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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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 ...
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Gauss law use not in free space

Gauss' law specifies permitivity for free space. what happens if electric field is not in free space. does the law apply?
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Why is the electric field of a conducting sheet of charge double the electric field of just a sheet of charge?

I was reading Feynman's Lecture on the Application of Gauss' Law and I came across this: Source This really confused me. What are the "other" charges he talks about? How does the additional field ...
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Tangential component of electrostatic field on a charged surface?

This is a question from class 12 Physics NCERT Part I: Show that the tangential component of electrostatic field is continuous from one side of a charged surface to another. [Hint: Use the fact ...
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Why don't capacitors hold charges on the outer walls of the plates? [on hold]

Suppose I have two metal plates in a vacuum and I give this system some electric charge,the charge would distribute itself according to Gauss law on both the inner and outer walls of both plates...but ...
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How do I apply Gauss's law to coaxial conducting cylinders?

$$ \vert \vec E\vert =\frac{\lambda}{2\pi \varepsilon_0 r} $$ So I know this is the magnitude of the electric field of a line of charge using a cylindrical Gaussian surface. But, now let's say I have ...
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1answer
279 views

Confused about a question about a dielectric sphere

A dielectric sphere of radius R with uniform dielectric constant ε has an azimuthally symmetric density charge σ = σ0 cos θ placed on the surface. Outside the sphere is vacuum. (a) Obtain ...
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464 views

Determining electric displacement using Gauss's law

This is an example problem from my E&M textbook that I don't quite understand: A metal sphere of radius a carries a charge $Q$. It is surrounded, out to radius b, by linear dielectric material ...
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Doubt in the derivation of Gauss's law in dielectrics

so in the 2nd page,when the dielectric material is introduced the gauss's law becomes $$\oint _ { S } \vec { E } \cdot \vec { d S } = \frac { ( q - q _ { i } ) } { \epsilon _ { 0 } }$$.But my ...
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Electric Flux - Vector Components

How is $vcos(\theta)$ the perpendicular vector? I think I'm missing something fundamental in my trig and vector knowledge...
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Electric flux through an infinite plane due to point charge

What would be the total electric flux $\Phi_E$ through an infinite plane due to a point charge $q$ at a distance $d$ from the plane? I think it should be ${q/2\epsilon_0}$ but I cannot justify that. ...
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Infinite parallel plates have the same electric field between no matter the distance?

I saw this in a lecture about gausses law in application to infinite charged planes: How is it possible that the electric field above the top plane and below the bottom plane is always zero, given ...
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Confusion when applying Gauss's Law to a charged sphere

We have a charged sphere with charge Q and the charge is uniformly distributed with a charge density ρ. The sphere has a radius R. If we construct a Gaussian Surface with radius r, with r < R. If ...
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Gaussian Shell for a non-uniformly charged insulator

If I've already found the total charge for an insulating sphere of non-uniform charge, and I want to find the field inside the sphere, can I just set my Gaussian surface to be the surface of that same ...
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748 views

Principle of capacitor

It is said that second conductor reduces the potential of fist conductor and hence increases charge taking ability of first conductor My confusion... As per my limited knowledge it is electric field ...
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Why does the electric field of an infinite line depend on the distance, but not on an infinite plane?

I understand that with an infinite plane, as you get closer, the infinitesimal contributions to the electric field become greater in module. The direction of the vectors become less perpendicular to ...
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2answers
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Why is electric flux through a closed surface with charge inside non zero?

"If a closed surface does not have any charge inside where an electric field line can terminate, then any electric field line entering the surface at one point must necessarily exit at some other ...
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Signs in application of Gauss's law to a sheet of charge

In Purcell's Electricity and Magnetism, page 52, the author said that in the following situation: [Where we have a slab of positive charge with uniform density $\rho$. $\,\bf{E_{1}}\,$ is the $E$-...
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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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Please explain the given statement [duplicate]

There is a statement in my physics textbook in gravitation chapter - The force of attraction due to hollow spherical shell of uniform density on a point mass situated inside it is zero Is it valid for ...
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Electric field line density : Theory vs Reality

I've already went through this post. Yet, I still can't understand the meaning of "density" of electric field lines whose number is, in reality, infinite. One of the answers , for instance, states ...
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Electric Flux; Number of lines passing through a unit surface?

Most of the definitions on flux and flux density, show a plot consisting of a positive charge emanating a field, and describe that as the number of field lines decrease, the field strength decreases. ...
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1answer
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Gauss' law for two point charges and a factor of $4\pi$

When we model electric field as something that represents the "flow" of something that is conserved, we can prove that the flux due to a single point charge, through the following surface, Flux ...
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Infinite charge distribution [duplicate]

I've been thinking about a distribution of charge that does not follow Maxwell's euations, and I can't understand what's wrong with my reasoning. If we have a constant distribution of charge $\rho(x,y,...
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2answers
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Intuition of Maxwell's Equations [duplicate]

Is there an intuitive explanation for Maxwell's equations? I know they are axioms but is there a logical understanding of why instead of mathematical. Both forms don't explicate the scientific ...
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1answer
143 views

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 a ...
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Understanding of Gauss law using vector fields

I was going through the conventions and terminologies followed to describe the magnetic interactions. I understood that the field lines are just a simpler representation of the magnetic interaction ...
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Electrostatics and electric field inside conductor

I have tried for a while finding an answer to this question. Similar ones have been explained earlier by using Gauss law. However I am wondering about the physical change happening to the conductor in ...
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Applying Gauss's law on a disc

Shouldn't the electric flux through a circular disc due to a point charge kept at some finite distance from it be zero as all field lines which enter it exit it also and hence the net would be zero?
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How is the $E$-field getting canceled between outer and inner surface of a neutral conducting spherical shell?

