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. H

    Gauss' law and parallel plates

    Homework Statement Two large, flat metal plates are separated by a distance that is very small compared to their height and width. The conductors are given equal but opposite uniform surface charge densities +- \sigma. Ignore edge effects and use Gauss's law to show a) that for points far...
  2. Aristotle

    Solid Insulator Sphere Inside Hollow Sphere Conductor

    Homework Statement I was looking for some practice problems in my textbook and found this problem that I was just a little stuck on. I drew the diagram from my textbook with the givens of the problem. Homework Equations ∲E*dA = Q (inside) / ɛ0 The Attempt at a Solution For r less...
  3. F

    Maxwell distribution in thermal equilibrium

    Homework Statement In thermal equilibrium, the particle in a gas are distributed in velocity space according to the Maxwell distribution f(v) = A*exp(-mv^2/(2KT)) What is the average velocity ? What is the most probable velocity ? Homework Equations <v> = ∫∫∫vf(v)d3v = (0 to infinty)...
  4. M

    Gauss' Law: Spherical Symmetry

    Homework Statement Figure 23.52 gives the magnitude of the electric field inside and outside a sphere with a positive charge distributed uniformly throughout its volume. The scale of the vertical axis is set by Es = 5.0 x 10e7 N/C. What is the charge on the sphere? Homework Equations Net Flux...
  5. V

    Flux through various Gauss' surfaces

    Homework Statement I have uploaded a file that shows the question.[/B]Homework Equations I believe the only relevant equation is: flux = Q(enclosed)/E(knot)[/B]The Attempt at a Solution Well I have some questions first. The problem statement says that the sphere on the left has a net...
  6. S

    Solve Gauss' Law Homework: Charge of Insulating Sphere & Conductor Shell

    Homework Statement A solid insulating sphere of radius 5.0 cm shown in blue has a uniform charge density throughout its volume. Concentric with this sphere is a conducting thick hollow spherical shell of inner radius 20.0 cm and outer radius 25.0 cm shown in grey. The electric field at a point...
  7. ZARATHUSTRA

    Solving Gauss' Law Confusion: q/ε & Changing Surfaces

    Ok, so a lot people said that 1. the charge outside of the enclosed surface wouldn't influence the total flux that penetrate the surface 2. q/ε wouldn't change if the charge inside the surface does not change (see my painting, so it can help you understand what i meant) i was ok with these...
  8. L

    Induced Electric Fields: Exploring Gauss' & Lenz's Laws

    In electrostatics, ∇ × E = 0 so E that is a conservative field and there must be sources of E from which E flows. We know that this sources are the electrical charges given by Gauss' Law. But when B changes in time, ∇ × E = - ∂ B / ∂t. Now the Gauss' Law no longer applies and if there are not...
  9. P

    Electric field at point Gauss law

    Homework Statement We won't to find out the electric field at a point p due to a point charge q placed at o as shown in the figure [/B] Consider a sphere of radius r passing through the point p. Let the electric field at p be E then by Gauss law my problem is how we get the last step? I...
  10. Hijaz Aslam

    Gauss Law of Cube in non-uniform linear Electric Field.

    Gauss's Law states that if a Gaussian Surface encloses a charge ##q_{enc}## then the electric flux through the Gaussian Surface is given by ##\phi=q_{enc}/\varepsilon_{o}## . It also states that any external field does not contribute to the Electric Flux through the Gaussian Surface. I am bit...
  11. W

    Energy of a magnet/iron system (eg. gauss rifle)

    Homework Statement I want to calculate the energy of a system of iron pieces and a magnet on an axis. The configuration can be thought to be like this: http://www.wired.com/images_blogs/wiredscience/2011/12/drawingskey1.jpg Homework Equations dE = 1/2B^2/µdv The Attempt at a Solution I tried...
  12. Breo

    Gauss - Bonnet Gravity -> Curvature variations

    So I am working on the next quadratic Lagrangian: $$ L = \alpha R_{\mu\nu}R^{\mu\nu} + \beta R_{\mu\nu\rho\sigma}R^{\mu\nu\rho\sigma} + \gamma R² $$ I have already derived $$ \delta (R_{\mu\nu}R^{\mu\nu}) = [- \frac{1}{2}g_{\mu\nu}R_{\alpha\beta}R^{\alpha\beta} +...
  13. Shackleford

    Prove its Gauss curvature K = 1

    Homework Statement Assume that the surface has the first fundamental form as E = G = 4(1+u2+v2)-2 F = 0[/B] Homework Equations K = \frac{-1}{2\sqrt{EG}}[(\frac{E_v}{\sqrt{EG}})_v + (\frac{G_u}{\sqrt{EG}})_u][/B]The Attempt at a Solution Ev = -16v*(1+u2+v2)-3 Gu = -16u*(1+u2+v2)-3 When...
  14. B

    Differential form of gauss's law.

