Gauss Definition and 622 Threads

Homework Statement When I try working out the example below from PlanetPhysics, I wind up with 2PI rather than 4PI in my answer. Should I be considering my result valid for only a hemisphere and double it for a sphere--or am I just making a mistake in my math? "As an example of the...

2 questions: 1. A point charge of 1.84 microC is at the center of a cubical Gaussian surface 55cm on edge. Find \Phi_E through the surface. So here I was thinking, well the shape doesn't matter so the surface can be a sphere, so I calculated it for a sphere and it was correct (taking the...

I've seen many examples of spheres, cylinders, and planes and I'm trying to understand when to use r or R in the equation E A = 1/4piEo * Qenc. I've seen examples where the r's will cancel giving a simplified answer and then others where you have something like R^2 / r^2. So my question is...

Homework Statement A solid sphere of radius R carries a volume charge density \rho = \rho_0e^{r/R}, where \rho_0 is a constant and r is the distance from the center. Find an expression for the electric field strength at the sphere's surface. Homework Equations \int\vec{E}.d\vec{A} =...

I have a few questions related to finding the electric field of an object. 1. What's the difference between a conducting object (sphere, cylinder) vs. a non conducting object? Is the charge inside a conducting and nonconducting sphere both zero if the surface charge density is uniform? What...

Homework Statement The plates of a large area parallel plate capacitor of area A are separated by a short distance. The plates carry an equal but opposite charge \pm q. (a) What is the electric field strength E(q,A) inside the capacitor? (b) By how many percent does the electric field...

Homework Statement A hollow sphere of radius r_1 is placed at the centre of a larger hollow sphere of radius r_2. Both spheres have a uniformly distributed total charge of +q Find the preassure p(r_2 , q) which acts on the outer sphere. Homework Equations \oint\textbf{E.n}dS = 4\pi k Q p =...

Homework Statement The problem statement has been attached with this post. Homework Equations I considered u = ux i + uy j and unit normal n = nx i + ny j. The Attempt at a Solution I used gauss' divergence theorem. Then it came as integral [(dux/dx) d(omega)] + integral...

I'm having trouble using Guass' law to find electric fields. Where is the magnitude of the Electic field that you end up calculating? I had assumed it would be anywhere on the Gaussian surface, but it doesn't make sense now that I think of it. for instance, calculating the field of a charged...

The differential form of Gauss' law states that \nabla \cdot \vec{E} = \frac{\rho}{\epsilon_0}. So the divergence of the electric field is the chargedensity divided by epsilon zero. I just wondered.. since divergence is a local or "point" property. Is the chargedensity in this law also...

Homework Statement An infinitely long, non-conducting cylinder of radius R carries a uniform volume charge density ρ. Find the magnitude of the electric field for 0 < r < R Homework Equations EA=Qin/εo The Attempt at a Solution I am debating whether the answer should be ρr^2/2εoR...

An infinite line of charge with linear density λ = 7.6 μC/m is positioned along the axis of a thick insulating shell of inner radius a = 3 cm and outer radius b = 5 cm. The insulating shell is uniformly charged with a volume density of ρ = -611 μC/m3. (see attachment) What is Ex(R), the value...

1. An infinitely long cylinder of radius R contains a uniform charge density Rho. Calculate the electric field using Gauss' law for r> R and R>r 3. I attached a pdf with my attempt at r>R. My answer doesn't agree with those given...

Hi all, A closed cylinder of Length L, with a radius r and a thickness d is filled with m1q1+m2q2 charges. Their respective volume charge densities are \rho1 and \rho2. The volume is surrounded with a neutral solute (n1q1+n2q2=0) with a volume charge density of \rho3. (see picture)...

I have a 5mm diameter, 10mm long magnet, a short (6mm) coil of 50mm diameter, and an oscilloscope. When I move the magnet through the coil, the oscilloscope shows that the signal (voltage) looks pretty much like the derivative of a Gaussian function. So there must be magnetic flux maximum when...

I'm a little stuck, how can I go about calculating the gravitational field on the surface of a mass in the shape of a torus using Gauss' Law.

