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. K

    Gauss Law/Electric Potential Question(s)

    Homework Statement http://ft.trillian.im/b0f9eae6eee2cb82091d0bd460ed09948b0cf819/6b66r5cGJrRSOCQPbItbRmtMARJhR.jpg Homework Equations http://ft.trillian.im/b0f9eae6eee2cb82091d0bd460ed09948b0cf819/6b674JdPpi29mGe8SqWkcnh8K6bmA.jpg The Attempt at a Solution I know how it works...
  2. P

    How do I know when to use the charge density or not in a Gauss problem?

    I feel that I'm always struggling with these kinds of problems since I never know if the information is to be considered a density or not. Is there any trick/key words I should be on the look-out to determine whether they gave me a density charge or a point charge?
  3. B

    Drilled hole through earth - Diff EQ w/ Gauss' Law

    Homework Statement Suppose that a hole has been drilled through the center of the earth, and that an object is droppped into this hole. Write a first order linear differential equaiton for the object's velocity, v as a function of the distance r from the Earth's center (i.e, and equation...
  4. E

    Difficulty in differential form of gauss law

    hi all, im new at electromagnetics and vector calculus, so facing these trivial problems. The differential form of gauss's law for empty space states ∇E = ρ/ε .The right side refers to charge density at the point of calculation of divergence? If a point charge(or a small uniformly charged...
  5. C

    MHB C F Gauss, on how to add all numbers of 1 to 100?

    Mark on Yahoo answers asks: Allegedly his method was something like: $(1+100)+(2+99)+ ... +(99+2)+(100+1)=2(1+2+...+100)$ But the left hand side is $101\times 100$, so $1+2+..100=101\times 100/2$ (Like Marlow's Dr Faustus he could sum them forwards and backwards - but had no need of...
  6. 1

    Calculating Electric Field Strength Using Gauss' Law

    Homework Statement Attached Homework Equations Gauss' Law The Attempt at a Solution \epsilon_{0} E(4\pi r^{2}) = q_{enc} = -1.738x10^{-19}
  7. estro

    Calculating line integral using Stokes' and Gauss' theorems

    Hi, I'm trying to calculate some line integral with both Gauss' and Stokes' theorems, but for some strange reasons I get different results. Since the solution with Stokes' theorem seems to be somewhat easy I doubt that this question was meant to be solved by Gauss' theorem but I still want to...
  8. M

    Finding the electric field of a uniformly charged cylinder using Gauss' law

    Homework Statement A very long cylinder has charge density L/m and radius a. Find the electric field at a distance r, with r > a. The Attempt at a Solution I construct a gaussian cylinder around it with radius r, and then from Gauss' law the field at any point on it's side surface is E=...
  9. H

    For remember this great man (Karl Friedrich Gauss)

    Karl Friedrich Gauss German mathematician and astronomer (1777–1855) Gauss received a doctoral degree in mathematics from the University of Helmstedt in 1799. In addition to his work in electromagnetism, he made contributions to mathematics and science in number theory, statistics, non-Euclidean...
  10. Q

    Gauss' Law with Superposition Principle

    Homework Statement A very long cylinder of radius R has positive charge uniformly distributed over its volume. The amount of charge is λ Coulombs per meter of length of the cylinder. A spherical cavity of radius R' < R, centered on the axis of the cylinder, has been cut out of this cylinder...
  11. P

    Electrostats, Gauss Theorem qusetion: Struck in middle

    1. The question is to find the volume charge density. Given is non uniform, but spherically symmetric electric field, E=K.r4, K being a constant. Original question can be viewed in image: * Question no. 53 Homework Equations Answer is: ρ=6Kr3ε The Attempt at a Solution...
  12. F

    MATLAB Need help with Matlab code for gauss siedel i get errors, need imediat help

    Please I need HELP IMEDIATLY This is the error message that i get ? Error using ==> gauss_sied Too many input arguments. Error in ==> HW_14 at 23 [x_wo, cnt, x_w,cntt] = gauss_sied(xo, A, b, es, lam); clc clearC = [-8 1 -2 -20 2 -6 -1 -38 -3 -1 7 -34]; A = C(:,1:end-1); b = C(:,end);nr =...
  13. V

