Gauss Definition and 648 Threads

Hey! :o With appropriate conditions, I want to show that $$\iiint_{\Omega}(\nabla \phi)\cdot \textbf{f}\ dV=\iint_{\Sigma}\phi\textbf{f}\cdot \textbf{N}\ dA-\iiint_{\Omega}\phi\nabla\cdot \textbf{f}\ dV$$ With appropriate conditions, I want to prove Green's identities...

Hey! :o Using Gauss theorem I want to calculate $\iint_{\Sigma}f\cdot NdA$, where $\Sigma$ is the closed boundary surface of the pyramid with vertices $(0,0,0), (1,0,0), (0,1,0), (0,0,1), (1,1,0)$ and $f(x,y,z)=(x^2y, 3y^2z, 9xz^2)$ and the perpendicular vectors $N$ to the inside of the...

Say you had two isolated hydrogen atoms. Because of the spherical distribution of electronic charge on each hydrogen and the net charge of 0 outside each atom, wouldn't Gauss's law dictate a 0 net electric field outside each atom? If this is the case, why does diatomic hydrogen so readily form...

For the proof I've read that verifies transverse electromagnetic waves are consistent with Gauss' Law, there seems to be the suggestion that the magnetic and electric field at a given small length c(dt), along which the waves travel, propagate infinitely backwards and forwards in their...

I noticed the other day something odd in how we use Electric and Magnetic flux. The definitions I refer to are magnetic flux density (B), magnetic flux intensity (H), electric displacement field (D) or Electric field density (D) and electric field (E): B = μH ΦB = B*Area & D = εE ΦE = E*Area...

Homework Statement No variables, just a conceptual question. Homework Equations Flux = EA = Q/ε The Attempt at a Solution Given a uniformly charged rod of FINITE length, could we use Gauss' law for electric flux to calculate the field at a point p a distance x away from the rod, so long as the...

So, this has been bothering me for a few days and I'm having trouble understanding where the fault is. If we consider a uniform charge density ##\rho## extending through all space, then by symmetry, I would argue that ##\mathbf{E}=0## in all space. However, this does not agree with what a naive...

Homework Statement A charge Q=5.14 nC is located at the center is located at the center of a Gaussian sphere of radius R=10.0 cm . The sphere lies within a uniform upward electric field E=2100 NC The net outward electric flux through the sphere is What? Second problem (bonus round!) A...

I have done it by the parametric form of σ, but if I change σ to implicit form that is G(x,y,z)=x^2+y*2+z^2-R^2=0 I don't know how continue. The theory is: where Rxy is the projection of σ in plane xy so it's the circumference x^2+y^2=R^2

I WAS THINKING ABOUT A REGION OF SPACE WITH ELECTRIC FIELD ALONG POSITIVE X DIRECTION AND Varying WITH SPACE COORDINATE(x) NOW IF ONE IMAGINES A CUBE IN SPACE SUCH THAT FIELD CROSSES ITS TWO FACES AT RIGHT ANGLES ,A SIMPLE Application of...

Homework Statement I have an elementary doubt with the calculation of the capacitance of a capacitor of parallel plates that has a dielectric in the middle. https://ibb.co/b0W4BQ Homework Equations ∫D⋅ds=Q D=E+γP C=Q/V The Attempt at a Solution Suppose the top plate has a positive charge...

Homework Statement An infinite metal plate has a surface density of charge σL=-6μC/m² , Left side and a surface density Of load σR=+4μC/m² , in the right side. A Gaussian surface In the form of a circular cylinder, with area A 12 cm², is Located with the left side inside the plaque and a thin...

Homework Statement So for those who aren't familiar with the Gauss Gun here is a video demonstrating its function: As you can see in the video, a steel ball is rolled towards a sequence of magnets and other steel balls and as the incoming ball strikes the magnet, the ball on the other end...

Hi, I'm currently doing my extended essay for the IB in physics and I'm basing mine around the Gauss gun (similar post that explains it really well here https://www.physicsforums.com/threads/physics-behind-gaussian-accelerator-magnetic-linear-accelerator.320389/). What I was wondering was how I...

According to Gauss Law, we only consider charges which are inside the surface to produce net flux. We disregard the charges outside the surface because they produce zero net flux (as the electric field lines enter the surface and leave the surface producing zero net flux) My question is, since...