I am reading Purcell's E&M book and in one of the example questions, it shows that there is no E field between outer and inner surface after a a point charge is located at an arbitrary position ...
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1answer
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Electric field between capacitor plates

When we try to find the electric field between the capacitor plates, what is the right way to do it? This is one of the ways I've seen and I don't understand why: Using a Gaussian cylinder on the ...
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1answer
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Electric field from the intersection of two spheres with different charges

This question is repeated a lot, but I for two spheres with different charge densities, sphere one with radius a centered at the origin and charge density $\rho_1$, and sphere two with radius centered ...
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1answer
183 views

Maxwell's equations UPML in FDTD with inhomogeneous media

I'm looking at matching the UPML (uniaxial perfectly matched layer) defined in Taflove&Hagness' Computational electrodynamics to an inhomogeneous media (inhomogeneous w.r.t. both $\varepsilon$ and ...
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Gauss's Law on Parallel Conducting Plates

I have a question regarding the application of Gauss's law to find the E-fields produced by two parallel conducting plates. My textbook (Halliday and Resnick 9e) states that there is no E-field above ...
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1answer
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Contradictions in electric field of infinite uniform charge distribution [duplicate]

This question stems from the exercise 2.50 of Griffith's Introduction to Electrodynamics, which I am rereading. In the problem, he asks to find the charge density of a volume when the electric field ...
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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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1answer
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$E$ in a solid uniformly charged conductor: Is my reasoning here correct?

Suppose we take spherical conductor which is having both positive and negative charges but as a whole is electrically uncharged and is not under the influence of any external Electric field, We can ...
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Why is the $\vec E$ field inside a sphere = 0? [closed]

I was taught Electric Field inside a sphere is 0, because of Gauss Law. But inside a uniformly charged sphere, if I go at a distance of $r$ from the centre, I will be closer to the +ve charge and ...
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1answer
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Value of E on a point inside a solid uniformly charged sphere due to the part of the solid sphere on the outside of the point

Suppose there is a uniformly charged solid sphere of radius $R$ and we choose a gaussian surface of radius $r$ centered about the center of the solid uniformly charged sphere where $R>r$. Then is ...
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1answer
291 views

Spherical conducting shells behaviour

My textbook provides the following problem: Consider a spherical conducting shell with inner radius $R_2$ and outer radius $R_3$, that has other spherical conductor inside it with radius $R_1$ (...
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The value of $E$ in the LHS of Gauss law equation

Suppose there are multiple point charges in a region and I only take the Gaussian surface which encloses only one of the charges $q$. I have read that the $E$ term on the LHS of the Gauss law equation ...
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Is anything lost by simply saying that a charge is nothing but the divergence of a field?

If we propose that 1) there are fields and 2) that some fields can have places where they converge (that is to say, places where del dot the field is not zero) then we have the definition of such a ...
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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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Analogies between electrostatics and steady state heat equation?

In electrostatics we have $$\nabla \cdot E = \rho/\varepsilon$$ and using the divergence theorem we get $$\int_{\partial\Omega} E \cdot \hat{n} dS = \int_\Omega \rho/\varepsilon dV.$$ This states ...
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Magnetic flux through a loop the same as flux through the plane outside the loop?

Let's say we have a current loop of radius $a$ in $x-y$ plane. Let's consider the flux ($\phi=BA$) through the loop, and the flux through the rest of the plane, outside the loop. (to clarify, if the ...
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How does charge movement vary between insulators and conductors?

I've been reading A Student's Guide to Maxwell's Equations by Daniel Fleisch, and he states: in nonconducting materials (called "insulators" or "dielectrics"), charge does not move freely, but may ...
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Electric field outside and inside of a sphere

An insulating sphere of radius a carries a total charge $q$ which is uniformly distributed over the volume of the sphere. I'm trying to find the electric field distribution both inside and outside ...
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1answer
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Electric field related to conducting materials containing charge containing cavity

In my physics class we were analyzing a scenario where a charge has been placed inside the cavity of a conducting material like this: What my teacher did was to assume a Gaussian surface in the ...
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3answers
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Why do we use a cylinder as a Gaussian surface for infinitely long charged wire?

Why do we use a cylinder as a Gaussian surface for infinitely long charged wire and not some other shape like cube?
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Divergence of $\frac{ \hat {\bf r}}{r^2}$ , what is the 'paradox'?

I just started in Griffith's Introduction to electrodynamics and I stumbled upon the divergence of $\frac{ \hat r}{r^2}$ , now from the book, Griffiths says: Now what is the paradox, exactly? ...