Gauss Definition and 647 Threads

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. L

    Application of Gauss' law - some doubts

    Application of Gauss' law -- some doubts Homework Statement Revered Members, I have attached images of applications of Gauss' law namely 1) Electric field due to an infinitely long charged wire and 2) Electric field due to an infinite charged plane sheet. In both cases Gaussian surface is...
  2. J

    Sphere 1: +100 C Sphere 2: +1 C

    Homework Statement A solid, insulating sphere of radius a has a uniform charge density 1 and a total charge Q. Concentric with this sphere is an uncharged, conducting hollow sphere whose inner and outer radii are b and c, Find the magnitude of the electric field in the regions r=b and r=...
  3. P

    Gauss elimination vs Solution with Inverse

    Homework Statement Using Octave or Matlab solve random binary matrices(with 1s and 0s) of size N and plot them together. Draw a conclusion. The Attempt at a Solution http://img703.imageshack.us/img703/7803/plotm.png I was just wondering if this looks correct to you. I previously had...
  4. Geofleur

    2D Gauss' Law applied to an infinite cylinder

    Hello, I've been working my way through Mathematics for Physicists by Dennery and Krzywicki and, on page 65, they assert that Gauss' law applied to a 2D cross-section along an infinite charged cylinder is: ∫E.n dl = 4πσ where E is the electric field on the Gauss surface (a circle around...
  5. C

    Why is k = 9 * 10^9 and how is it related to Pi?

    Why use k = 1/[4(pi)(epislon)] and epsilon = 8.8 * 10^(-12) and subsequently, k = 9 * 10^9 It could simply be k = 9 * 10^9, and different k for different medium instead of different permittivity for different medium. What I mean is why does Pi, (I can handle the 4) comes into the...
  6. N

    Gauss' Law - difficulty understanding this example

    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...
  7. T

    Gauss elimination algorithm for matrix inversion

    Hello guys, I'm writing a C++ function for matrix inversion. I saw many algorithms online, but I'm concerned about the case when a diagonal element equals zero, which is, for some reason, not taken into account by those websites. When we do the elimination for solving a system of linear...
  8. M

    Finding Electric Field: Gauss' Law & Charge Distribution

    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...
  9. T

    Why Must the Real Part of \(c-a-b\) Be Positive in Gauss's Summation Formula?

    Why is the Gauss summation formula for complex parameters a,b,c: \displaystyle _2 F_1 (a,b;c;1) = \frac{\Gamma (c) \Gamma (c-a-b)}{\Gamma (c-a) \Gamma (c-b)} only valid for \text{Re}(c-a-b)>0,\;c\neq 0,-1,-2,-3,...?
  10. J

    Integral form of Gauss' Law, Parallel Plate Capacitor

    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...
  11. B

    What is the Electric Field Strength in a Plane-Limited Charge Distribution?

    Homework Statement Space distribution of electric charge is limited by to planes. Charge has the same intensity in planes parallel to these planes, but in dependence of the x coordinate, charge density is being distributed like: \rho (x)=A\cdot x\cdot (d-x) d is distance between those to...
  12. P

    Prove Convergence of Series Using Gauss' Test

    Homework Statement I just got done proving Gauss' test, which is given in the book as: If there is an N\ge 1, an s>1, and an M>0 such that \frac{a_{n+1}}{a_n}=1 - \frac{A}{n} + \frac{f(n)}{n^s} where |f(n)|\le M for all n, then \sum a_n converges if A>1 and diverges if A \le 1. This...
  13. H

    How Does Gauss' Law Apply to Non-Symmetrical Shapes and Charge Distributions?

