A law in Classical Electromagnetism and Newtonian Gravity.

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Scaling of Static Electric Field

The electric field of a point charge goes like $\displaystyle\frac{1}{r^2}$ The electric field of an infinite line goes like $\displaystyle\frac{1}{s}$ The electric field of an infinite plane is ...
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What does the Dirac delta function physically do while deriving Gauss Law form Coulomb's law?

While doing this derivation, the the source coordinates are mentioned as "$s$" and the coordinate of the point at which field is to be calculated is mentioned as "$r$". Kindly follow this Wikipedia ...
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Difference between $E$ field configuration, sheet of charge: infinite sheet of charge, conducting vs. non-conducting

This is a very easy question, but I often confused myself. Perhaps someone could explain this concept again: A non-conducting infinite sheet of charge has the electric field configuration ...
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Can Gauss' Law in differential form apply to surface charges?

I'm calculating the electric field outside a coaxial cable using only Gauss' Law in differential form. The charge density on the interior solid conducting cylinder is exactly cancelled by the surface ...
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Electric field of a capacitor in dielectric medium with weird size

I have been learning gauss's law in capacitor recently, recently I come up with this problem that I couldn't solve myself. If we have a capacitor,and a dielectric medium with half the volume between ...
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Is Gauss' law valid for time-dependent electric fields?

The Maxwell's equation $\boldsymbol{\nabla}\cdot \textbf{E}(\textbf{r})=\frac{\rho(\textbf{r})}{\epsilon_0}$ is derived from the Gauss law in electrostatics (which is in turn derived from Coulomb'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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Gauss' law - changes in the magnitude of E field inside the closed surface

Gauss's law says that the flux through a closed surface which contains neither a sink nor a source will be zero. It's quite clear that all field lines will have to exit somehow, but the strength of ...
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How to approximate trajectories and movement of two oppositely charged particles?

Imagine a single, stationary charged atomic ion, say a Lithium anion or cation (Li+ or Li-). Now imagine another a single free, oppositely charged particle--perhaps an electron or Hydrogen ion ...
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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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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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Where is the flaw in deriving Gauss's law in its differential form?

From the divergence theorem for any vector field E, $\displaystyle\oint E\cdot da=\int (\nabla\cdot E) ~d\tau$ and from Gauss's law $\displaystyle\oint E\cdot ...
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Gauss' law giving zero field where field is not zero?

Two plastic sheets with charged densities as shown: I'm trying to find the field at $B$. I obtained the correct answer by adding up the fields created by each charge density. But I realized that ...
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Calculate the flux of a point charge with Gauss's law

I know from my class that to calculate the flux of a point charge with Gauss's law, I have to make a surface that intersects with all of the flux lines resulting from the charge, and then make this ...
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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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Formula of Gauss' Law of Gravitation

Gauss's law for Gravitation: $$\int g\cdot \mathrm{d}S=4\pi GM$$ where $g$ is the gravitational field and $S$ is the surface area. Am I correct?
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What is meant by “unique direction” in most of the arguments in application of Gauss' Law?

This term is really bothering me a lot. While explaining the radial direction of electric field of a uniformly charged sphere, my book writes: Notice the use of argument of symmetry. There is no ...
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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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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 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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What are the applications of Gauss's law in technology? [closed]

Freshmen physics textbooks use Gauss's law plus symmetry to calculate the electric field. I was wondering if this method of finding the electric field using a symmetry is used in real applications in ...
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656 views

In which cases is it better to use Gauss' law?

I could, for example calculate the electric field near a charged rod of infinite length using the classic definition of the electric field, and integrating the: $$ \overrightarrow{dE} = \frac{dq}{4 ...
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Charge outside Gaussian Surface doesn't contribute to Flux?

I roughly understand the explanation for this: any electric field line that enters the surface, must leave it, since field lines can't terminate abruptly in space. My question is, what if you have a ...
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Does the induced charge on a conductor stay at the surface?

My textbook says that when a conductor is placed in an electric field, the electrons in it realign so that the net electric field inside the conductor is zero. There isn't a proof for this. It merely ...
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Why Gauss' law is applied?

