Gauss' law Definition and 334 Threads

Hello, i'm doing some practice problems using Gauss' law, but I feel like my work is 'sloppy'. I'll show an example, where I think I get the right answer, but it feels like I'm neglecting to treat the summation properly, or perhaps I don;t quite understand why what I'm doing is fine...

Suppose that you have a region of space with no fields and the only matter is in the form of a cloud of point-masses. On the one hand, within the cloud, the stress-energy tensor vanishes almost everywhere (except right at the point-mass, in which case it is infinite). So the Einstein tensor...

How do I find the direction of area vector of a surface?

Hi, I know that for the electric displacement vector field \oint D.dS=\sum Q_{c} does this mean that I can just use a Gaussian surface to explain why the displacement vector field for a sphere is radial or not without having to talk about the electric field. If not what is the reasoning to...

Homework Statement Three parallel, infinite, insulating planes (sheets) of charge are arranged as shown (see attached image). Note carefully the charge desnitties and distances given. From left to right the charge densities are -3σ, +σ, +σ. How does the magnitude of the electric field at point...

Homework Statement A nonconducting spherical shell has a thickness b-a, where b is the outer radius and a the inner radius has a volume charge density \rho=\frac{A}{r}, r\in[a,b]. If there is a charge +q located at the center, what must A be in order for the electric field to be uniform in the...

Hey everyone, I'm not sure if this belongs in the math or physics section of this forum, but I figure since my question is more related to the mathematical manipulation of what I am dealing with, I figured I would ask it here and then if it has to be moved, it can be. My question has to do...

Homework Statement Gauss Divergence Law: Gauss' law Can we obtain the Gauss' Law from Gauss Divergence Law? Homework Equations In Spherical coordinates, electric field strength (Q/4\piεr^2,0,0) Then ∇\cdotE=0+0+0=0 The Attempt at a Solution We can not obtain the...

Homework Statement A hollow sphere of outer radius R2 and inner radius of R1 carries a uniform charge 2Q. The sphere is then cut in half to create a hemispherical shell of charge Q. Calculate E at the center point (origin) P. Homework Equations equation of a hollow sphere =...

Homework Statement The cross section of a long coaxial cable is shown in the figure, with radii as given. The linear charge density on the inner conductor is -80 nC/m and the linear charge density on the outer conductor is -10 nC/m. The inner and outer cylindrical surfaces are respectively...

I actually have solved the problem and received the answers that the book provided. However I am second guessing what I did, This is the problem: let rho v be 10/r^2 mC/m^3 between 1<r<4 let rho v be zero elsewhere a)find the net flux crossing the surface at r=2 m, r= 6m b)determine...

Shalom We are used to hearing that Coulomb's law doesn't settle with the relativity principle that nothing moves faster than the speed of light, in the sense that it embeds 'Action in a Distance'. Meaning that if somthing changes in r1 at time t1, and we write the law for any t before...

Homework Statement a spherical shell has an outer radius R and a inner radius R/2 and carries a total charge -q, distributed with uniform charge density. A point charge +q is at the centre of the sphere. Calculate the electric field strength for R/2<r<R Homework Equations Gauss' Law The...

I am in general physics III (E&M) at Cal Poly and I have a midterm tomorrow... my professor didn't go over Gauss' Law too much, so I'm having issues with this problem that is on his review. I will write the question exactly as it appears on the sheet. Homework Statement "You have a hollow...

Homework Statement 1. Positive charge Q is placed on a conducting spherical shell with inner radius R1 and outer radius R2. A point charge q is placed at the center of the cavity. The magnitude of the electric field produced by the charge on the inner surface at a point in the interior of...

Homework Statement I'm almost done writing a paper on Gauss' Law and for my final body paragraph I want to include some interesting applications of Gauss' Law. I mean applications as in what has Gauss' Law helped to create or invent- something relatively tangible. Homework Equations...

Gauss' Law problem! Help please! infinite sheet with charge density? In the figure below, a small circular hole of radius R = 1.80 cm has been cut in the middle of an infinite, flat, nonconducting surface that has uniform charge density σ = 4.50 pC/m2. A z-axis, with its origin at the hole's...