    Homework Statement Gauss' Law states: ∫∫ E.dS = ∫∫∫ div(E) dV = Qenc/ε₀ The proof is as follows (this is from Marsden's Vector Calculus 5e): Let M be a elementary region in ℝ3. Then if (0,0,0) ∉ ∂M, we have: ∫∫∂M r.n/r3 dS = 4π if (0,0,0) ∈ M = 0 if (0,0,0) ∉ M Construct a sphere of...
  14. L

    Gauss Law Problem With A Spherical Conductive Shell

    You are a hollow metallic sphere of inner radius r1, and outer radius r2. Inside is a charge of magnitude Q and a distance d<r1 from the centre. First I need to draw the electric field lines for regions r<r1, r1<r<r2, and r2<r Since the sphere is a conductor the only place where there is...
  15. jegues

    Gauss' Law - Infinite Sheet of Charge

    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...
  16. K

    Confirming Gauss' Law: Finding Flux

    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...
  17. DocZaius

    Is Left Side of Gauss' Law equation not the total electric flux?

    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...
  18. E

    How Does Charge Density Affect Electric Field Strength Between Two Cables?

    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...
  19. J

    Archived Finding the electric field between two lines of charges using Gauss Law

    Homework Statement The problem is given in the attachment belowHomework Equations (i)EA= Q/epsilon naught (ii)Area of cylinder used = 2pi*r*L (iii)The integral of E*dA =Q/4pi*epsilon naught (iv) Llamda= Q/LThe Attempt at a Solution Well I know I needed to choose a suitable Gaussian surface...
  20. I

    Calculating Electric Field for a Point Charge Inside a Hollow Sphere

    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...
  21. J

    What Is the Charge Distribution p(rho) for This 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.)...
  22. C

    Gauss' Law for finding E between metal plates

    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...
  23. B

    Determining Electric Field Inside a Hollow Conducting Sphere with Gauss Law

    Homework Statement A hollow conducting sphere carries a charge of 72nC and has an inner radius of 44cm and an outer radius of 68cm. At the center of the hollow sphere is a point charge (-89)nC, insulated from the sphere. What is the magnitude of the electric field inside the sphere at a...
  24. B

    Using Gauss' theorem ande exploiting the cylindrical symmetry of the system, show

    Homework Statement A wire of length L and negligible transverse dimensions, made of an insulating material, is placed on the x-axis between the origin and the point (L,0). The wire has a uniform line charge density lambda. using Gauss' theorem and exploiting the cylindrical symmetry of...
  25. B

    Gauss law and insulating sphere

    imagine a charge placed inside a closed conducting shell (a hollow metal box or sphere) Feynman says: - no static distribution of charges inside a closed conductor can produce any fields outside. The fields on the two sides of a closed conducting shell are completely independent. but...
  26. A

    How does the Einstein tensor contribute to the equations of motion in 4d?

    Hello, in a paper http://www-library.desy.de/preparch/conf/theo-ws/workshop2004/data/Chatillon.pdf . says that. 1) In 4d, it is a total derivative, then does not contribute to the equations of motion A total derivative respect to time does not contribute to equation of motion?, ¿or...
  27. R

    Electric Field from Gauss' Law - Vector Form

    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?
  28. K

    Who Are Today's Top 5 Mathematicians Destined for Greatness?

    Who are the current greats that will go down as "Gods equal to Gauss, Euler, etc.)? Each generation of mathematics (dunno how long a generation is) have great mathematicians. Last generation was Hilbert, Poincare, cantor, and prolly 1-2 more. Alot of the works that these mathematicians have...
  29. T

    Gauss' law which formula to use

    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
  30. T

    Gauss law for gravitational fields

    For electrostatic fields gauss law depends on three factors viz inverse square nature ,central character and principle of linear superposition of electrostatic force.Now,within the Newton's framework of gravitation the gravitational force has all of the above properties.Then why does one does...
  31. B

    Conservation of energy and momentum in a gauss gun

    Hi, I'm doing a project on the Gauss gun and Newton's cradle. I'm trying to produce little models in MatLab and have come across some problems. Namely with the gauss gun, using different types of balls, hollow and solid (I've not even got round to adding acceleration from a magnet yet)...
  32. T

