A law in Classical Electromagnetism and Newtonian Gravity.

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Does Coulomb's Law, with Gauss's Law, imply the existence of only three spatial dimensions?

Coulomb's Law states that the fall-off of the strength of the electrostatic force is inversely proportional to the distance squared of the charges. Gauss's law implies that a the total flux through a ...
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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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Paradox with Gauss' law when space is uniformly charged everywhere

Consider that space is uniformly charged everywhere, i.e., filled with a uniform charge distribution, $\rho$, everywhere. By symmetry, the electric field is zero everywhere. (If I take any point in ...
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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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Is there a limitation on Gauss' law? [duplicate]

Recently I had a question to find the electric field at a distance $R$ from the origin, where the space is filled with charge of density $\rho$. I did this by assuming a Gaussian surface of radius ...
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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 ...
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“Find the net force the southern hemisphere of a uniformly charged sphere exerts on the northern hemisphere”

This is Griffiths, Introduction to Electrodynamics, 2.43, if you have the book. The problem states Find the net force that the southern hemisphere of a uniformly charged sphere exerts on the ...
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Why does acceleration seem not to be the gradient of gravitational potential?

Consider a spherically symmetric distribution of density $\rho(r)$. We can define the mass enclosed within each radius $r$ using $\frac{dM(r)}{dr} = 4\pi r^2 \rho(r)$, with the condition that $M(r=0) ...
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Why $1/r^2$ and not another power of $r$ in Newton's law of gravitation?

My book introduces the force of gravitation as a non-contact force between two bodies of mass $M_1$ and $M_2$ separated by a distance $r$ . Then it says it is directly proportional to the product of ...
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Divergence of a field and its interpretation

The divergence of an electric field due to a point charge (according to Coulomb's law) is zero. In literature the divergence of a field indicates presence/absence of a sink/source for the field. ...
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What is the purpose of differential form of Gauss Law?

I am learning the differential form of Gauss Law derived from the divergence theorem. $${\rm div}~ \vec{E} =\frac{\rho}{\epsilon_0}.$$ So far in my study of math and physics, the word "differential" ...
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Why can charges outside be ignored in Gauss's Law?

In MIT's 8.02 course, it is shown in lecture 3 that we can derive Gauss's Law from Coulomb's to get $ \phi = \oint \vec{E} \cdot \vec{dA} = \frac{Q_{enc}}{\epsilon_{0}} $ However, in the lecture, it ...
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Gravitational field intensity inside a hollow sphere

It is quite easy to derive the gravitational field intensity at a point within a hollow sphere. However, the result is quite surprising. The field intensity at any point within a hollow sphere is ...
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What is the electric field in a parallel plate capacitor?

When we find the electric field between the plates of a parallel plate capacitor we assume that the electric field from both plates is $${\bf E}=\frac{\sigma}{2\epsilon_0}\hat{n.}$$ The factor of two ...
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Is the electrostatic field inside of any closed, uniformly charged surface zero?

We know that a simple application of Gauss's law tells us that the field inside of a uniformly charged spherical shell is zero. Does this hold for all uniformly charged closed surfaces? If so, how ...
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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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Infinitely charged wire and Differential form of Gauss' Law

I have tried calculating the potential of a charged wire the direct way. If lambda is the charge density of the wire, then I get $$\phi(r) = \frac{\lambda}{4 \pi \epsilon_0 r} \int_{-\infty}^\infty ...
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Integral form of Gauss's law for magnetism from Stokes' theorem?

How can the integral form of Gauss's law for magnetism be described as a version of general Stokes' theorem? How does it follow?
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Why is the electric field inside a conductor zero in equilibrium?

My textbook says the field inside a conductor must be zero in order for the system to be equilibrium and therefore there must be no excess charge inside. Their proof: 1) Place a gaussian surface ...
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Gauss law in classical U(1) gauge theory

I can see that $a_{0}$ is not an independent field and Gauss law is a constraint on the theory arising from field equations. But, I don't get the geometrical picture. Let $A$ be the space of all ...
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Charge Distribution on a Parallel Plate Capacitor

If a parallel plate capacitor is formed by placing two infinite grounded conducting sheets, one at potential $V_1$ and another at $V_2$, a distance $d$ away from each other, then the charge on either ...
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Why is the electric field of an infinite insulated plane of charge perpendicular to the plane?