Why Gauss' law is applied? Why is there a need of finding electric field by Gauss' law if we can find the electric field through Coulomb's law? or has it got more applications than Coulomb's law?
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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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Gauss' law in differential form for a point charge

I'm trying to understand how the integral form is derived from the differential form of Gauss' law. I have several issues: 1) The law states that $ \nabla\cdot E=\frac{1}{\epsilon 0}\rho$, but when ...
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Divergence Theorem, mathematical approach to Gauss's Law?

Let $D$ be a compact region in $\mathbb{R}^3$ with a smooth boundary $S$. Assume $0 \in \text{Int}(D)$. If an electric charge of magnitude $q$ is placed at $0$, the resulting force field is ...
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Why inverse square not inverse cube law? [duplicate]

So as I understand, the inverse-square law which shows up in a variety of physical laws (Newton's universal law of gravitation, Coulomb's law, etc.) is a mathematical consequence of point-like ...
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Is it equivalent to derive Gauss's law from discrete and continuous source distributions?

I've seen two derivations for Gauss's law in electrostatics. The first assumes a discrete charge distribution, the second a continuous one: Use superposition $$\vec{E}=\sum_{i=1}^n\vec{E}_i,$$ so ...
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Electric Field in Conductor Zero?

My textbook claims that the electric field in a conductor is zero in a static condition, as otherwise, a current would flow. But what if I go infinitely close to a proton; there will be an electric ...
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What would happen if charged plates are placed horizontally?

My idea is placing charged conducting plates in such a way that they won't see each others' surfaces unlikely to the typical design of parallel plates. If they are placed like this, would be the force ...
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Gauss' law question

It's actually a teaching conflict at my school. They said that $$\text{Flux}=\frac{q}{\varepsilon_0}.$$ Say for a point charge at the centre of the sphere and let's say we not put water into the ...
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Electric field in a cylinder

We have electric charge density $\rho(r) = kr$ in a cylinder of infinite height and radius $a$. I'm asked to find the electric field. I'm doing it using two methods and I don't undesrtand why then ...
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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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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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Would a non-conducting body ever acquire a uniform static charge throughout it's volume?

I'm studying electromagnetism and optics in first year and solving a lot of problems involving conveniently symmetrical conducting and non-conducting bodies having various uniformly distributed ...
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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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Is there an analogous Gauss' law which is applicable for a gravitational field?

Consider the Earth to be a flat infinite plane having linear mass density equal to the mass density of the actual earth. Can there be an analogous Gauss' law that can give the gravitational field ...
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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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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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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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Electric potential of sphere

(a) I am a little confused about this part. The point at A to B isn't radial. The electric field is radially outward, but if I look at the integral $$\int_{a}^{b}\mathbf{E}\cdot d\mathbf{s} = ...
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Gauss' Law and Electric Field Close to a Ball

So I've learned about Gauss' law and I have something in my head. Why does electric field that is very close to a ball is not close to infinity. Take a look at this image: As we can see, if we make ...
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Symmetry arguments and plane sheet of charge [duplicate]

The electric field due to a infinite plane sheet of charge is given by $\sigma/\epsilon_o$. Now could we have deduced by symmetry that the electric field's magnitude won't depend on distance?
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What are the reasons for accepting Coulomb's law? [duplicate]

I read the Coulomb's first memoir on Electricity and Magnetism (Louis L. Bucciarelli english translated version), and found it to contain only three trials (as complained by many) to reach the ...
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Electric field of a Uniformly charged sphere with a cavity [closed]

I have the following question: Consider a sphere of radius $R$, uniformly charged with a volume density $\rho$. The sphere has a spherical hole of radius $R/4$ at a distance $R/2$ from the ...
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In Newton's gravity, is the inverse square law related to the fact that our Universe has (apparently) 3 dimensions? [duplicate]

I read, long ago, a book, whose title I can't remember but I think the author was Carl Sagan. In the book was saying that gravity follows the inverse square law because of our Universe was 3 ...
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Is Gauss electric flux law valid in all coordinate systems?

The derivation of Gauss electric flux is as follows : $$\iint{\vec{E}}\cdot{\vec{dS}}=\iint E \, dS \cos\theta \, .$$ The projection of infinitesimal area on the surface $\vec{dS}$ on the radial ...
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Newton's shell theorem in 2d [closed]

I was wondering how to prove the analog of Newton's shell theorem for 2 dimensions, in which gravity obeys an inverse-linear law. Meaning: that an anywhere inside a circle, the gravitational field ...