    Solution of Airy's Equation in Terms of Gauss Hypergeometric Series

    Homework Statement Find the general solution of Airy's equation f'' - zf=0 satisfying the initial conditions f(0)=1, f'(0)=0 as a power series expansion at z=0. Express the result in terms of the Gauss hypergeometric series. The Attempt at a Solution After subbing...
  33. J

    Infinite lines of charge, Gauss' Law

    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...
  34. A

    Gauss law and infinite spherical charge distribution

    1. The problem statement Consider an infinite spherical charge distribution with constant charge density. According to symmetry of the problem, I expect the electric field at any point to be zero. But if you construct a Gaussian sphere and apply Gauss theorem, it will give you some finite field...
  35. R

    Does Gauss' law imply that the universe isn't compactified?

    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...
  36. A

    Gauss' Law and charges placed within a spherical conductor

    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...
  37. M

    Proving Gauss's Lemma Extension in Polynomial Factoring

    Ok, the book I'm reading states Gauss's lemma as such: If f(x) is a monic polynomial with integral coefficients that factors into two monic polynomials with coefficients that are rational, f(x) = g(x)h(x), then g(x), h(x) \in \mathbb{Z}[x]. Now one of the exercises says to prove that: If...
  38. Q

    What is the effect of time-varying current on Gauss law in electrodynamics?

    if i have a current carrying straight long wire, I = I0sin(wt) why is gauss law ∇.E = 0? i thought only for steady currents , then the charges reside on surface, that's why 0 charge enclosed, and hence gauss law gives 0 right? so now since i have a time varying current, what should...
  39. C

    Help Needed: Understanding Gauss' Law for Magnetism & 'Local Form

    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...
  40. W

    Gauss-Lucas Theorem: Show Zeros of p(z) in Unit Disc

    Homework Statement So I am told that p(z)=1+2z+3z^2+...+nz^(n-1). Now I need to use the Gauss-Lucas Theorem to show that all the zeroes of p(z) lie within the unit disc. Homework Equations Gauss-Lucas Theorem The Attempt at a Solution So I was thinking that I could integrate p(z)...
  41. K

    Gauss Law and Flux: Calculate Charge Inside Box

    Homework Statement The electric field has been measured to be horizontal and to the right everywhere on the closed box shown in the figure. All over the left side of the box E1 = 90 V/m, and all over the right, slanting, side of the box E2 = 400 V/m. On the top the average field is E3 = 120...
  42. L

    Understanding the Gauss Bonnet Theorem for 2D Riemann Surfaces

    I am looking at the proof of the Gauss Bonnet theorem for two dimensional Riemann surfaces. There are many versions but this one escapes my intuition and I am asking for help "seeing" what it means though I can follow the arguments in the proofs. View the surface as a Riemann surface and...
  43. I

    Electric Potential and Gauss' Laws Stuff (I think)

    Homework Statement [PLAIN]http://img203.imageshack.us/img203/5679/physics2h.png Homework Equations Included above I believe... The Attempt at a Solution a) i think dq=\lambda2\pidy Some of the calculus that we are using I am shaky on and I just don't understand what is being asked here...
  44. N

    Why Is Choosing the Right Gaussian Surface Crucial in Gauss' Law Calculations?

    Homework Statement I know D . n(hat)dS =Qencl I do not really have problems with the dS or Qencl but I do not really know why they choose the gaussian surfaces. Like on the second page where z> pi/2 It seems to me that one would go from (pi/2) to z but won't z effectively just be...
  45. S

    Electric Fields and Gauss' Law with a Conducting Sphere

    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...
  46. K

    How Does Gauss' Law Apply to Coaxial Cable Charge Distribution?

    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 ...
  47. U

    How Does Charge Distribution Affect Electric Field and Work Done?

    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...
  48. C

    Help Solving Gauss' Law Homework Problem

    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)...
  49. D

    Using Gauss' Law on a Solid Annular Sphere

    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...
  50. C

    Quick q on gauss' law (cylinders)

    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...
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