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. A

    Gaussian gun: Where does the extra kinetic energy come from?

    Probably a stupid question, but I do not get it... Here you can see an experiment demonstrating the Gaussian gun: Here I understand how momentum is conserved, i.e. the smaller mass of the ejected ball times its high speed is equal the bigger total mass of the recoiling masses times its...
  2. P

    B Gaussian Curvature and Riemmanian Geometry

    Please bear with me because I'm only in Pre-calculus and am taking basic high school physics. This is completely outside of my realm but curiosity has taken the better of me. I just learned last week about the difference between Euclidean Geometry and Riemmanian Geometry (from another thread...
  3. T

    Can Gauss' Law Be Applied Here?

    Homework Statement Homework Equations Gauss' Law: ∫E⋅da = qenc/ε0 E-field: E = kq/r2 The Attempt at a Solution I solved this using electric field equation, differential elements, and integration. The correct answer is, I think, E=-q/(8πε0R2) QUESTION: Can this be done via Gauss' Law? The...
  4. annoyingdude666

    Why infinite conducting rod - Gauss's Law , uses lambda?

    hi, i still don't understand why infinite thin-walled cylindrical shell or conducting rod use lambda rather than sigma ? lambda = C/m ,,, sigma = C/m^2 i mean when we look at conducting rod, the charges inside the conductor is zero, so the charges spread on the surface of conducting rod(have...
  5. R

    How Does Gauss' Law Apply to an Infinite Charged Wall?

    Homework Statement [/B] Assume that the infinite wall −2 < y < 2 is filled with a uniform charge of density ρv = 3 C/m3. Obtain an expression for Ey at a general point (0,y,0) and plot Ey as a function of y over −5 < y < 5. Homework Equations E = ρv / ( 4 π ε0 ρ) ∫∫∫D⋅ds = Qenc The Attempt at...
  6. A

    Does Gauss' Law use line integrals or surface integrals?

    In my physics textbook, I see Gauss' Law as https://upload.wikimedia.org/math/0/3/5/035b153014908c0431f00b5ddb60c999.png\ointE dA but in other places I see it as...
  7. S

    Gauss' Law vector form problem

    Homework Statement (a) A spherical insulating shell of radius R = 3.00 m has its centre at the origin and carries a surface charge density σ = 3.00 nC/m2. Use Gauss’s law to find the electric field on the x-axis at (i) x = 2.00m and (ii) x = 4.00 m. Give you answers in the vector form. (b) A...
  8. Elvis 123456789

    Calculating Electric Field Using Gauss' Law for a Charged Insulating Slab

    Homework Statement 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. Let the charge...
  9. N

    Verify Divergence Theorem for V = xy i − y^2 j + z k and Enclosed Surface

    Homework Statement Verify the divergence theorem for the function V = xy i − y^2 j + z k and the surface enclosed by the three parts (i) z = 0, s < 1, s^2 = x^2 + y^2, (ii) s = 1, 0 ≤ z ≤ 1 and (iii) z^2 = a^2 + (1 − a^2)s^2, 1 ≤ z ≤ a, a > 1. Homework Equations [/B]...
  10. L

    Can Gauss Be Converted to A/m?

    Apart from which is the numerical value of the conversion factor, is it allowed to make a conversion from gauss (unit of measure of the magnetic field B in CGS) to A/m (unit of measure of the magnetizing field H in SI)? -- lightarrow
  11. L

    Analog of Gauss' law in gravity

    Gauss law in case of sphere which has charge ##q## is ##\oint \vec{E}\cdot d\vec{S}=\frac{q}{\epsilon_0}## Is there some anologone for case of sphere with mass ##m## such that ##\oint \vec{G}\cdot d\vec{S}=4\pi \gamma m ## and what is ##\vec{G}## in that case?
  12. R

    Gauss' Law for a Nonuniform Field

    Homework Statement A closed rectangular surface with dimensions a = b and c where the faces perpendicular to the field are a*b. The left edge of the closed surface is located at position x = a, for c > a.The electric field throughout the region is nonuniform and given by E = 3*x xhat N/C...
  13. Omega0

    How to Calculate Gauss Curvature from a Mesh Surface?

