Questions tagged [gauss-law]

A law in classical electromagnetism and Newtonian gravity which relates (charge) density to the divergence of a field, or alternatively the charge in a volume to the flux through the bounding surface.

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6answers
6k views

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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Basis for the Generalization of Physics to a Different Number of Dimensions

I am reading this really interesting book by Zwiebach called "A First Course in String Theory". Therein, he generalizes the laws of electrodynamics to the cases where dimensions are not 3+1. It's an ...
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Why does the density of electric field lines make sense, if there is a field line through every point?

When we're dealing with problems in electrostatics (especially when we use Gauss' law) we often refer to the density of electric field lines, which is inversely proportional to the radius in the case ...
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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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“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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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 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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Field between the plates of a parallel plate capacitor using Gauss's Law

Consider the following parallel plate capacitor made of two plates with equal area $A$ and equal surface charge density $\sigma$: The electric field due to the positive plate is $$\frac{\sigma}{\...
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2answers
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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 zero....
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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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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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4answers
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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 $R$....
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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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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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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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Aren't Gauss's law for magnetism and Faraday's law of induction contradictory?

Gauss's law states that $\int_S \vec B\cdot d\vec S=0$. But law of induction states that $\xi=-\frac {d\phi}{dt}$, where $\phi=\int_S \vec B\cdot d\vec S$. So if Gauss's law was to be correct there ...
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If Ampere's law implies the Biot-Savart law, which implies Gauss's law for magnetism, does that mean Maxwell's equations are redundant?

Studying electromagnetism, I came across the following fact: Maxwell's third equation (divergence of magnetic field is zero) can be derived from the Biot-Savart Law. The Biot-Savart Law can be ...
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1answer
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Deriving Coulomb's Law from Gauss's Law

I've been thinking about this for the past couple of days. I apologize if my explanation isn't very clear. I have already seen derivations of this, but I'm still not satisfied. In the derivations of ...
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Why is the electric field due to a charged infinite cylinder identical to that produced by an infinite line of charge?

Assume that the linear charge density is the same for the charged infinite cylinder and the infinite line. By Gauss' Law, I know the charge enclosed is the same given a Gaussian cylinder of a certain ...
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Calculating the potential on a surface from the potential on another surface

The question is short: If a charge (or mass) distribution $\rho$ is enclosed by surface $S_1$, I can calculate the electrostatic (or gravitational) potential on that surface by integrating $\rho(r') \ ...
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1answer
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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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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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Period of oscillation through a hole in the earth

Special mention to the QI episode that kicked this off: Anyway, the host points out that a tunnel that connects a pair of points on the earth's surface can be thought of as a gravity train - where ...
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4answers
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Can Newton’s law of gravitation be derived from Coulomb’s law? [duplicate]

I’m casually learning physics and have noticed that Newton’s law of gravitation and the electrostatic force formulas look similar. I’ve asked this question before but would really appreciate another ...
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How does superstring theory explain the inverse square gravity law, given that it requires 9 spatial dimension?

In superstring theory, the spacetime dimension is either 10, one of them is time, the rest are spatial dimensions. But based on geometrical argument, we can say that $F\propto r^{1-D}$, where $D$ is ...
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Flux received by a negative charge

Consider two charges $+q$ and $-Q$ placed at a distance, note- charge q and Q are different In terms of magnitude. My question: is number of flux lines received by $-Q$ proportional to its own 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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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 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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4answers
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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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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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4answers
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Why can we neglect surface terms in Field Theory?

My teacher says that the integral $$\int _{-\infty }^{\infty }\frac{\partial J^{\mu }}{\partial x^{\mu}}d^4x$$ that we met in QFT can always be neglected since $$\int _{-\infty }^{\infty }\frac{\...
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2answers
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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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1answer
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How do you account for the fact that the field points in a particular direction when the charge density is uniform? [duplicate]

Suppose an electric field ${\mathbf E}(x,y,z)$, $$E(x)=ax, \quad E(y)=E(z)=0,$$ where $a$ is a constant. So we can calculate its charge density is $$\rho = \varepsilon \nabla\cdot{\mathbf E} = \...
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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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4answers
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Electric field outside a capacitor

I know that the electric field outside of a capacitor is zero 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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5answers
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How to show mathematically that the electric field inside a conductor is zero?

The electric field is characterized by the equations $$\nabla\cdot \mathbf{E} = \dfrac{\rho}{\epsilon_0}$$ $$\nabla \times \mathbf{E} = 0$$ Or equivalently, $\nabla^2 V = -\rho/\epsilon_0$ and then ...
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1answer
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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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Significance of electrical fields of infinite objects

I've noticed a pattern with the electric fields of charged objects of infinite dimensions. A point charge, which can be considered a charge of 0 dimensions, has an electric field that goes as $r^{-2}$...
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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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2answers
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Find electric potential due to line charge distribution?

I need help how to set up this integral $$V(\mathbf r)=\frac{1}{4\pi\epsilon_0} \int_L \frac{\rho'_l}{\lvert \mathbf r - \mathbf{r'} \rvert}\mathrm{d}l'. $$ I have a uniform line charge along the $z$...
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4answers
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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 \begin{...
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3answers
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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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0answers
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Modified Coulomb potential [closed]

I'm working through Byron and Fuller's "Mathematics of Classical and Quantum Physics" and came across this problem: If the electric potential of a point charge were $\phi(r) = \frac{q}{r^{1-\...
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5answers
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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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5answers
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What is the electric field flux through the base of a cube from a point charge infinitesimally close to a vertex?

I'm having some trouble with the following problem: A charge $q$ is placed on the body diagonal of the cube very close to one of the corners (distance $\delta$ from the corner, $\delta$ tending to ...
5
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4answers
859 views

Why is electric field inside a cavity of a non-conducting sphere not zero? [closed]

Consider a charged non conducting solid sphere of uniform charge density, and it as hole of some radius at the centre. Now suppose I apply Gauss law. As there is no charge inside the cavity, no ...
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5answers
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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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3answers
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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 ...