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. B

    Maximizing Power and Arrangement of Electromagnets in a Gauss Gun

    For a high school Physics project, I am supposed to create an electromagnetic device (like a generator, a motor, a Magnetohydrodynamic boat, etc.) I was thinking about building a Gauss gun, but was wondering if I could replace the individual magnets with electromagnets. I have a bunch of 1/2"...
  2. X

    Gauss' Law and Infinite plane sheet of charge

    Hi All, I am studying Gauss' law and have learned that using symmetry, we need to select a cyclinder in order to calculate electric field of an infinite plane sheet of charge. 2EA = \frac {\sigma A} {\epsilon} That equation is written using Gauss' law and hence E field is found...
  3. J

    Electric Field inside a Sphere (Gauss' Law)

    Homework Statement A sphere has outer radius 15 and inner radius 5. Between r= 5 and 15, the sphere is solid and contains a total charge of 20 C. At r < 5, the sphere is hollow. Calculate the electric field at r = 8. Homework Equations Gauss' Law --> EA = (q)/epsilon zero...
  4. C

    Gauss: Conducting Spherical Shell w/ Point Charge

    Homework Statement Consider a conducting spherical shell with inner radius 0.8 m and outer radius 1.3 m. There is a net charge 3 μC on the shell. At its center, within the hollow cavity, there is a point charge 3 μC. Determine the flux through the spherical Gaussian surface S, which has a...
  5. E

    How Does Charge Distribution Affect Electric Field Inside a Shell?

    Homework Statement http://img21.imageshack.us/img21/8079/orderyy3.th.jpg Homework Equations The Attempt at a Solution Well all I know that the smallest will be C, as it's 0 (inside the conductor), I think the next one is A, and I don't know about B and D
  6. L

    Use Gauss' Law to find the electric field

    Use Gauss' Law to find the electric field, everywhere,of charge of uniform density \rho occupying the region a<r<b, where r is the distance from the origin. Having done this, find the potential. Ok, so far I said that by Gauss' Law, \Phi=\oint_S \vec{E} \cdot \vec{dS} = \int_V \nabla \cdot...
  7. J

    Gauss' Law differential form

    Homework Statement I just have a little question about Gauss' Law (differential form). If divE = p/e0 where p is the charge density and e0 is permittivity of free space. But if we had a sphere with a total net charge of Q, then outside the sphere, the field is E=k/r^2 I think. Then...
  8. J

    Is Gauss' Law Accurate for Point Charge Divergence in Electrostatics?

    I've "derived" the first Maxwell equation of the divergence of the E-field starting at the Coulomb force of a point charge using Gauss law and even the Dirac delta function to justify the divergence at the origin. Now I'm wondering: when you state the law in differential form, i.e. not...
  9. S

    Probability and gauss integral

    Homework Statement 1) Find the area under the curve for: a) P( 0 <= Z <= 2.07) b) P(-.64 <= Z < -.11) c) P( Z > -1.06) d) P(Z < -2.33) e) P(Z >= 4.61) 2) a) Evaluate integral from 0 to 1.24 of e^(-x^2/2) b) Evaluate the integral from -inf to inf of 6*e^(-x^2/2) Homework...
  10. O

    SOlving power flow using gauss seidel and matlab, HELP

    Homework Statement We were asked to do a course project using to solve a powerflow system usign gauss seidel and Newton raphson methods. after writing down the equations at each bus and double checking them this is the final code2. The attempt at a solution c=1 V1=1 P2=-8 Q2=-2.8 V3=1.05...
  11. M

    [Calc 3] Gauss' Law for Elecricity over a hemisphere

    Hello, Thank you very much for takign the time to help me out. This is an applied calculus 3 (multivariable calc) level problem. I have an answer, but it is nonsensical as the units are not in accordance with units of charge, C. Homework Statement Instructions: Use Gauss' Law for...
  12. I

    Is Gauss' Law Applicable to Gravitational Fields?

    Can gauss law in its equivalent form be used to determine the gravitational field?? If so how??
  13. J

    How can I optimize the velocity and power of a Gauss Cannon with magnets?

