The gauss-law tag has no wiki summary.
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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 ...
13
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4answers
505 views
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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2answers
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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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5answers
291 views
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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5answers
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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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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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4answers
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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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3answers
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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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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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3answers
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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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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 ...
3
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1answer
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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 ...
3
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1answer
239 views
Calculating capacitance of arbitrary plate shape and arrangement.
Looking for suggestions on how to approach calculating the capacitance of a capacitor where the plates have an arbitrary shape. I've seen derivations of capacitance for a few highly symmetric ...
3
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1answer
95 views
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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3answers
199 views
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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2answers
313 views
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 ...
2
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1answer
307 views
Formula of Gauss' Law of Gravitation
Gauss's law for Gravitation:
$$\int g\cdot \mathrm{d}S=4\pi GM$$
where $g$ is the gravitational field and $S$ is the surface area.
Am I correct?
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3answers
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What are the applications of Gauss's law in technology? [closed]
Freshmen physics textbooks use Gauss's law plus symmetry to calculate the electric field.
I was wondering if this method of finding the electric field using a symmetry is used in real applications in ...
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1answer
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Newtonian Gravity on a Riemannian $3$-Manifold
To solve the Poisson equation for the Newton Potential, say $\phi$, one can use the divergence theorem, such that
$$\int_U \nabla^2 \phi \sqrt{g}~ dV= \int_{\partial U} <\nabla \phi,n> ...
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2answers
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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
$$\int_{a}^{b}\mathbf{E}\cdot d\mathbf{s} = ...
2
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1answer
982 views
Electric field due to a solid sphere of charge
I have been trying to understand the last step of this derivation. Consider a sphere made up of charge $+q$. Let $R$ be the radius of the sphere and $O$, its center.
A point $P$ lies inside the ...
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3answers
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Is Newtonian gravity consistent with an infinite universe? [duplicate]
Let us assume that we have have an infinite Newtonian space-time and the universe is uniformly filled with matter of constant density (no fluctuations whatsoever), all of it at rest. By symmetry, the ...
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2answers
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A closed surface, no charge enclosed, yet flux not 0?
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The book says it is $E_0\pi r^2$ because the flux through the circle is equal to the curved part of the paraboloid.
I don't understand this, shouldn't the total flux be 0 for the whole surface? ...
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2answers
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In which cases is it better to use Gauss' law?
I could, for example calculate the electric field near a charged rod of infinite length using the classic definition of the electric field, and integrating the: $$
\overrightarrow{dE} = \frac{dq}{4 ...
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1answer
254 views
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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1answer
103 views
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 ...
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1answer
153 views
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
123 views
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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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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1answer
554 views
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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1answer
68 views
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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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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1answer
207 views
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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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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2answers
212 views
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
121 views
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
56 views
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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2answers
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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 ),
$$
where $\varphi$ - polar angle ...
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1answer
162 views
What is discontinuity in Vector Fields
I am reading David J. Griffiths and have a problem understanding the concept of discontinuity for E-field.
The E-field has apparently to components. (How does he decompose the vector field into the ...
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1answer
164 views
Finding Electric Field outside a Charged Cylinder
I'm trying to solve a problem that involves finding the electric field due to a uniformly cylinder of radius $r$, length $L$ and total charge $Q$. Well, my thought was: if I am to use Gauss' Law, I'll ...
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2answers
135 views
Electric lines of force
Why cant electric lines of force pass through the charged sphere? Well, basically that's how a Faraday cage works, but how can it be so?
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Newton's Law of Gravitation, Gauss Law and GR
From One of My Unpublished Papers
$$\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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1answer
270 views
Electric Flux Density - Ring Charge
A ring placed along $y^{2}$ + $z^{2}$ = 4, x = 0 carries a uniform charge of 5 $\mu$C/m. Find D at P(3,0,0)
Should I be using Gauss's Law to solve this problem? I was considering using a spherical ...
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0answers
152 views
Flux from a point charge at the center of a cube [closed]
A charge of $145 \times 10^{-6} C$ is at the center of a cube of edge $.5m$. What is the flux through each face of the cube?
I would write what I have so far, but I don't know how to use MathJax.
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1answer
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Gauss's Law vs Newton's Law
This is thought experiment. I couldn't get a good answer because I keep getting negative mass.
Gauss's Law say that eletric field is proportional to charge, how much charged is enclosed. Newton's ...
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1answer
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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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Electric fields in/around conductors
So according to my notes, the field inside a conductor is zero. But what, exactly, is meant by inside?
I think we are in electrostatics for the purpose of this question.
The reason it is zero is ...
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1answer
91 views
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 ...
