Gauss' law Definition and 334 Threads

Homework Statement [PLAIN]http://img851.imageshack.us/img851/5741/86853377.jpg The Attempt at a Solution For the long straight wire, the charge per unit length λ is already given, this is distributed on the surface of the wire. The electric field is zero for anything less than r1...

What is the electric field for the following charge distribution: ρ = ρ0 x/a for -a < x < a 0 elsewhere Use the differential form of Gauss' Law. I know that the differential form is \nabla . D = ρv and that E = D/ε, but how do I find D from what is given...

Homework Statement If one were to consider a parallel plate capacitor with a distance d between them connected to a battery and a vacuum space between the plates. Will the integral form of Gauss' Law to any closed surface between the plates that does not cross either plate hold? If not, what...

Homework Statement Using Gauss' law, derive the expression for the electric field intensity vector of an infinite sheet of charge in free space. Homework Equations The Attempt at a Solution See figure attached for their solution and the figure that goes with the problem. What...

In general I just wanted to see if I was setting this problem up correctly. We have a cube centered around the origin and a point charge at the origin. The task is to find the flux & confirm Gauss' Law. We are however to complete the integral ourselves. So imagining the top of the cube...

Homework Statement The total electric flux from a cubical box 40.0 cm on a side is 4700 Nm^2/C. What charge is enclosed by the box? Homework Equations Gauss Law: surface integral of E-field-vector * dA-vector = Q_enclosed/epsilon naught The Attempt at a Solution The reason I am...

1. As a member of a team of storm physicists, you are attempting to replicate lightning by chargeing two long cables stretched over a canyon. one cable will attain a highly positive and uniform density of -\lambda and the other will attain the same amount of charge density, but opposite in...

Homework Statement A point charge, q, is at the center of an insulating hollow sphere with inside radius, a, and outside radius, b. The spherical shell has charge per unit volume, rho. You may assume that q and rho are positive. Using Gauss' law, find the magnitude of the electric field...

Homework Statement The Electric field E produced by an unknown charge distribution p (rho) is E(r)= (constant)*((exp(-ar))/r^2)*(r_hat). a.) Use Gauss' law in differential for to determine p(rho) b.) Find the total charge q_tot by directly integrating p(rho), and show that it is 0. c.)...

I'm having some difficulty applying Gauss's Law to metal plates. From what I've studied it seems to me that Gauss's Law only really works when there is spherical symmetry, in all other cases it is an approximation. Am I correct in inferring this? However, in a case where the distance between...

Gauss' Law-Can't we find the Electric Field (In the vector form) from Gauss' Law? Because in most of the problems I have been doing like the case of a Charge in a solid sphere, I can find the Magnitude of Electric Field by Gauss' Law but not the Electric Field. Am I wrong here?

Homework Statement how do I know which equation to use for electric field? E=a/2e0 or E=a/e0 when a = surface charge density. Homework Equations The Attempt at a Solution

Homework Statement [PLAIN]http://smartphysics.com/images/content/EM/03/h3_lineF.png A cylinder of radius a = 6.1 cm and height h = 9.7 cm is aligned with its axis along the y-axis. An infinite line of charge is placed at x=3.05cm where λ1 = -2 μC/cm and λ2 = 6 μC/cm at x=-3.05 cm. Point P is...

The first Maxwell equation, Gauss' law makes a clear distinction between "inside" and "outside". But such a distinction can't be made in a compactified space (e.g. circle). Does that mean that the universe isn't compactified in a sense that if one was to move in a "straight" line one would never...

Homework Statement A hollow sherical conducting shell is suspended in air by an insulated string. The total charge on the conductor is -6 microCoulombs. If an additional point charge of +2 microCoulombs is placed in the hollow region inside the shell what is the total charge induced on the...

I'm stumped on a problem about Gauss' Law for Magnetism because I don't know what "local form" is. From context, I suspect that local form refers to the expression of an equation with the del operator (i.e. del x E = (charge density/(E0)), but I'm not sure. I've been self-teaching with Tipler...

Homework Statement This isn't about a specific problem, but it is based off of a homework problem. There is an insulating sphere (from radius 0 to a), and it is concentric with a spherical conducting shell (from radius b to c). If I know the charge of the insulating sphere and the net charge...

Homework Statement A high voltage coaxial cable is used to supply power to an x-ray generator. The cable consists of an inner wire of radius r=1 mm and a thin hollow outer conductor of radius R= 10 mm. The inner wire and the outer shield have the same charge density per unit length of ...

Homework Statement Charge is uniformly distributed along the x-axis with density ß. Use Gauss' Law to find the electric field it produces, and use this to calculate the work done on a charge Q that moves along the y-axis from y = a to y = b. Homework Equations Gauss' Law: e0 * electric...

Homework Statement Trying to find E field inside a sphere radius a with volume charge density rho = k/r Homework Equations Gauss' law The Attempt at a Solution I set up a spherical shell radius R (R<a) I found the charge inside by integrating rho from 0 to R (Q = 2*pi*a*R^2)...

Homework Statement Imagine a solid, annular sphere. At the center of the hollow is a point charge +Q. The inner radius of the sphere is r0, and the outer radius is R. Assume the charge density p = p0/r (for r0 < r < R). Calculate using the integral form of Gauss's Law the electric field in all...

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...

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...

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...

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 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 =...

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...

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...

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.

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 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?

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...

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...

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...

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...

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...

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 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...