    I don't understand what charge density is meant in the equation: div E = constant times charge density. I have the derivation in front of me and the last step follows from accepting that the rate of change of the integral of the field divergence per change in volume is the same as the rate of...
  15. M

    Gauss' Law -- When can it not be applied?

    Hello everyone. I've been asked the following question by someone and I'm not quite sure which is the correct answer. I'd appreciate some help with it. The question is pretty simple: When can't be Gauss's law applied? 1. When the electric field of a point charge is dependent on the angles...
  16. G

    Finding electric field of a hemisphere (without using Gauss' Law)

    Homework Statement A charge distribution is given by ##\rho(r,\theta,phi)=\gamma r^3cos\theta,a<r,b,0\leq\theta\leq\pi/2## and is zero everywhere else. The distance from the origin ##r=\sqrt{x^2+y^2+z^2}## and ##\gamma## is a constant. Write out the electric field P along the z-axis a distance...
  17. N

    Gauss' Law - find magnitude of the electric field

    A slab of insulating material has thickness 2d and is oriented so that its faces are parallel to the yz-plane and given by the planes x=d and x=−d. The y- and z-dimensions of the slab are very large compared to d and may be treated as essentially infinite. The slab has a uniform positive charge...
  18. deep838

    Gauss' Law in a dielectric material

    This is what we have in text-books and in Wikipedia: ρ=ρb+ρf and from there we get ∇.D=ρf. But I am unable to understand why we are not considering the bound surface charge in deriving this equation. Can anyone explain this to me.
  19. davidbenari

    Gauss' Law -- is there a general proof for all geometries?

    I know how to derive Gauss's law considering only one point charge and a sphere. I've seen other derivations for other geometrical shapes and I would say this is way too tedious as a method to prove that Gauss's law always holds true. I was wondering if there is a general proof that says...
  20. R

    Gauss' law and charged spheres

    Hi everyone, I am struggling with gauss law. I understand the basic concept , but I can not relate it to other physics problems. I have this physics problem. I want to really understand physics, but I can't. I have watched a lo of videos but I still don't understand. I am going to give my...
  21. T

    Orbit Determination Issue (Method of Gauss, in Escobal's text)

    So I'm coding up some initial orbit determination stuff in MATLAB (for personal education; I love this stuff), and I am using 'Methods of Orbit Determination' by Escobal as a guide. I already got Vallado's code to work, now I'm just comparing other methods. I'm having an issue with one of his...
  22. S

    Gauss' Law --> Electric field of an infinitely long, straight line

    Homework Statement Problem statement: An infinitely long, straight line has a uniform charge distribution of ρ C/m. Use Gauss' law to find the electric field at a point r m away from it. Solution: Consider a cylindrical volume of height ℓ with circular cross sectional area of radius r...
  23. K

    How do vectors and electric field lines differ in representing electric fields?

    I'm stuck on some high school physics, Gauss law... 1. It says this: The electric field outside the sphere is equal as if the charge of the sphere was in it's center. I don't understand this, why is this true? I get it - experiments have showed that and that's how you calculate it; but what's...
  24. V

    Electric Flux Comparison: Gauss's Theorem and Enclosed Charge

    Two concentric imaginary spherical surface of radius R and 3R, respectively, surrounds a point charge -Q, located at the center of the surface. When compared to the electric flux I1 through the surface of radius R, the electric flux I2 through the surface 3R is. I know the answer is that...
  25. F

    Q) Deriving Gauss' Law from Coulomb's Law for a Single Point Charge

    Homework Statement Q) Use Coulomb’s Law to DERIVE the Gauss Law result for the particular case of A SINGLE POINT CHARGE. That is, using Coulomb’s Law, find the ELECTRIC FLUX going through a sphere of radius r surrounding one point charge of charge-magnitude q. THANK YOU Homework...
  26. I

    How Does Gauss' Law Ensure E-field Perpendicularity on Irregular Conductors?

    For an infinite plane sheet of charge it is obvious that the E-field points directly perpendicular to the sheet. but for conductors of irregular shape. say, a wire, or even a sheet with imperfections in it, what guarantees that the E-field will point directly perpendicular from the emanating...
  27. V

    Gauss' Law and a Gaussian Sphere

    Homework Statement A Gaussian Sphere with a radius of 1m surrounds an unknown charge at the center. At this surface a uniform outward directed electric field is 1 N/C. Use Gauss' Law to calculate the amount of charge enclosed by the sphere. Homework Equations E = q/4∏εor^2 The Attempt at a...
  28. I

    Finding force using Gauss' Law

    Homework Statement The charge density of a spherically symmetric and uniform distribution of charge is ρ = 2*10^-3 C/m^3. An electron is released one centimeter from the center. Find the magnitude and direction of the force onto the electron.Homework Equations charge density = Q/V =...
  29. A

    Why do magnets in a Gauss gun exhibit backward drift after being hit?

