What is Gauss: Definition and 645 Discussions

Johann Carl Friedrich Gauss (; German: Gauß [kaʁl ˈfʁiːdʁɪç ˈɡaʊs] (listen); Latin: Carolus Fridericus Gauss; 30 April 1777 – 23 February 1855) was a German mathematician and physicist who made significant contributions to many fields in mathematics and science. Sometimes referred to as the Princeps mathematicorum (Latin for '"the foremost of mathematicians"') and "the greatest mathematician since antiquity", Gauss had an exceptional influence in many fields of mathematics and science, and is ranked among history's most influential mathematicians.

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  1. N

    Using the div-flux theorem (Gauss) to derive divergence in polar coördinates?

    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?
  2. H

    Gauss' Law Hollow Sphere with Charged Ball

    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...
  3. S

    Can we use gauss' law to find the e field of a finite line of charge?

  4. M

    How Can I Measure Tesla's or Gauss Without a Gauss-Meter?

    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
  5. BitWiz

    Calculating Ship Acceleration with Gauss Gun Propulsion

    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...
  6. U

    Integration of products of the Gauss Error Function

    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...
  7. H

    Understanding the Contradiction in Gauss Law for Planar Capacitors

    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.
  8. F

    Linear Simultaneous Eqns - Gauss Elim Problem

    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...
  9. E

    Gauss' Law and gaussian surface

    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...
  10. R

    Deriving Coulomb's Law from Gauss' Law

    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...
  11. M

    Can Gauss' Law be applied to point charges on non-spherical surfaces?

    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...
  12. F

    When do you use R or r for Gauss' Law

    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...
  13. S

    EM: Gauss' law for electricity

    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} =...
  14. F

    Electric Fields and Gauss' Law

    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...
  15. K

    Application of Gauss' Laws: Large area parallel plate capacitor

    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...
  16. K

    Applications of Gauss' Law - two hollow spheres

    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 =...
  17. C

    Gauss Divergence Theorem - Silly doubt - Almost solved

    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...
  18. M

    Understanding Gauss' Shell Theorms?

    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...
  19. M

    Help with gauss, Sheet vs conducting surface

    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...
  20. F

    Gauss' Law, Spherical Charge Distribution

    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...
  21. C

    Gauss' law on differential form.

    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...
  22. P

    Gauss Law Problem with Cylinders

    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...
  23. M

    Gauss's Law for Electric Field Components in a Charged Sphere

    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...
  24. J

    Derive Electric Field of Cylinder Via Gauss' Law

    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...
  25. somasimple

    Gauss' Law: Charge Density in Cylinders

    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)...
  26. H

    Experimental evidence against Gauss' law

    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...
  27. A

    Calculate Gravitational Field on Torus Using Gauss' Law

    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.
  28. S

    Confirming Gauss Theorem with Cylindrical Co-ordinates

    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?
  29. N

    Can Gauss's Law Be Applied to a Charged Circular Ring?

    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...
  30. G

    Is Gauss' Law Applicable to Dynamic Charges and All Surfaces?

    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...
  31. ?

    Gauss' Law and it's meaning

    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...
  32. G

    When is dA not integrated into A for Gauss' law?

    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.
  33. T

    Boundary conditions, Sturm-Liouville, & Gauss Divergence

    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...
  34. C

    Solving Gauss Law Question: Q/(πR^4)

    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...
  35. H

    Solving Gauss Divergence Theorem on a Closed Surface

    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...
  36. B

    Shape operator and The Gauss tangent map

    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...
  37. B

    Tangent map, gauss map, and shape operator

    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...
  38. K

    Exploring Gauss' Law: Induction by Charges Outside a Shell

    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?
  39. E

    Flux & Gauss Law: Electric Field Lines & Types of Areas

    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...
  40. J

    Deriving Gauss' Variational Equation for True Anomaly

    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...
  41. Z

    Pretty much worked out, but stuck Gauss' Law problem

    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...
  42. Z

    From Charge Density -> Electric Field(r) using Gauss

    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...
  43. S

    Inner/Outer Spherical Shells - Gauss' Law

    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...
  44. S

    Applying Gauss Test to Series: A Guide

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

    Gauss' Law: Cylindrical sheath

    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...
  46. Z

    Residue calculus and gauss bonnet surfaces

    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...
  47. P

    Building Gauss Meter with Hall Effect or Mosfets - CoolMagnetMan

    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...
  48. G

    Why is the Electric Field Constant Along a Charged Cylinder's Surface?

    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...
  49. B

    Gauss' Law symmetry of charge distribution

    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...
  50. D

    How do you calculate the total E-field for a cube with a 3D vector E-field?

    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...
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