How would you go about confirming the Gauss theorem using cylindrical co-ordinates? Could it be just like Cartesian co-ordinates, or what is the transformation?

Homework Statement A circular ring of radius a carries a uniform charge q C/m and is placed on x-y plane with axis same as z axis. To determine E at P(0,0,h). My ques is can't we apply gauss theorem? if yes then what will be the gaussian surface? if no then why not? Homework Equations...

According to various EM texts (Feynman, Griffiths, ...) Gauss’ law holds only in electrostatic situations. But using the point charge electric field solutions, I have found to date that it holds for a relativistically oscillating charge (wA = .99c) within at least 3 flux integration surfaces...

Hello all. I have been trying to learn some Physics in my spare time and I came across Gauss' Law. I've been thinking about different cases and conditions and I have been confused by the actual meaning of Electric flux being 0. Homework Statement If I consider a sheet of uniform charge per...

I have been studying Gauss' law and almost all of the problems I have been doing just have me integrate dA alone into A. I was wondering when do you actually have to do some more in depth integration.

Homework Statement I'm getting through a paper and have a few things I can't wrap my head around. 1. In defining the boundary conditions for a membrane (a function of vector 'r'), the author claims that for a small displacement (u) and a boundary movement (f), the boundary condition can be...

Hi Im getting a slightly different answer to the one that is needed for the following question: 2) A positive charge Q is distributed throughout a spherical volume of radius R in vacuum. The charge density rho varies with the radius according to the linear law rho = a r. Show that the...

Homework Statement Verify Gauss Divergence Theorem ∭∇.F dxdydz=∬F. (N)dA Where the closed surface S is the sphere x^2+y^2+z^2=9 and the vector field F = xz^2i+x^2yj+y^2zk The Attempt at a Solution I have tried to solve the left hand side which appear to be (972*pi)/5 However, I...

Can anyone help me with this problem?? Let M be a surface in R^3 oriented by a unit normal vector field U=g1U1+g2U2+g3U3 Then the Gauss map G:M\rightarrow\Sigma of M sends each point p of M to the point (g1(p),g2(p),g3(p)) of the unit sphere \Sigma. Show that the shape operator of M is...

Homework Statement http://img685.imageshack.us/img685/9501/10953060.png" Homework Equations The Attempt at a Solution I know you use Gauss' Law, but why wouldn't the charges outside of the shell induce a charge on the shell, which would then affect the field at P?

I know that electric flux is defined as the number of electric field lines passing through an area but what kinda area are we talking about. Does it have to be perpendicular to the field lines like this or could it be at an angle like this does it have to be a flat area on 1 plane like the...

Homework Statement Derive the Gauss Variational differential equation for the true anomaly, f, with respect to time using components along the radius, angular velocity, and a unit vector orthogonal to those two (ir,itheta,ih). Homework Equations Sorry, I don't know how to use Latex. But...

Pretty much worked out, but stuck! Gauss' Law problem Homework Statement "Consider a charge density distribution in space given by \rho = \rho_0 e^{-r/a}, where \rho_0 and a are constants. Using Gauss' Law, derive an expression for the electric field as a function of radial distance, r...

Homework Statement "Consider a charge density distribution in space given by [rho] = [rho]_0 * e^(-r/a), where [rho]_0 and a are constants. Using Gauss' Law, derive an expression for the electric field as a function of radial distance, r. Sketch the E vs. r graph. Was a question on a quiz...

A small conducting spherical shell with inner radius a and outer radius b is concentric with a larger conducting spherical shell with inner radius c and outer radius d. The inner shell has a total charge of -1q and the outer shell has a total charge of +4q...

Can Gauss test be applied to second and third series. I am totally confused which test to apply on the first series.

Homework Statement A non-conducting, infinitely long, cylindrical sheath has inner radius r=10 m, outer radius r=15 m and a uniform charge density of 9 nC/m^3 spread throughout the sheath. Magnitude of electric field at r=5, r=12, r=17? Homework Equations Q=rho(Volume) and phi=EA...