    Four dimensional version of Gauss' law

    I'm having trouble interpreting the four dimensional version of Gauss' law. In the original version, a vector would be integrated around a closed 2D surface and this would be equal to the integral of divergence over the enclosed volume. In the newer version, the vector(or tensor) is integrated...
  14. C

    Gauss' law in one-dimensional space

    Hello I am new here. Here is the situation: There is a 1-dimensional closed loop and this loop spans a one-dimensional space. If there are a +ve and a -ve charge at rest on some points in the loop, what should be the electric field in the loop? The only thing I can think of is...
  15. E

    Gauss Law and potential Which one to use

    Given a symmetric Charge distribution where Gauss Law can be applied which method will one select to obtain Electric field. Potential or Gauss Law. I feel that Gauss law must be used because using Gauss law one can calculate electric field easily as compared to Potential. Which is advantageous...
  16. F

    Gauss hypergeometric function derivative

    Homework Statement I want to differentiate the Gauss hypergeometric function: _2F_1[a,b;c;\frac{k-x}{z-x}] with respect to z Homework Equations The derivative of _2F_1[a,b;c;z] with respect to z is: \frac{ab}{c} _2F_1[1+a,1+b;1+c;z] The Attempt at a Solution Can I treat this as...
  17. I

    Discuss a system of equations by Gauss

    Hello, How would you discuss this system of equations by Gauss's method? \begin{bmatrix}{x}&{y}&{(m-1)z}&{1}\\{x}&{(m-1)y}&{z}&{m-1}\\{(m-1)x}&{y}&{z}&{m+2}\end{bmatrix} NOTE: the last column are the independent terms Thank you very much
  18. A

    What is Gauss' Law for Dielectrics and How Does it Account for Polarization?

    Inside a dielectric we have: ∇\cdotε0E = ρbound + ρfree , where ρbound refers to the fact that these charges come from polarization. We can write this as: ∇\cdotε0E = -∇\cdotP + ρfree where P is the polarization of the material. And combing the two divergence terms...
  19. S

    How Much Charge Does a 3cm Section of a Charged Line Hold?

    The electric field 0.475m from a very long uniform line of charge is 830 N/C. How much charge is contained in a section of the line of length 3.00cm? My solution: the Electric field from an infinite plane is E=σ/(2*ε0), so σ=E*ε0*2=1.47*10^-8 3.00cm=.03m...
  20. S

    Gauss' law and conducting spheres

    Homework Statement A conducting sphere of radius R2 has a central cavity of radius R1 that holds a charge q in its centre. Determine the electrical field for r > R2, r < R1 and R1 < r < R2 and determine the charge density induced by q. I'm not allowed to include a link to my figure, but I'm...
  21. T

    Reading through Jackson: Gauss Theorem

    Homework Statement I'm reading through Jackson and ran into the following: An application of Gauss's theorem to ∇'^{2}G=-4πδ(x-x') shows that \oint(\partialG/\partialn')da'= -4∏ where G is a Green function given by 1/|x-x'| + F, and F is a function whose Laplacian is zero. (Sec. 1.10...
  22. A

    How Does Gauss' Law Apply to Gravitational Fields?

    Homework Statement The gravitational field g due to a point mass M may be obtained by analogy with the electric field by writing an expression for the gravitational force on a test mass, and dividing by the magnitude of the test mass, m. Show that Gauss' law for the gravitational field reads...
  23. sunrah

    Fitting a Gauss curve to lab data

    I have 100 data points that I want to fit in Excel I can do this with NORMDIST no problem but I'm also trying to do it without it to no avail! I'v tried plotting the data using the Gauss function: y(x) = \frac{1}{\sqrt{\pi \sigma^{2}}}e^{\frac{-(x - x_{0})^2}{2\sigma^{2}}} where x is a data...
  24. Z