    Hi! I would like to calculate the curvature for a surface S:R^2->R'3 numerically. The problem: I simply have the surface as a mesh like you see in the image attached. I calculated the linearly interpolated face normals in the nodes, too. You see the vectors. Question: How would you calculate...
  14. W

    I think this is about the Central Limit Theorem

    Homework Statement An engineer is measuring a quantity q. It is assumed that there is a random error in each measurement, so the engineer will take n measurements and reports the average of the measurements as the estimated value of q. Specifically, if Yi is the value that is obtained in the...
  15. PrincessYams

    What is the electric field inside a coaxial cable with given charge densities?

    Homework Statement A coaxial cable consists of two concentric cylindrical conductors as shown here: http://puu.sh/luFZx/7f3e1ccb07.png . The inner cylinder has a linear charge density of +λ1, meaning that each meter of the cable will have λ C of charge on the inner cylinder. The outer cylinder...
  16. THE HARLEQUIN

    Gauss' Differential law intuition

    Hi , while trying to prove gauss law for electric field from gauss theorem i came up with this problem . as Gauss' differential law expresses ∇⋅E = ρ/εο what i get from that is ... the divergence of electric field which is the flux density is related to the charge density ...but i can't get...
  17. W

    Conditional Expectation of Multiple Independent Random Varia

    Homework Statement Given X,Y,Z are 3 N(1,1) random variables, (1) Find E[ XY | Y + Z = 1] Homework EquationsThe Attempt at a Solution I'm honestly completely lost in statistics... I didn't quite grasp the intuitive aspect of expectation because my professor lives in the numbers side and...
  18. B

    Electric Field Inside a Dielectric-Filled Spherical Capacitor

    Homework Statement A spherical capacitor consists of two concentric spherical conductors of radii ##R_{1}## and ##R_2, (R_2 > R_1)##. The space between the two conductors is filled with a linear inhomogeneous dielectric whose relative permittivity varies with the distance ##r## from the...
  19. engnrshyckh

    Surface Charge Density of Coaxial Cylinder with Canceling Electric Fields

    a long straight wire has fixed -ve charge density of 39nC/m. the wire is enclosed by thin wall non conducting coaxial cylinder of radius 1.7m. the shall has positive charge density and its Field is such as that it will cancel the field due to wire. what will be the surface charge density of...
  20. N

    Capacitors in a series circuit W/ one dielectric

    Problem: When a dielectric slab is inserted between the plates of one of the two identical capacitors in Fig. 25-23, do the following properties of that capacitor increase, decrease, or remain the same: (a) capacitance, (b) charge, (c) potential difference (d) How about the same properties of...
  21. SnakeDoc

    Gauss' Law: Infinite plane with charge

    Homework Statement An infinite plane of charge has surface charge density 6.8 µC/m2. How far apart are the equipotential surfaces whose potentials differ by 100 V? In mm Homework Equations E=σ/(2ε0) The Attempt at a Solution So first I solved for E= 6.8e-6/(2*8.85e-12) = 384170.791 then...
  22. F

    Gauss' Theorem - Divergence Theorem for Sphere

    Homework Statement Using the fact that \nabla \cdot r^3 \vec{r} = 6 r^2 (where \vec{F(\vec{r})} = r^3 \vec{r}) where S is the surface of a sphere of radius R centred at the origin. Homework Equations \int \int \int_V \nabla \cdot \vec{F} dV =\int \int_S \vec{F} \cdot d \vec{S} That is meant...
  23. D

    Electric field inside and around a hollow sphere

    Hi everyone, I am wondering if anybody could help me out. For my study I got the following question but I got stuck in part C (see image below). I Found at A that due to symmetry all components which are not in Ar direction will get canceled out I found at B that there is only charge density at...
  24. SarahAlbert

    How to Find Electric Field for Concentric Spheres Using Gauss's Law?