Homework Statement A metallic sphere of radius a is placed concentrically with a metallic spherical shell with inner radius b and outer radius c. The sphere has a total charge of 2Q and the shell has a total charge of 3Q. (a) What is the charge distribution? Specifically, what is...

Homework Statement Uniform Slab: Consider an infinite slab of charge with thickness 2a. We choose the origin inside the slab at an equal distance from both faces (so that the faces of the slab are at z = +a and z = −a). The charge density ρ inside the slab is uniform (i.e., ρ =const). Consider a...

Homework Statement I keep getting confused about this part of Gauss' law. Is the da on the left side the surface area of the the Gaussian surface? and on the right side when I am integrating. I say that q = the charge density multiplied by something. Is that something surface area of the...

Homework Statement Using the circled formula , here's what i gt (photo3) , , why the author ignore the blue circled part ? Is the author wrong ... If the blue part isn't ignored , i gt this pls refer to the photo 3 which is correct ? The author or me ? Or I'm misunderstanding something ...

Homework Statement For my extended essay as part of the IB, I am investigating the effect of changing the distance and the number of stationary ball bearings in a Gaussian gun. I was hoping to look at the energy transfer during each stage of magnets and therefore calculate the efficiency...

Homework Statement An isolated conductor has a net charge of +14.0 × 10- 6 C and a cavity with a particle of charge q = +4.30 × 10-6 C. What is the charge (a) on the cavity wall and (b) on the outer surface? Homework EquationsThe Attempt at a Solution So I understand that B is just adding the...

Knowing that Gauss' law states that the closed integral of e * dA = q(enclosed)/e naut, how would you find exactly what A is in any given problem? I know it varies from situation to situation depending on the geometry of the charge. For instance, I know that for an infinite wire/line of...

Firstly I appologize, that I am not native english speaker and I don't study physics(but cybernetics we are getting just some general knowledge about physics), but hopeffuly I will write this right. Homework Statement We know that inside of a conductive object is protected from influence of...

If ##M^{2} \subset \mathbb{R}^{3}## is a surface with given normal field, we define the Gauss (normal) map $$n:M^{2} \rightarrow \text{unit sphere}\ S^{2}$$ by $$n(p) = \textbf{N}(p), \qquad \text{the unit normal to $M$ at $p$}.$$...

Homework Statement [/B] Find the electric force between the two spheres. Sphere r=b-a has a volumetric density of p=K, where K is a constant Sphere r=a has a volumetric density of p=θ*r Homework Equations As you can see the sphere of radius 'a' doesn't have a uniform electric field because...

Hi. I'd like to show that a conducting, charged spherical shell can shield the field of an inside opposite point charge even if this charge is not at the center. I was thinking about a Gaussian surface just outside the sphere, such that if there were electric field vectors they would be...

Hi. Is it possible to derive the properties of a Faraday cage from Gauss' law alone? I found some "derivations" which I find rather unconvincing since they somehow conclude from a vanishing flux that the E field must vanish as well. Some slightly more elaborate derivations use a combination of...

Hi. Is the Maxwell equation $$\nabla\cdot\vec{E}=\frac{\rho}{\varepsilon_0}$$ even true in the stronger form $$\frac{\partial E_i}{\partial x_i}=\frac{\rho}{3\cdot\varepsilon_0}\enspace ?$$ I guess not, since I haven't found a source suggesting this. But shouldn't the isotropic electric field...

Hey guys can we derive the formula of Electric Field Intensity around a uniformly charged ring if yes please share the derivation thanks

Lets consider a hollow sphere with charge +q and than a larger hollow sphere that encloses it with -q, so two spheres one inside the other. Now we use draw an even larger Gaussian sphere that encloses both of these, ∫EdA = Qinclosed/ ∈_0 the total enclosed charge is +q + -q = 0 so ∫EdA = 0 E...

I was looking for a derivation of E=(2kλ)/r for an infinite line of charge. I understood that you need to use Gauss's Law and a cylinder around the line. When looked it up, I found this: http://www.vizitsolutions.com/portfolio/gausslaw/lineCharge.html He starts out with ∫E⋅dA=4πq. I have never...

Homework Statement What I basically want to do is to prove Gauss Law with a cylinder perpendicular to an infinite charged wire (I know I can do this simple, but I want to do it this way) This is what I have done so far: Homework Equations $$\Phi=\int \frac{dq}{4\pi \varepsilon_0 r^2} \hat{r}...