Homework Statement A long line of charge with density λ (C/m) is surrounded by a concentric cylindrical conducting shell of inner radius R1 and an outer radius of R2. The shell carries a net charge of -2λ (C/m). Use Gauss' Law to determine the electric field as a function of the distance 'r'...

Given a spherical shell insulator as 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 insulator). What is Ey, the y-component of the...

Gauss' Law has been fairly tough for me and I seem to be struggling to analyze situations properly and, specifically, decided on the net charge included in arbitrary symmetrical-shapes used for this law. Specifically, this one includes two spherical shells. Homework Statement A point charge q1...

An electric field is E = 250 N/C i for x > 0 and E = -250 N/C i for x < 0. A cylinder of length 20 cm and radius 3 cm has its center at the origin and its axis along the x-axis such that one end is at x = +10 cm and the other is at x = -10 cm. What is the outward flux through each end? a) +x...

Homework Statement How do I find the electric field at a point above the center of a charged sphere? Assume the sphere is a shell.Homework EquationsThe Attempt at a Solution\ I know there will only be a z component to the electric field, because x and y components will cancel by symmetry. I...

I'm trying to explain Gauss' Law to a bunch of high school kids. They want to know why the total electric flux through a closed surface does not depend on the shape and volume of the closed surface and the orientation of the enclosed charges. I know the math, but conceptually, I'm at a...

Homework Statement Calculate the electric field at a point 2.79 cm perpendicular to the midpoint of a 2.02 m long thin wire carrying a total charge of 5.04 uC. You could integrate BUT if the wire is very long compared to the distance from the wire to where you are calculating the electric...

hey guys and gals, I'm normally pretty good at my physics homework, but this problem has my STUMPED, I think I am starting it right, but I have no idea how to proceed or if I am on a good path. Homework Statement A Very Long Cylinder with a radius of 7.2cm (.072m) has a uniform density of...

Homework Statement Suppose that a hole has been drilled through the center of the earth, and that an object is droppped into this hole. Write a first order linear differential equaiton for the object's velocity, v as a function of the distance r from the Earth's center (i.e, and equation...

Homework Statement A very long cylinder has charge density L/m and radius a. Find the electric field at a distance r, with r > a. The Attempt at a Solution I construct a gaussian cylinder around it with radius r, and then from Gauss' law the field at any point on it's side surface is E=...

Homework Statement A very long cylinder of radius R has positive charge uniformly distributed over its volume. The amount of charge is λ Coulombs per meter of length of the cylinder. A spherical cavity of radius R' < R, centered on the axis of the cylinder, has been cut out of this cylinder...

I'm having trouble interpreting the four dimensional version of Gauss' law. In the original version, a vector would be integrated around a closed 2D surface and this would be equal to the integral of divergence over the enclosed volume. In the newer version, the vector(or tensor) is integrated...

Hello I am new here. Here is the situation: There is a 1-dimensional closed loop and this loop spans a one-dimensional space. If there are a +ve and a -ve charge at rest on some points in the loop, what should be the electric field in the loop? The only thing I can think of is...

Inside a dielectric we have: ∇\cdotε0E = ρbound + ρfree , where ρbound refers to the fact that these charges come from polarization. We can write this as: ∇\cdotε0E = -∇\cdotP + ρfree where P is the polarization of the material. And combing the two divergence terms...

The electric field 0.475m from a very long uniform line of charge is 830 N/C. How much charge is contained in a section of the line of length 3.00cm? My solution: the Electric field from an infinite plane is E=σ/(2*ε0), so σ=E*ε0*2=1.47*10^-8 3.00cm=.03m...

Homework Statement A conducting sphere of radius R2 has a central cavity of radius R1 that holds a charge q in its centre. Determine the electrical field for r > R2, r < R1 and R1 < r < R2 and determine the charge density induced by q. I'm not allowed to include a link to my figure, but I'm...

Homework Statement The gravitational field g due to a point mass M may be obtained by analogy with the electric field by writing an expression for the gravitational force on a test mass, and dividing by the magnitude of the test mass, m. Show that Gauss' law for the gravitational field reads...

