Gauss Definition and 648 Threads

Homework Statement show that the E outside an infinitely long rod of radius R with a uniform charge density p is E = pR^2/2r(e_0) Homework Equations gauss' law EA=q/e_0 The Attempt at a Solution I know how to solve this and get the correct answer but I don't totally understand it...

For a semester long experiment, I am to build a coil (gauss) gun. I also need to hand in a paper including all equations and theory relevant to the experiment, but I have not been able to find any equations that actually work for the purposes I require. Any help to guide me in the right...

Homework Statement A long, solid, non-conducting cylinder of radius 8 cm has a non-uniform volume density, ρ, that is a function of the radial distance r from the axis of the cylinder. ρ = A*r2 where A is a constant of value 2.9 μC/m5. What is the magnitude of the electric field 7 cm...

Apparently one can deduce the form of divergence in polar (and spherical) coördinates using the theorem of Gauss and Ostrogradsky, namely that the volume integral over the divergence is equal to the flux integral over the surface. I can't see a way to do that, do you?

Homework Statement A uniformly charged ball of radius a and charge -Q is at the center of a hollow metal shell with inner raduis b and outer radius c. \The hollow sphere has net charge +2Q. Determine the Electric Field Strength at r when r is, r < a a < r < b b< r < c r > c...

Hello, Im wondering how I would go about getting the amount of tesla's or gauss from an electromagnet without using a gauss-meter. Thank you in advance, Michael

Hi, Say I have a spaceship in ideal gravity-free, friction-free space. I have a source of power capable of producing a maximum of E joules per second, and I want to use some form of continuous electric propulsion, such as a Gauss gun or ion thruster, to get around. I have these questions...

Homework Statement Given that the integral from negative to positive infinity of e^(-(x^2))dx is equal to sqrt pi. Find the values of the integrals from negative to positive infinity of e^(-u*(x^2))dx and (x^2)*e^(-(x^2))dx. Homework Equations The Attempt at a Solution I did the first one and...

we know that the electric field between the planes of planar capacitor is σ/ε (according to gauss law) however we have two conducting plate that each plate produe this electric field that are in the same direction therefore we must have E=2σ/ε what is the reason for this contradiction.

Hello, I'm stuck on a simultaneous eqns problem. From what I can see it seems the easiest way would be to get the matrix into row echelon form, but I'm not sure if another way would be better. I can see a pattern here but not sure what it means. I attached the problem to the page. Any help...

Hey there, just had a question about Gauss' law, should be relativity simple however the explanation we were given was quite poor and only seems to apply well to the examples we were given. (This isn't homework). I (think I ) know the equation for Gauss' Law and what it means, that basically...

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...

So there are two theorems: 1. A shell of uniform charge attracts or repels a charged particle that is outside the shell as if all the shell's charge were concentrated at its center. 2. If a charged particle is located inside a shell of uniform charge, there is no net electrostatic force on...

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...

Before I get into the question I'd just like to state that this is not homework, but questions in my book that I'm going through to prepare myself for the midterm in one week. I got stuck at a few questions, here's the first one. I won't ask the next until I'm done with this and so forth...

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...

Let M be a surface in R3 oriented by a unit normal vector field U=g1U1+g2U2+g3U3 Then, the Gauss Map G: M to E, of M sends each point p of M to the point (g1(p),g2(p),g3(p)) of the unit sphere E. Show that the shape operator of M is (minus) the tangent map of its Gauss map: If S and G are...

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...