Find E(r) inside and outside a uniformly charged spherical volume by superposing the electric fields produced by a collection of uniformly charged disks. a+b) Given equations, sketch of problem This is the equation in the handbook for a disk (but in the exercises the z becomes x, without loss of...

Hi. Assume a long hollow wire that both carries a nonzero net charge and a current. Is it still true that all charge sits on the outer surface of the cable and that the empty space inside is field-free (Faraday cage)? I know proofs of those facts in electrostatics using Gauss' theorem, but they...

Homework Statement I need help in figuring out if I have done this problem correctly. From what I understand ∫E * dA = E*A, where E is the electric field and A is the area of a side. My biggest concern is if I can plug in the length "L" for the "x" and "z" variables within "E = -5x * E0/L i +...

Hello all, I have this integral, and currently I'm evaluating it using Mathematica numerically, which takes time to be evaluated. Can I write it in a way that the integral has a formula in the Table of Integrals? \int_0^{\infty} F\left(a_1,a_2;a_3;a_4-a_5x\right) e^{-x}\,dx where...

So, I know that the gauss law states that the Flux of the electric field through a closed surface is Q/ε , but does the gauss theorem works also for non inverse square law Fields? I think not because in order to not have a Flux depending on distance but a constant one we need that r^2 of the...

Which one is correct?? 1) electric field calculated by gauss law is the field due to charges inside the closed surface. 2) the flux of the electric field through a closed surface due to all charges is equal to the flux due to charges enclosed by the surface

Homework Statement An insulator is in the shape of a spherical shell. The insulator is defined by an inner radius a = 4 cm and an outer radius b = 6 cm and carries a total charge of Q = + 9 C (1 C = 10-6 C). You may assume that the charge is distributed uniformly throughout the volume of the...

Why does Gauss' law hold for any closed surface? and can you show this mathematically. Many thanks :)

Homework Statement Hi, I am studying gauss's law via this book below.[/B] http://faculty.polytechnic.org/cfletcher/Phys%20With%20Calc_Vol_2_web_pdfs_2010/i-Ch14-PCALC--GAUSS'S%20LAW.pdf On page 8, and 9, the book describes the shell method of finding the volume of the sphere and then using...

Homework Statement The volume between two infinite plates located at x=L and x=-L respectively is filled with a uniform charge density ##\rho##. Calculate the electric field in the regions above, between and below the plates. Calculate the potential difference between the points x=-L and x=L...

Hello everyone, I am trying to find effect of collimated lens on gaussian beam propagation. Do you know how to solve that? I need any equations ,then going to use them via matlab. Thanks

Homework Statement I have attached the problem Homework Equations E*A = Qenc/ E0 The Attempt at a Solution At the moment I am looking at the problem more conceptually and seeing what is happening at each point and I wanted to know If I was on the right track. r<a As all charge would...

Homework Statement Three concentric hollow spherical conductors are charged as follows: the inner conductor carries charge Q, the middle conductor carries charge -2Q, and the outer conductor carries charge -Q. What is the charge on the outer surface of the middle conductor? Homework Equations...

Homework Statement We have a wire of the length L=0.2m which is uniformly charged with a linear density of Lambda = 3nC/cm. Find the intensity (E) of the electric field in point A1 whose perpendicular distance from the wire is a=0.05m. The wire is in a vacuum. Compare the intensity with the...

I am stuck with this (d) all the other (a),(b),(c) were just like (a) E= −∇φ (b) ∇ · E= −∇2φ (c) ∇ × E I know only very basic about Gauss' law, the problem is not from Electrodynamics course. I don't know what should I do to solve (d)

Divergence theorem states that $\int \int\vec{E}\cdot\vec{ds}=\int\int\int div(\vec{E})dV$ And Gauss law states that $\int \int\vec{E}\cdot\vec{ds}=\int\int\int \rho(x,y,z)dV$ If $\vec{E}$ to be electric field vector then i could say that $div(\vec{E})=\rho(x,y,z)$ However i can't see any...

1. Homework Statement I need to find the total charge inside the small metal sphere, inside the big metal sphere as well as outside the big metal sphere. Homework Equations What confuses me is the electric field vector. Since it's only poiting in one direction it can't originate from a...

I need to prove that the field charge of 2 infinite, oppositely charged plates is 0 using Gauss' law. I know that the sum of E=4PiK(Sum of q) but I don't know how to prove the charge is 0.