Sometimes you want to find the electric field of a loong cylinder carrying for instance a uniform volume charge. Then for easy calculations you approximate the cylinder with an infinitely long one and then put a gaussian surface over the entire thing. Symmetry then dictates that the field point...

The essence of Gauss' law is that the total flux through a closed surface only depends on the charge inside the surface. So two spheres with different radii will have the same flux. This is of course due to the 1/r2 property of coulombs law. Because, since the area increases with r2 this...

Is proven in my book using field lines. I stumbled upon something that I however can't understand. They say that a charge outside a closed surfrace contributes nothing to the total flux out of the surface since every field line that goes into the surface also comes out. But what if it terminates...

I've been told that electric and gravitational fields have a lot in common, and both are practically analogous to each other. Also, the conclusions made through Gauss' Law apply just as well (analogously) to gravitational fields. One of Gauss' Law's predictions is for a solid (conducting)...

Let's say I have a Gaussian sphere 1 light year across with synchronized clocks and sensors all over its surface. All clocks are co-moving, not accelerating, and the spatial curvature is negligible. If I have only one charge inside the Gaussian sphere, 1 centimeter from its surface for an entire...

Homework Statement There is a nonconducting solid sphere with uniform charge density rho and radius R=15 but it has a smaller hollow spherical cavity of radius a = 5, it is not centered: the distance between the center of the larger sphere is a distance b = 6 I'm trying to find the...

Homework Statement A hollow spherical shell carries charge density \rho=k/r^2 in the region a\leq r\leq b. Use Gauss' Law in integral form to find the electric field in three regions: (i) r<a, (ii) a<r<b, (iii) r>b. Homework Equations Gauss' Law in integral form...

Homework Statement A sphere of radius a has a charge density that varies with distance from its center d(r) = do*(r/a)**2. Express the electric field as a function of distance from the center of the sphere r, a, do, and the permitivity of free space ez for each of the falling regions...

Homework Statement The cylindrical drum of a copy machine is .38 m long with .05 m radius. If charge is uniformly distributed over the cylindrical surface (the top and bottom flat circular ends of the drum have no charge) and the electric field very close to this surface midway along the...

So I was doing some practice problems and one of them asked for the flux through one side of a cube that has a point charge(Q) at its center, it seems intuitive that it would be 1/6 of the charge but how would i show this? if I do ∫E dA → E∫dA the surface area of a cube is 6L2 so i would...

Homework Statement http://i.minus.com/jbxXiQZmmiOQtS.png Homework Equations Elecric flux = Integral of closed surface of E dotted into dA = qenclosed / ε0 Rho = 50 x 10^-6 abs(z) The Attempt at a Solution Integral of closed surface of E dotted into dA will end up being EA when E is...

Homework Statement A hollow insulating sphere with an inner radius of 6.58 cm and outer radius of 11.7 cm has a uniform charge density of 79.9 μC/m3 distributed throughout the volume between. If we want to use Gauss' Law to find the electric field at r = 17.2 cm, what "charge enclosed"...

While I do see how this makes sense using Newton’s Shell method, I don’t see how Gauss’ Law of Flux for a closed surface proves the same thing. Both Gauss’ Law of Flux and Newton’s Shell method make perfect sense to me in showing that when dealing with a point outside the hollow conducting...

http://einstein1.byu.edu/~masong/emsite/S1Q50/EQMakerSL1.gif Hi guys, I have a little confusion about the Gauss' law in differential form over here, obviously, many textbook wrote it in the above form, but actually, the only place at which divE is not zero is at the locations where the...

Application of Gauss' law -- some doubts Homework Statement Revered Members, I have attached images of applications of Gauss' law namely 1) Electric field due to an infinitely long charged wire and 2) Electric field due to an infinite charged plane sheet. In both cases Gaussian surface is...

Hello, I've been working my way through Mathematics for Physicists by Dennery and Krzywicki and, on page 65, they assert that Gauss' law applied to a 2D cross-section along an infinite charged cylinder is: ∫E.n dl = 4πσ where E is the electric field on the Gauss surface (a circle around...