    Infinite long cylinder for Gauss' law

    Sometimes you want to find the electric field of a loong cylinder carrying for instance a uniform volume charge. Then for easy calculations you approximate the cylinder with an infinitely long one and then put a gaussian surface over the entire thing. Symmetry then dictates that the field point...
  25. D

    What typical voltages are induced from a typical magnet (50-75 gauss)

    Hi, I'd like to use a millivoltmeter to research voltages induced from a basic ceramic magnet brushing by a conductor. So, I need to buy a millivolt meter. What voltage ranges will be required, and what read-rate should the millivolt meter have (in order for it to register the voltage in a...
  26. Z

    Proving Gauss' Law for Any Topologically Closed Surface

    The essence of Gauss' law is that the total flux through a closed surface only depends on the charge inside the surface. So two spheres with different radii will have the same flux. This is of course due to the 1/r2 property of coulombs law. Because, since the area increases with r2 this...
  27. Z

    Gauss' law when charge terminates

    Is proven in my book using field lines. I stumbled upon something that I however can't understand. They say that a charge outside a closed surfrace contributes nothing to the total flux out of the surface since every field line that goes into the surface also comes out. But what if it terminates...
  28. T

    Gauss hypergeometric series

    Homework Statement Express \sum_{n=0}^{\infty} \frac{1}{(\frac{2}{3})_n} \frac{(z^3/9)^n}{n!} in terms of the Gauss hypergeometric series. Homework Equations The Gauss hypergeometric series has 3 parameters a,b,c: _2 F_1 (a,b;c;z) = \sum_{n=0}^{\infty}...
  29. T

    How Does Gauss's Law Apply to Oscillating Bars in an Electrical System?

    Question about Gauss flux?? Homework Statement Two bars, each 30cm long, and each having a resistance of 2-ohms, are connected to a 1,500 volt battery. The bars are attached to each other with 3 insulating springs, each having a spring constant of 9N/m. The two bars are initially at rest...
  30. M

    Gauss' Law Conclusion in Gravitational Fields

    I've been told that electric and gravitational fields have a lot in common, and both are practically analogous to each other. Also, the conclusions made through Gauss' Law apply just as well (analogously) to gravitational fields. One of Gauss' Law's predictions is for a solid (conducting)...
  31. K

    +2uC and -2uC charges inside a closed gauss box.

    Electric Field inside a closed gauss box. Homework Statement there are +2uC and -2uC charges inside a close "Gauss" box. Which of the following statement is true? Homework Equations given option are: 1) the net electric flux through the box is zero 2) the electric field is zero...
  32. K

    Why I doubt the generality of Gauss' law: A Gaussian sphere 1 light year across

    Let's say I have a Gaussian sphere 1 light year across with synchronized clocks and sensors all over its surface. All clocks are co-moving, not accelerating, and the spatial curvature is negligible. If I have only one charge inside the Gaussian sphere, 1 centimeter from its surface for an entire...
  33. A

    Gauss' Law for nonconducting sphere

    Homework Statement There is a nonconducting solid sphere with uniform charge density rho and radius R=15 but it has a smaller hollow spherical cavity of radius a = 5, it is not centered: the distance between the center of the larger sphere is a distance b = 6 I'm trying to find the...
  34. H

    I don't understand Gauss' law

    Homework Statement A hollow spherical shell carries charge density \rho=k/r^2 in the region a\leq r\leq b. Use Gauss' Law in integral form to find the electric field in three regions: (i) r<a, (ii) a<r<b, (iii) r>b. Homework Equations Gauss' Law in integral form...
  35. M

    Comp Sci Using fortran to Solve linear equations using gauss elimination and back substitution

    Homework Statement What will be the value of the variable ipvt and AMD when the input value of lud to the following subroutine (solver) is zero ? subroutine Solver (A,B,N,lud,Z) integer lda,N,ipvt(1000),info,lud,IDAMAX &j,k,kp1,l,nm1,kb double precision...
  36. I

    Question on the Gauss' Law's Qenc

    I understand Gauss' Law is: Phi = integral(E)dA = Qenc/epsilon0 I never understood how you determine that Qenc. I know it varies from shape to shape. Can someone help me?
  37. A