    Homework Statement Two concentric spheres have radii a and b with b>a. The region between them is filled with charge of constant density. The charge density is zero everywhere else. Find E at all points and express it in terms of the total charge Q. Do your results reduce to the correct values...
  25. gracy

    Gauss' law for concentric circles

    Homework Statement 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 total charge -2q and the outer shell has charge +4q. a) calculate the electric field...
  26. Q

    Gauss' law in differential form

    I'm trying to understand how the integral form is derived from the differential form of Gauss' law. I have several issues: 1) The law states that ## \nabla\cdot E=\frac{1}{\epsilon 0}\rho##, but when I calculate it directly I get that ## \nabla\cdot E=0## (at least for ## r\neq0##). 2) Now ##...
  27. T

    Exploring the Limitations of Gauss's Law: A Case Study of a Line Charge in Air

    Homework Statement A line charge exists in air along the z-axis between z=0 and z=5 cm. It has a uniform charge density given by: ρl = 4(uC/m) Determine E at (0,10 cm, 0) Homework EquationsThe Attempt at a Solution [/B] I am using gauss law so I draw a cylinder around the wire Qenc = ρl *...
  28. A

    Gauss' Law: Charge enclosed zero = E field zero?

    Homework Statement A cylindrical shell of radius R and length H has its charge uniformly distributed on its curved surface Find the electric field at a point P from the axis, a distance r away, measured radially outward from the midpoint of the shell such that R>r Homework Equations φ =...
  29. P

    Using Gauss' law for spherical charge distribution

    Homework Statement The Earth is constantly being bombarded by cosmic rays, which consist mostly of protons. Assume that these protons are incident on the Earth’s atmosphere from all directions at a rate of 1366. protons per square meter per second. Assuming that the depth of Earth’s atmosphere...
  30. Rishabh076

    Gauss' theorem due to thin infinitely long sheet

    Our teacher derived an expression for electric field due to thin sheet using gauss law which was sigma/2*epsilon naught which was independent of r but dies that mean the field will be same even if r is 10000km but field is also equal to kq/r^2
  31. Domenico94

    Electric field outside of a cavity

    Homework Statement Hi everyone. I m just studying capacitors but I have problems with gauss law. In one exercise it says that we have a sphere(cavity) of radius r, with a charge q placed inside the sphere of it. Wie have to find the electric field inside and outside sphere. The solution says...
  32. K

    Dot product vs trigonometry in Gauss' law

    I'm currently writing my EP on various physical equations including Maxwell's equations, and I had to justify using the dot product of the normal unit vector and the electric field in the integral version. However, I can't think of a reason for not using trigonometry as opposed to the...
  33. amjad-sh

    Gauss' Law -- How did he come up with it?

    How did Gauss came out with his law εΦ=Qenc,where Φ is the flux and Qenc is the net charge inside the gaussian surface?Was it an experimental work or just a theoretical one? thanks.
  34. M

    Proof of Gauss' Law for Electrodynamics?

    I’ve been searching for a proof, using the equation for the electric field due to a moving point charge – given, for example, on page 438 of the Third Edition of David Griffith’s Introduction to Electrodynamics (equation 10.65) – that Gauss’s law holds for a moving point charge. There is no such...
  35. sergiokapone

    Convert Oersted to Gauss: Multiply by 4π

    How to convert 1 Oersted to 1 Gauus of magnetization vector? Simply multiplying by ##4\pi## ?
  36. gimak

    Gauss' law for point charge inside sphere off center

    Homework Statement If a point charge is inside a Gaussian sphere but is off center, why is its electric field still Qenc/(e0*4*pi*r^2)?Homework Equations surface integral of E*da=Qenc/e0The Attempt at a Solution If we draw cones out from the charge. the 2 surfaces from the cones' intersection...
  37. w3dnesday

    Where is the Force on a Proton 0.79FR Relative to the Surface of a Charged Ball?

    Homework Statement Assume that a ball of charged particles has a uniformly distributed negative charge density except for a narrow radial tunnel through its center, from the surface on one side to the surface on the opposite side. Also assume that we can position a proton anywhere along the...
  38. diracdelta

    How Far from the Target Does a Machine Gun Hit 50% of Its Bullets?