    I am currently working on constructing a Gauss Cannon using the simple method of some chrome balls with a neodymium magnet on a track arranged thus: 0_____||0000____ so when the ball (0) on the left is released it is attracted by the two magnets (|) and smashed into them, and with the same...
  14. M

    Question on Gauss law & charged disks

    hey everyone... i want to know why can't we use Gauss law to calculate the electric flux density of a charged disk? and how to calculate it "everywhere"? as coulomb's law calculates it at a certain point only...
  15. F

    Solving Gauss' Law Problem: Electric Field in Hole of Solid Insulating Cylinder

    Homework Statement A very long, solid insulating cylinder with radius R has a cylindrical hole with radius a bored along its entire length. The axis of the hole is a distance b from the axis of the cylinder, where a < b < R. The solid material has a uniform volume charge density, ρ. Find...
  16. M

    Applying Gauss's Lemma to Calculate Legendre Symbol (6/13)

    Use Gauss Lemma (Number theory) to calculate the Legendre Symbol (\frac{6}{13}). I know how to use Gauss Lemma. However we use the book: Ireland and Rosen. They define Gauss Lemma as: (\frac{a}{p})=(-1)^n. They say: Let \pm m_t be the least residue of ta, where m_t is positive. As t ranges...
  17. M

    Gauss Law - Conducting cylindrical shell

    1. A thick conducting cylindrical shell has an inner radius Rsub1 and outer radius Rsub2. It has a net excess charge = Q, and it is L long. Find electric field at certain points given. Ok, when r is less than Rsub 1, the electric field is zero. And when r is greater than Rsub2, it is easy to...
  18. R

    Generating a 400,000 Gauss EMF

    Hello all, first time post here. I was curious, hypothetically, how much juice would you need to generate a 400,000 Gauss magnetic field?
  19. F

    Gauss Jordan Elemination Method (Stucked)

    Gauss Jordan Elemination Method (Stucked)! Homework Statement 5x1+3x2+2x3=4 3x1+3x2+2x3=2 +x2+x3 =5 I have to solve this problem by calcutaing the inverse if this equation's augmented matrix Homework Equations I used this method to find its inverse 5 3 2 1 0 0 3 3 2 0 1...
  20. G

    How Does Distance Affect Electric Field Calculation Above a Charged Sheet?

    Homework Statement what is the approx electric field 1cm above a typical sheet of paper with a surface charge density of sigma = 45 nC/m^2?Homework Equations electric field E = sigma/epsilon_0 where epsilon_0 = 8.85*10^-12 E = kq/r^2 where k = 9*10^9, r is distance in meters assume paper...
  21. S

    Gauss' Law - Sphere with spherical cavity

    Gauss' Law - Sphere with spherical cavity - Please help Homework Statement A sphere of radius 2a is made of nonconducting material that has a uniform volume charge density . (Assume that the material does not affect the electric field.) A spherical cavity of radius a is now removed from the...
  22. R

    Gauss Law: Dielectric Homework - Find Electric Field and Polarization Charge

    Homework Statement A positive charge q is in the center of an espheric hole of radius R inside a dielectric material with constant Ke. Find the electric field module inside the dielectric in a point very near to the hole surface and the polarization charge over the surface. Homework...
  23. A

    Gauss' Law: Cylindrical Symmetry

    Say we are looking at a positively charged rod with uniform charge density and a radius of R. When using Gauss' law and taking a cylindrical surface we use the formula E = lambda/2*pi*epsilon*r When we derive this equation we are assuming R is significantly smaller than L and so we...
  24. D

    Help with 7x7 gauss jordan elimination program

    Homework Statement Hi, I am new to gauss jordan elimination and our teacher onlt taught us how to solve a 3x3 equation and gave us a 7x7 problem to answer due tom. 2m + 3n - p + q + 2r - s + 2t = 1 m - n + p - q + r + s + t = 2 2m + 2n - 2p + q - 2r + s - t = 1 m - 2p + q - r - s + t =...
  25. S

    Gauss' Law: Enclosed Cylinder in a Hollow Shell

    A long non-conducting cylinder has a charge density p = a*r, where a = 4.73 C/m^4 and r is in meters, and a radius of 0.0437m . Concentric around it is a hollow metallic cylindrical shell with an inner radius of 0.119m and an outer radius of 0.158m. 1) What is the electric field at 0.172m...
  26. F