    Finding Electric Field with Gauss's Law on a Sphere with Varying Charge Density

    Homework Statement A sphere of radius a has a charge density that varies with distance from its center d(r) = do*(r/a)**2. Express the electric field as a function of distance from the center of the sphere r, a, do, and the permitivity of free space ez for each of the falling regions...
  38. A

    Total Charge on the Cylinder (Gauss' Law)

    Homework Statement The cylindrical drum of a copy machine is .38 m long with .05 m radius. If charge is uniformly distributed over the cylindrical surface (the top and bottom flat circular ends of the drum have no charge) and the electric field very close to this surface midway along the...
  39. H

    Gauss' law cubes, how to prove

    So I was doing some practice problems and one of them asked for the flux through one side of a cube that has a point charge(Q) at its center, it seems intuitive that it would be 1/6 of the charge but how would i show this? if I do ∫E dA → E∫dA the surface area of a cube is 6L2 so i would...
  40. S

    Is the Electric Field Inside a Nonconducting Charged Hollow Sphere Zero?

    What is the electrical field inside a nonconducting charged hollow sphere? My Explanation: In both cases, conducting and nonconducting hollow sphere, the flux inside is zero because there is no charge inside However in conducting sphere electrical field is zero anywhere inside due to...
  41. P

    Electric Fields using Gauss' law

    Homework Statement http://i.minus.com/jbxXiQZmmiOQtS.png Homework Equations Elecric flux = Integral of closed surface of E dotted into dA = qenclosed / ε0 Rho = 50 x 10^-6 abs(z) The Attempt at a Solution Integral of closed surface of E dotted into dA will end up being EA when E is...
  42. G

    [Gauss' Law] Hollow insulating sphere?

    Homework Statement A hollow insulating sphere with an inner radius of 6.58 cm and outer radius of 11.7 cm has a uniform charge density of 79.9 μC/m3 distributed throughout the volume between. If we want to use Gauss' Law to find the electric field at r = 17.2 cm, what "charge enclosed"...
  43. DryRun

    Green's, Gauss divergence and Stoke's theorems

    Homework Statement What's the difference between Green's theorem, Gauss divergence theorem and Stoke's theorem? The attempt at a solution I'm struggling to understand when i should apply each of those theorems. Here is what i understand. Please correct my statements below, if needed. Green's...
  44. E

    Gauss Law and Flux for variable charge density in a sphere

    Gauss Law and Flux for variable charge density in a sphere Homework Statement The charge density within a sphere varies as a constant, a, times its radius, r. Find an expression for the direction and magnitude of the electric flux, D, within the sphereHomework Equations Gauss' Law sphere...
  45. P

    Exploring Gauss' Law of Flux & Newton's Shell Method for Hollow Spheres

    While I do see how this makes sense using Newton’s Shell method, I don’t see how Gauss’ Law of Flux for a closed surface proves the same thing. Both Gauss’ Law of Flux and Newton’s Shell method make perfect sense to me in showing that when dealing with a point outside the hollow conducting...
  46. C

    Confusion about Gauss' law differential form

    http://einstein1.byu.edu/~masong/emsite/S1Q50/EQMakerSL1.gif Hi guys, I have a little confusion about the Gauss' law in differential form over here, obviously, many textbook wrote it in the above form, but actually, the only place at which divE is not zero is at the locations where the...
  47. R

    Matrix prerequisities for Gauss elimination

    hi all, Is there any matrix pre-requisities for Gauss elimination. Working on linear equations, I think I 've composed the global(stiffness) matrix of the LHS of linear equation.And found on the net the working code which uses Gauss elimination method, in the code beginning it checks...
  48. M

    Gauss Composition? and a naive composition law

    What exactly is gauss composition? I've heard of Manjul Bhargava's work, which apparently generalized gauss composition, but what is gauss composition? I would like to add that I've been thinking about quadratics polynomials with rational coefficients, and I discovered this composition law that...
  49. 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...
  50. 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=...
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