I'm studying Gauss' Law, and I came across a section where we're supposed to find the electric field of various shapes (like an infinite line of charges, etc), and for an infinite plane with a uniform ...
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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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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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2D Gauss law vs residue theorem

I used to have a vague feeling that the residue theorem is a close analogy to 2D electrostatics in which the residues themselves play a role of point charges. However, the equations don't seem to add ...
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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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Why we cannot use Gauss's Law to find the Electric Field of a finite-length charged wire?

One of my physics books has a nice example on how to use Gauss's Law to find the electric field of a long (infinite) charged wire. However, at the very end of the example, the author ends by saying ...
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Electric field on the surface of a charged sphere

We know that the electric field for a point charge is $$ E = \frac{KQ}{R^2}. $$ If $R$, i.e. distance from the electric field producer to the point where we want to find the electric field becomes ...
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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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How is Gauss' Law (integral form) arrived at from Coulomb's Law, and how is the differential form arrived at from that?

On a similar note: when using Gauss' Law, do you even begin with Coulomb's law, or does one take it as given that flux is the surface integral of the Electric field in the direction of the normal to ...
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Spherical Shell with Electric Field Zero Everywhere Inside It

If an isolated, charged spherical shell has a uniform charge distribution, the electric field everywhere inside it is 0, by Gauss' Law. Is the converse true? That is, given an isolated, charged ...
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Shouldn't the electric field in a solid insulating sphere be linear with radius?

I am a senior in High School who is taking the course AP Physics Electricity and Magnetism. I was studying Gauss's laws and I found this problem: A solid insulating sphere of radius R contains a ...
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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 the electric field $\vec{E}$ is constant (=position independent) for an infinite 2D sheet of constant charge?

So I'm reading a text on electricity and it talks about using the integral to compute the total charge of a collection of points, which I mostly understand. But then we get to finding the electric ...
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A closed surface, no charge enclosed, yet flux not 0?

! The book says it is $E_0\pi r^2$ because the flux through the circle is equal to the curved part of the paraboloid. I don't understand this, shouldn't the total flux be 0 for the whole surface? ...
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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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The discontinuity of Electric Field

''electric field always undergoes a discontinuity when you cross a surface charge $\sigma$'' GRIFFITHS In the derivation; Suppose we draw a wafer-thin Gaussian Pillbox, extended just barely over the ...
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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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Electric field outside a capacitor

I know that the electric field outside of a capacitor is 0 and I know it is easy to calculate using Gauss's law. We create cylindrical envelope that holds the same amount of charges (of opposite ...
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Gauss's law in a uniform charge distribution extending infinitely in all directions

Let us assume the universe filled with positive charge. About a particular point, all the positive charged particles will be symmetrical. Now consider a sphere of radius $r < \infty$ and apply ...
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Flux of electric field through a closed surface with no charge inside? [duplicate]

I'm reading the Feynman lectures on electromagnetism and in Vol II, Chapter 1.4 Vol. II, Chapter 1-4 he talks about the flux of the electric field and says that flux of $E$ through and closed surface ...
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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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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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Electric Field of Hollow Cylinder

Let's say we have a hollow cylinder with a charge $q$, radius $r$ and height $h$ as in the figure below. I am trying to find the electric field perpendicular to the surface of the hollow cylinder. I ...
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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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Electric Field “at” the surface of a conductor

It has been pointed out to me that the Electric field exactly on the surface of the conductor is conventionally taken to be $E=\frac{\sigma}{2\epsilon_0}$; does this come from taking the midpoint of ...
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Electric field due to a charged conductor

I have this grave confusion that I have been having since a while. When we calculate the electric field due to an infinite plane sheet of charge then the answer comes out to be $σ/2ε$. In this case we ...
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Gauss Law with a hollow asymmetric surface

In this video, Walter Lewin argues that no charge will appear on the inside surface of a hollow conductor in electrostatic equilibrium. He uses a Gaussian surface contained entirely within the ...
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Electric field due to a charged irregularly shaped balloon

There is a question in my textbook that says: A rubber balloon is given a charge $Q$ distributed uniformly over its surface. Is the field inside the balloon zero everywhere if the balloon does not ...
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Solved Gauss' Law for $\vec{E}$ without boundary conditions?

Why can I solve for the electric field of a point charge Q at the origin without boundary conditions? $\nabla\cdot\vec{E}=\rho/\varepsilon_0 = \delta(\vec{r})/\varepsilon_0$ is a 1st order ...