    Electric fields (Gauss' Law)

    Two large flat metal sheets are a distance L apart. The separation L is small compared to the lateral dimensions of the sheets. Each sheet has a total surface area A, which includes both top and bottom surfaces of the sheet. The thickness of each sheet is very small compared to its lateral...
  27. B

    Explaining Gauss' Law and Electric Field Direction on a Charged Square Sheet

    Can someone explain the following? A positive charge Q is placed on a square sheet of nonconducting material of side x cm in the yz plane. What's the magnitude and direction of the electric field next to the sheet and proximate to the center of the sheet? I don't understand why the...
  28. U

    Gauss' Law: Net Electric Field of Two Spheres

    Homework Statement Two nonconducting spheres, of r1=3.0cm and r2=2.0cm, are placed of an x-axis. They have surface charge densities of +6.0mC/m2 and +4.0 mC/m2, respectively, on their outside surfaces. The center of sphere r1 is on the origin and the center of sphere r2 is 10 cm away. What is...
  29. T

    Would Gauss still make his comment today?

    Gauss said: "Mathematics is the queen of the sciences and number theory is the queen of mathematics." But would he still make this comment today after learning the new abstraction and foundations that mathematics has taken on?
  30. C

    Calculating Charge in an Earth Electric Field: Gauss' Law

    The earth’s electric field is measured at a height of 200 m and is found to be directed vertically downwards and to have a strength of 100 Vm1. At a height of 300 m, the direction of the field is found to be the same, but the field’s strength has decreased to 60 Vm1. Use Gauss’ law to...
  31. A

    Is There a Gauss' Law for Gravitation?

    hello, I was wondering if there is an equivalent gauss' law for gravitation like: \Phi=4\piG*Menclosed any help would be appreciated. Thank you.
  32. T

    Gauss' Law and electric fields

    I really just want to know if I'm doing this correctly, as I don't have access to the answer to check. Homework Statement A cylindrical shell of radius 7.00 cm and length 240 cm has its charge uniformly distributed on its curved surface. The magnitude of the electric field at a point 19.0 cm...
  33. D

    Calculating q2 and q3 on a Conducting Shell?

    Consider an insulating sphere with radius of 7 cm. A charge of 13.8561 µC is uniformly distributed throughout this sphere. It is surrounded by a conducting shell. Denote the charge on the inner surface of the shell to be q2 and the charge on the outer surface of the shell to be q3. The total...
  34. D

    Gauss' Law and electric fields in non-conducting cylinder

    A long non-conducting cylinder has a charge density ρ = α*r, where α = 4.95 C/m4 and r is in meters. Concentric around it is a hollow metallic cylindrical shell. https://www.physicsforums.com/attachment.php?attachmentid=14741&d=1216404841 1. What is the electric field at 2 cm from the...
  35. P

    Solving Gauss Law Problem 1: Electric Field of a Charged Copper Shell and Wire

    1. Homework Statement A thin, cylindrical copper shell of diameter ds = 6 cm has along its axis a thin metal wire of diameter dw = 7.05 × 10-3 cm. (as shown in the diagram below.) The wire and the shell carry equal and opposite charges of 5.90 × 10-9C/cm, distributed uniformly. What is the...
  36. C

    Gauss' Law and an infinite sheet

    Homework Statement a small circular hole of radius R = 2.03 cm has been cut in the middle of an infinite, flat, nonconducting surface that has a uniform charge density σ = 4.61 pC/m^2. A z axis, with its origin at the hole's center, is perpendicular to the surface. What is the magnitude (in...
  37. C

    Gauss' Law using linear charge density

    Homework Statement A charge of uniform linear density 2.80 nC/m is distributed along a long, thin, nonconducting rod. The rod is coaxial with a long conducting cylindrical shell (inner radius = 5.20 cm, outer radius = 10.8 cm). The net charge on the shell is zero. (a) What is the magnitude...
  38. C

    How Do You Determine the Constant b in an Electric Field Using Gauss' Law?

