The gauss-law tag has no wiki summary.
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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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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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1answer
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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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“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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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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1answer
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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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1answer
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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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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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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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1answer
116 views
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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1answer
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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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1answer
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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
$$\int_U \nabla^2 \phi \sqrt{g}~ dV= \int_{\partial U} <\nabla \phi,n> ...
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Electric lines of force
Why cant electric lines of force pass through the charged sphere? Well, basically that's how a Faraday cage works, but how can it be so?
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1answer
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Gravity force strength in 1D, 2D, 3D and higher spatial dimensions
Let's say that we want to measure the gravity force in 1D, 2D, 3D and higher spatial dimensions.
Will we get the same force strength in the first 3 dimensions and then it will go up? How about if ...
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3answers
192 views
Why can we use Gauss' law to compute electric field?
For simplicity I'm considering only the sphere case.
In the Gauss' Law formulation we have some field E introduced by charges $Q$ inside some sphere, then we compute flux and integrate, and we get ...
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Finding the electric field on a point (x,y,z) using Coulomb's Law
Using Gauss' Law, the answer is $$\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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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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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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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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1answer
415 views
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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1answer
322 views
Divergence of non conservative electric field
I'm looking for the proof that the 1st Maxwell equation is valid also on non conservative electric field.
When we are talking about a electrostatic field, the equation is ok. We can apply the Gauss ...
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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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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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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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How does one come up with the Coulomb's law?
My teacher mentioned that field line density = no. of lines / area and the total area of a sphere is $4\pi r^2$ and so an electric force is inversely proportional to $r^2$. Actually, why can the total ...
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Find the quantity of charge - given potential function
A potential function is given by $V(r)=\frac{Ae^{-\lambda r}}{r}$ Find charge density and hence charge.
I first took the gradient of potential to get $\vec{E}(r)=\frac{Ae^{-\lambda ...
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1answer
980 views
Electric field due to a solid sphere of charge
I have been trying to understand the last step of this derivation. Consider a sphere made up of charge $+q$. Let $R$ be the radius of the sphere and $O$, its center.
A point $P$ lies inside the ...
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3answers
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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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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
$$\phi(r) = \frac{\lambda}{4 \pi \epsilon_0 r} \int_{-\infty}^\infty ...
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1answer
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Gaussian surface question
There is an infinite slab of charge, and a (Gaussian surface) cylinder whose ends are both outside of the slab.
$\phi_A$ is the flux through this cylinder, by symmetry the component of the flux ...
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1answer
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Shouldn't the electric field in a solid insulating sphere be linear with radius?
I am a senior in High School who is taking the course AP Physics Electricity and Magnetism.
I was studying Gauss's laws and I found this problem:
A solid insulating sphere of radius R contains a ...
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Conducting surface inside conducting surface
Let's say there's a closed conducting surface. Then by Gauss's Law the E field bound by the surface must equal the charge inside. There's no charge inside, so the E field cancels. This is a Faraday ...
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Gauss law in classical U(1) gauge theory
I can see that $a_{0}$ is not an independent field and Gauss law is a constraint on the theory arising from field equations. But, I don't get the geometrical picture.
Let $A$ be the space of all ...
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Is it really to solve problem below by using, in the main, Gauss law?
There is an infinite cylinder surface which uniformly charged along and has a surface charge density, which can be represented as
$$
\sigma = \sigma_{0}cos(\varphi ),
$$
where $\varphi$ - polar angle ...
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Newton's Law of Gravitation, Gauss Law and GR
From One of My Unpublished Papers
$$\frac{d^2 x^{\alpha}}{d\tau^2}=-\Gamma^{\alpha}_{\beta \gamma}\frac{dx^{\beta}}{d\tau}\frac{dx^{\gamma}}{d\tau} \tag{1}$$
For radial motion in Schwarzschild’s ...
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Using Gauss's Law to calculate electric fields between plates
I have two earthed metal plates, separated by a distance $d$ with a plane of charge density $\sigma$ placed a distance $a$ from the lower plate. I want to derive expressions for the strength of the ...
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Gauss's Law in action
Need someone to tell me if I got this done correctly
(a) Draw Gaussuian cylinder inside the black cylinder to find charge enclosed
$Q_{en} = Q(\frac{r}{a})^2$
Apply Gauss's Law
$E2\pi r \ell = ...
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What is discontinuity in Vector Fields
I am reading David J. Griffiths and have a problem understanding the concept of discontinuity for E-field.
The E-field has apparently to components. (How does he decompose the vector field into the ...
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In which cases is it better to use Gauss' law?
I could, for example calculate the electric field near a charged rod of infinite length using the classic definition of the electric field, and integrating the: $$
\overrightarrow{dE} = \frac{dq}{4 ...
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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
$$\int_{a}^{b}\mathbf{E}\cdot d\mathbf{s} = ...
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1answer
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Gauss Law for Magnetism,Non Instantaneous Field Propagation
Is the magnetic force instantaneous? And, are all field lines established simultaneously? Otherwise, for example, the field line marked 'L' will take longer time to propagate than the ones above it, ...
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Gravimagnetic monopole and General relativity
Review and hystorical background:
Gravitomagnetism (GM), refers to a set of formal analogies between Maxwell's field equations and an approximation, valid under certain conditions, to the Einstein ...
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Could someone remind me of what we mean by zero electric field “inside” a conductor?
If I have a spherical conductor (perhaps a shell) and "inside", as in the hollow area there is nothing. The electric field is 0. But what happens if there is a charge "inside" (not like inside the ...
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1answer
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Gaussian Unit of Charge and Force
I just read that in the Gaussian Units of charge The Final equation in Coulomb's law is as simple as $$\boldsymbol{F}=\frac{q_1q_2}{r^2}$$
No $\epsilon_0$ no $4\pi$ like you have in the $\mbox{SI}$ ...
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Gauss' Law… Neglect Edge effects [closed]
Two Large Metal plates of area $1.0$ $m^2$ face each other. They are $5$ $cm$ apart and carry equal and opposite charge on their inner surfaces. If $E$ between the plates is $55$ $N/C$, what is ...
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A closed surface, no charge enclosed, yet flux not 0?
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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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Flux if there were only one type of charge in the universe
There was this question that i saw in a book and it also had an answer given.
The Question was:
If there were only one type of charge in the universe, then:
$\phi = \oint ...
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Why is the flux 0? I don't understand this concept
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Why does it say that the flux due to q_2 and q_3 through S is 0? Doesn't it contain a nonzero charge q_1?
Does anyone also know the difference between "no charge" vs "net charge is 0"? My book ...