I am not a mathematician but I have noticed how strangley similar the treatments of curvature and residues are when you compare the residues of residue calculus and the curviture of the gauss bonet forumlation of surfaces. Is there some generalization of things that contains both of these...

im working in a project requires a measuring of magnetic Fields all i need right now is a device to build up a gauss meter i have found a one using a hall effect transistor here in this link http://www.coolmagnetman.com/magmeter.htm but these hall effect transistor isn't found in Egypt so...

Am really suprised when deriving electric field due to a uniform charged thin long rod! It was suprising to have a cylinder as a gausian surface! actualy is that posible, that all along the surface of the cylinder has same field intensity and why? also why are there no electric flux along...

This is a general question, I was reading my textbook and this statement confuses me: "The symmetry of the electric field must match the symmetry of the charge distribution" this is said regarding symmetry in relation to GAuss' law. I do not understand what they mean by symmetry of charge...

I have a cube with sides l and therefore a total volume of l^3. The E-field is ax + by + cz where a, b, and c are known constants. It says to find the total E-field. The answer is (a + b + c)*l^3. I have no idea how they get this. I tried summing up all of the sides separately bit I kept getting...

Homework Statement For the given flux density: \vec{D}=(2y2+z)\widehat{x}+(4xy)\widehat{y}^+(xz)\widehat{z} a)Determine the charge density. b)Find the total charge enclosed if the surface is 0<x<1, 0<y<1, 0<z<1 (unit cube) c)Confirm Gauss’s law by finding the net flux through the surface of...

hi, im trying to calculate the spectral radius (gauss seidel method) to test whether or not its converges. i no that if the modulus is less than one it converges. however, my answer gives a mixture of solutions which are above and below one - 0.45 and 2.15 and 0. so is this divergent or...

Three large but thin charged sheets are parallel to each other as shown in the figure . Sheet I has a total surface charge density of 7.9 nC/m^2, sheet II a charge of -3.3 nC/m^2, and sheet III a charge of 5.4 nC/m^2. Figure: ----------------(I) ----------------(II)----------------(III)...

Hi all, This is just wild shot, since my memory is not what it used to be ... I remembered reading about Feynman pointing out an interesting fact, that the integration of the gaussian function \int_-\infty^\infty e^(-x x) dx = \sqrt[\pi] has to do with Pi. He then went on to show...

If I have a hypothetical infinite 3 dimensional universe uniformly charged I can argue that the electric field is zero at any given point in space by symmetry. However, if I invoke Gauss' Law I find a non-zero flux of electric field through a gaussian surface encompassing any amount of charge...

there is a table for standart probility where we have an integral of exponent in x^2 power and we can't calculate it so we use a table to get values out of it where can i find it ?

I don't really know much about serious business electrostatics. I've only taken the AP Physics C E&M exam (using the integral form), but I was looking at wikipedia and I was curious about the differential form of Gauss' Law. I don't understand what I'm doing wrong with this. I'm trying to...

Homework Statement Use the divergence theorem to find the outward flux of a vector field F=\sqrt{x^2+y^2+z^2}(x\hat{i}+y\hat{j}+z\hat{k}) across the boundary of the region 1\leq x^2+y^2+z^2 \leq4 Homework Equations The Gauss Divergence Theorem states \int_D dV \nabla \bullet...

Homework Statement I actually just have two questions about the law itself. 1.) Is Gauss's Law just the projection of a shape onto a perpindicular surface to the E field,times the E field? I ask this because there is an example in my book which shows a 3D incline with a horizontal E...

Homework Statement A square plate of copper with 50.0-cm sides has no net charge and is placed in a region of uniform electric field of 80.0 kN/C directed perpendicularly to the plate. Find: (a) the charge density of each face of the plate and (b) the total charge on each face Homework...

Hey guys, help needed! Bad lecture, no idea what to do! The Q1 is: Q. 1 Three point charges are placed at the apexes of an equilateral triangle as shown in diagram. Calculate the net force on (a) the 5 μC (= 5 × 10‐6 C) charge and (b) the ‐6 μC charge. Give each answer in the form a i + b...

A certain region bounded by an imaginary closed surface contains no charge. Is the electric field always zero everywhere on the surface? If not, under what circumstances is it zero on the surface. I think it is zero everywhere because as the electric field is entering the closed surface, it...