    So I was building a Gaussian gun for physics filming it at 300fps. See video: http://youtu.be/hZcAk3uBp58 While skipping frame by frame, I realized that all the magnets started drifting backwards after being hit. Can someone explain in detail what is going on? Sorry if my physics is not...
  30. O

    Differential form of Gauss' theorem with dielectrics

    Hi all, I'm stuck on this incompatibility within the differential form of Gauss' thearem (or Maxwell's first equation) with dielectrics. \vec{\nabla}\cdot\vec{E}=\frac{\rho_{free}+\rho_{bound}}{\epsilon_{0}} \rho_{bound}=-\vec{\nabla}\cdot\vec{P} But with a linear, homogeneous...
  31. B

    Is Gauss' Law Summation Necessary for Uniform Electric Fields?

    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...
  32. stevendaryl

    Understanding Gauss' Law for GR in Point Mass Clouds

    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...
  33. A

    Vector circulation. Stokes, Gauss and maybe more?

    Hello. My first time posting here. So... My question is kinda hard to explain but I will try to. So we all know about the Kelvin-Stokes theorem (not talking about manifolds here) : And we also know about Ostrogradsky/Gauss Theorem ...
  34. Prashasti

    Calculating Area Vectors in Gauss' Law

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

    Gauss Law: Proofs and Electromagnetism Resources

    about gauss law! is there any precise proof for gauss law? why ø=q/ε always regardless how the charge is distributed inside the surface and if anyone know a good book for electromagnetism please type its name for me.. thank u
  36. P

    The electric displacement vector field and Gauss' law?

    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...
  37. H

    Gauss law and electric current

    According to the Gauss law, the extra charges gather on the surface of a conductor. When there is a current in a conducting wire, do the charges only move on the surface of the wire or we have current also inside the wire? If we also have current inside the wire how is it compatible with Gauss law?
  38. kazukamikaze

    Gauss' Law for Infinite Sheets of Charge

    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...
  39. S

    4-point Gauss Quadrature with MATLAB

    Homework Statement I need to evaluate a function using 4-point GQ. Homework Equations GQ theory The Attempt at a Solution I have got more of a programming issue in MATLAB. I am new to MATLAB. Actually this is for a numerical analysis course where we kind of learn MATLAB on the...
  40. M

    Calculate integral using Gauss theorem

    Homework Statement . Let ##D =\left\{\left(x,y\right)\ \in\ {\mathbb R}^{2}: x^{2} + y^{2} \leq 1\right\}## and let ##{\rm f}:D \to {\mathbb R}## defined as ##{\rm f}\left(x,y\right) = \left(1 - x^{2} -y^{2}\right)\exp\left(x^{4}y^{10}\right)##. Consider the surface ##S## given by the...
  41. T

    I need some tips about a Gauss measurement

    What can a gaussmeter tell me about a metal? I am just experimenting with various metal disc samples by setting them on the Hall probe of a gaussmeter. I have the meter zeroed out, then I pace the metal on the probe. The metals all effect the field measurement in different ways, but I...
  42. S

    Vectors in Stokes and Gauss theorem

    Homework Statement I have a couple of problems With normal vectors (this especially in Stokes theoerm where it get used often). 1) In some tasks they use unit normal vector, in some they use ordinary normal vector, is there any rules on when to use what? couse it seems pretty random, or dose...
  43. C

    Gauss' law electrostatics problem involving charge densities

    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...
  44. R

    Applying Gauss' Law to other situations

    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...
  45. A

    Is Gauss's Law Valid for Moving Charges?

    I found in this forum an old thread regarding this topic, but as it didn't have (in my opinion) a satisfactory answer, I decided to open a new one. Usually when one begins to study Electromagnetism, Coulomb's law in introduced as an experimental result valid for static point charges. From...
  46. N

    How to deduce Gauss' law from Gauss Divergence Law

    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...
  47. 4

    Prove equivalence of elementary operations in Gauss Algorithm

    Homework Statement Prove that replacing one equation in a system of linear equations by a non-zero multiple of itself does not change the solution of the system. The Attempt at a Solution I'm still relatively new to proofs, so this is what I have come up with: Let S be a system of...
  48. S

    Archived Gauss Law and the wrong Gaussian surface.

    Homework Statement The problem was to calculate the electric field inside an infinite length cylinder (with radius R) with a non uniform charge density. The charge density depended on r. Its easy enough to solve using a gaussian cylinder with r less than R. But what if I wanted to complicate...
  49. S

    Calculating Electric Field at the Center of a Hemispherical Shell of Charge

    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 =...
  50. E

    How Does Gauss' Law Apply to Nested Spherical Surfaces with Varying Radii?

    Hi all, Lets suppose we have a sphere. This sphere has density of \rho(r) from 0 to the sphere's final radius R. Now, we all know that from Gauss law, the charge inside the sphere equals to the integral of the surface of the sphere. If we set our normal vector to be as usual out of the...
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