    Homework Statement [/B] While shooting at target, soldier shoots from machine gun fixed in a way so it can rotate only around z axis. deviation from center of target due to twitching of machine gun is random variable with Gauss distribution. Deviations are such that inside of 20m from center of...
  39. ChrisVer

    Toss coin probabilities (Bino vs Gauss approx)

    Hi, I calculated the probability to this scenario: getting between 3 and 6 Heads after tossing a coin for n=10 trials... The binomial probability for this is: P(3 \le k \le 6) = \sum_{k=3}^6 Bi(k;p,n)= \sum_{k=3}^6 \frac{n!}{k!(n-k)!} p^k (1-p)^{n-k} =\sum_{k=3}^6 \frac{10!}{k!(10-k)!}...
  40. B

    Exploring Gauss' Law: Understanding Spheres and Flux in Closed Surfaces

    Flux through a closed surface is zero due to external charge but why it is not so in case of sphere
  41. N

    Integral Form of Gauss' Law at Center of Finite Wire

    At the exact center of a finite wire (i.e. a distance, say $L/2$ from each end), why can I not apply Gauss's Law in integral form to find an EXACT solution for the electric field? At the center of the wire, $E$ is entirely radial, so it seems like I should be able to draw an infinitesimally...
  42. P

    Foundations What's a good book for last year of A levels Maths?

    I'm looking for a book to self-study this summer before my last course of Bachillerato (A Levels or High School in other countries). My performance in Mathematics has only improved and I've just been given the maximum mark this last term (10/10 or A+). This has motivated me a lot to keep...
  43. V

    Divergence Theorem Question (Gauss' Law?)

    If F(x,y,z) is continuous and for all (x,y,z), show that R3 dot F dV = 0 I have been working on this problem all day, and I'm honestly not sure how to proceed. The hint given on this problem is, "Take Br to be a ball of radius r centered at the origin, apply divergence theorem, and let the...
  44. J

    MHB How to Use Gauss Chebyshev Formula for Approximating Integrals with n=3?

    Use Gauss Chebyshev formula with $n=3$ to approximate the value of the integral. $$\int \frac{x^4}{\sqrt{1-x^2}}dx$$ from -1 to 1. Also compare the result with true value, where the zeros and the corresponding weights of the following simple set of orthogonal polynomial is given as below...
  45. H

    Gauss Law for finite line/plate

    Homework Statement I just noticed that whenever I'm doing a problem involving Gauss Law, it always involves an infinite line/plate. I can't seem to figure out why it must be infinite large/long. Here is an explanation I read, but don't quite understand...
  46. H

    Gauss' Law: Calculating charge enclosed

    Homework Statement I've been doing a few Gauss' Law problems and I'm slightly confused about calculating charge enclosed by a nonconducting sphere. So I have done 2 problems that involve finding the electric field inside nonconducting spheres: 1. Charge is uniformly distributed 2. Charge per...
  47. B

    Power flow studies using Jacobi and Gauss Seidel

    I have been asked to solve the actual load flow distribution in a given power network using two iterative methods. I have chosen Jacobi and Gauss Seidel. we have to use MATLAB to find where the solution converges. I am fine with all of this, but we have been tasked with providing graphical...
  48. jlefevre76

    Understanding the Physics of a Coilgun: A Beginner's Guide

    Hey, I've seen a few posts on this without any responses I really thought helped (at least help answer my question). So, I was hoping somebody on the forums here could help walk me through the basic physics of a coilgun. Basically, how could you characterize the magnetic field inside the...
  49. P

    Gauss Law in a plane sheet, and thick sheet (Infinite)

    We have learned the below formula for a plane sheet of charge with thickness. E=σ/ϵ and the one below for with no thickness (negligible) E=σ/2ϵ The problem, I am facing is digesting the derived equations. It is one thing for sure that these formulas must be right. But then the fact that E...
  50. Th3HoopMan

    Correlation between Iterative Methods and Convolution Codes

    Hey guys so I have this Calc 3 project and the end is throwing me for a loop. I've done the encoding part, and I've coded the standard iterative methods, but I don't see how the two correlate so I can use the iterative methods to decode a "y stream" with the inputs specified...
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