge distribution

Imagine this: You have a sphere of air where you have no charge and around this sphere you have a charge distribution $\rho(r,\theta,\phi)$. (For instance, this could be ...
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The relation between Gauss's law and Coulomb law and why is it important that the electric field decrease proportionally to $\frac{1}{r^{2}}$?

My question relates to the third MIT's video lecture about Electricity and Magnetism, specifically from $21:18-22:00$ : http://youtu.be/XaaP1bWFjDA?t=21m18s I have watched the development of Gauss's ...
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Why is the radial direction the preferred one in spherical symmetry?

I am learning about electricity and magnetism by watching MIT video lectures. In the lecture about Gauss's law, while trying to calculate the flux through a sphere with charge in it, the lecturer ...
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How to find electric scalar potential of infinite wire with Poisson/Laplace equation?

I though it will be easier then calculating the electric field and then integrating, but I am stuck. lets say we have an infinite wire, charged $\lambda$ per unit of length and its located at the ...
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Why is electric flux defined as $\Phi = E \cdot S$?

Flux, as I understand it, is the amount of substance passing through a particular surface over some time. So, from a simple perspective, considering photons that go through some virtual surface $A$ ...
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Coulomb potential

It is known that the Coulomb potential can be obtained by Fourier transform of the propagator from E&M. Is this because one of Maxwell's equations have the form $\nabla \cdot \mathbf{E}=\rho$?
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In electrostatics total flux linked from the closed surface enclosing the charge is equal to $Q/\varepsilon_0$. This is according to Gauss Law

In electrostatics total flux linked from the closed surface enclosing the charge is equal to $Q/\varepsilon_0$. This is according to Gauss Law. Is this the experimental value or defined value. If ...
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How are excess charges distributed over non-spherical conductors?

My textbook gives the following explanation on how excess charges are spread over conductors: The excess charge on an isolated conductor moves entirely to the conductor's surface. However, ...
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Gauss's Law understanding

In the case of a point charge $q$ at the origin, the flux of $\vec{E}$ through a sphere of radius r is, \begin{equation} \oint \vec{E}\cdot d\vec{a} = \int \frac{1}{4 \pi \epsilon_0 ...
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Gauss's Law - Electric Field outside a Shell?

I'm somewhat confused as to why the electric field outside a spherical shell is $\frac{Q}{4\pi r^{2}\epsilon_{0}}$ Going through the work: $$ Q = 4 \pi r^{2} \sigma ; \frac{4\pi ...
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Behavior of the electric field on boundary surfaces

Consider this picture. Integrating over this infinitesimal box gives the following equivalencies: $$\int_{\Delta V} d^3r~{\rm div} \vec{E}(\vec{r}) = \int_{S(\Delta V)} d\vec{f} \cdot ...
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Is Gauss' law useful to determine the electric field strength of a charge distribution? [closed]

Under what conditions is useful Gauss' law to determine the electric field strength of a charge distribution? Can someone help me with this question?
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Charge inside conductor

I know that the $E$ field inside a conductor is zero. What happens if I put a source of charge inside the conductor? Say the conductor was spherical centered on the origin and there exists a charge ...
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Gauss' law and an external charge

Gauss' law states that the net outward normal electric flux through a closed surface is equal to $q_{total, inside}/\epsilon_0$. However, I'm a bit confused of why the presence of an external charge ...
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Gauss's Law with Moving Charges

My text claims that Gauss's Law has been proven to work for moving charges experimentally, is there a non-experimental way to verify this?
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Charges lying on a Gaussian Surface

Let's say you have a spherical charge distribution of radius R. This distribution has some charge density as a function of radius. I know that I can determine the electric field outside of the charge ...
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Electric field around charged cylinder

This is a homework question, so please don't give me the answer outright. I just need help conceptually. "A cylindrical shell of length 190 m and radius 4 cm carries a uniform surface charge density ...
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Is Newtonian gravity consistent with an infinite universe? [duplicate]

Let us assume that we have have an infinite Newtonian space-time and the universe is uniformly filled with matter of constant density (no fluctuations whatsoever), all of it at rest. By symmetry, the ...
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Finding Electric Field outside a Charged Cylinder

I'm trying to solve a problem that involves finding the electric field due to a uniformly cylinder of radius $r$, length $L$ and total charge $Q$. Well, my thought was: if I am to use Gauss' Law, I'll ...
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Why doesn't a gaussian surface pass through discrete charges?

I have read that Gaussian surface cannot pass through discrete charges. Why is it so? I have even seen in application of Gauss' Law when we imagine a Gaussian Surface passing through a charge ...
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Applying Gauss' Law to find Electric Field

I'm in doubt in the application of Gauss' Law to find electric fields when the charge distribution is symmetric. Well, first of all: I know how to find the magnitude of the field - we just enclose the ...
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Proof that flux through a surface is independent of the inner objects' arrangement

$$\Phi=\iint_{\partial V}\mathbf{g} \cdot d \mathbf{A}=-4 \pi G M$$ Essentially, why is $\Phi$ independent of the distribution of mass inside the surface $\partial V$, and the shape of surface ...
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Newtonian Gravity on a Riemannian $3$-Manifold

To solve the Poisson equation for the Newton Potential, say $\phi$, one can use the divergence theorem, such that $$\int_U \nabla^2 \phi \sqrt{g}~ dV= \int_{\partial U} <\nabla \phi,n> ...
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Electric lines of force

Why cant electric lines of force pass through the charged sphere? Well, basically that's how a Faraday cage works, but how can it be so?
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Why can we use Gauss' law to compute electric field?

For simplicity I'm considering only the sphere case. In the Gauss' Law formulation we have some field $E$ introduced by charges $Q$ inside some sphere, then we compute flux and integrate, and we get ...
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Finding the electric field on a point (x,y,z) using Coulomb's Law

Using Gauss' Law, the answer is $$\frac{Q}{4 \pi \epsilon R^2}.$$ However if I were to do the integration using Coulomb's Law, I get $$ \int_0^{2\pi} \int_{0}^{\pi}\int_r^a \frac{\rho \sin\theta dR ...
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Gravity force strength in 1D, 2D, 3D and higher spatial dimensions

Let's say that we want to measure the gravity force in 1D, 2D, 3D and higher spatial dimensions. Will we get the same force strength in the first 3 dimensions and then it will go up? How about if ...
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Intuitive explanation of the inverse square power $\frac{1}{r^2}$ in Newton's law of gravity

Is there an intuitive explanation why it is plausible that the gravitational force which acts between two point masses is proportional to the inverse square of the distance $r$ between the masses (and ...
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Why are so many forces explainable using inverse squares when space is three dimensional?

It seems paradoxical that the strength of so many phenomena (Newtonian gravity, Coulomb force) are calculable by the inverse square of distance. However, since volume is determined by three ...
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Electric field inside and outside a metallic hollow sphere

1) It is known that inside a metallic hollow sphere it will not experience outside electric field because of the charge separation of electrons and holes at the surface of sphere and creating an equal ...
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Would a gauss rifle based on generated magnetic fields have any kickback?

In the case of currently developing Gauss rifles, in which a slug is pulled down a line of electromagnets, facilitated by a micro-controller to achieve great speed in managing the switching of the ...