    Homework Statement The box-like Gaussian surface of the figure below encloses a net charge of +57.0ε0 C and lies in an electric field given by = [(10.3 + 2.4x)·i - 3.1·j + bz·k ] N/C, with x and z in meters and b a constant. The bottom face is in the xz plane; the top face is in the...
  39. S

    Differential Geometery: Images of Gauss Maps

    Homework Statement this is a 2 part problem let G: T-----> (Sigma) be the gaus map of the torus T derived from its outward unit normal U. What are the image curves under G of the meridians and parallels of T? What points of (Sigma) are the image of exactly two points of T? And Let...
  40. G

    How Is Gauss's Law Applied to Calculate Deflection Angle in Charge Interaction?

    Homework Statement A Particle of mass m and chargeq oves at high speed along the x axis. It is initially near x=-infinity and it ends up near x=+infinity. A second charge Q is fixed at the point x=0, y=-d. As the moving charge passes the stationary chrge, its x component o velocity does not...
  41. G

    Angle of Deflection for a Moving Charge Passing a Fixed Charge

    Homework Statement A Particle of mass m and chargeq oves at high speed along the x axis. It is initially near x=-infinity and it ends up near x=+infinity. A second charge Q is fixed at the point x=0, y=-d. As the moving charge passes the stationary chrge, its x component o velocity does not...
  42. D

    Why Is Gauss' Law Failing to Solve This Problem?

    http://imageupload.com/out.php/i120384_Untitled.gif I havnt had any luck with this question. The only possible approach i can think of is to use gauss' law for electric fields. I know I am supposed to show my working, but this really had me stumped, and I've really gotten nowhere. I...
  43. K

    How Does Gauss' Law Apply to the Electric Field Around a Charged Metal Ball?

    Homework Statement A metal ball with radius R = 0,6 m is charged with Q = 0.15 nC. Find the electrical field as function of the distance r from the center of the ball. The Attempt at a Solution Gauss law: Q = e0*E(r)*A = e0*E(r)*4*pi*R^2 which gives E(r) = Q /...
  44. G

    Solving Gauss Law Problems: Understanding Flux & Point Charges

    problem in flux / gauss law could someone please post me a link which can explain gauss law. i am having trouble understanding the basics regarding it. eg. if we have a point charge +q kept at the edge of a cube of say side 'a' , what will be the net flux through the remaining sides...
  45. F

    How Do You Solve the Gauss Units Relation for a Charged Particle's Trajectory?

    Hi all! Homework Statement The problem is: For a particle with electric charge equal to that of one electron, the trajectory radius R is related to the absolute value of the perpendicular component P_{\bot}of the relativistic moment perpendicular to \textbf{B} from the relation...
  46. S

    How Cooulomb's law follows from Gauss' law?

    Can anyone explain this to me?
  47. haushofer

    The Gauss Bonnet Lagrangian and the conserved current

    Hi, I have a computational question about the Hilbert action with an added Gauss-Bonnet term. The Lagrangian L ( seen here as a scalar density) then looks like this: L = {\cal L} \sqrt{g} = \Bigl(R+ R_{\mu\nu\rho\sigma}R^{\mu\nu\rho\sigma} - 4R_{\mu\nu}R^{\mu\nu} + R^{2}\Bigr)\sqrt{g}...
  48. rohanprabhu

    Gauss Law Anomaly: Potential Across a Capacitor

    I started having this doubt since i saw the derivation of potential across a capacitor using this method. So.. here i ask: Let there be two large sheets made of insulators, and charged to a planar charge density, \sigma (Sheet 1) and 2\sigma (Sheet 2). Since they are insulators, when placed...
  49. D

    Gauss' law problem with sphere

    Homework Statement In a spherical region, the voltage is measured to be spherically symmetrical, with v=v(r)=wr^p a. Find the radial electric field. b. Use Gauss’ Law to find the charge enclosed in a sphere of radius r. c. Find the charge enclosed by a sphere of radius...
  50. D

    Electric Field & Potential of Charged Spheres & Cylinders: Gauss' Law AP Problem

    1 A solid metal sphere of radius R has charge +2Q. A hollow spherical shell of radius 3R placed concentric with the first sphere has net charge -Q. a) Describe the electric field lines both inside and outside the spheres. b) Use Gauss' law to find an expression for the magnitude of the...
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