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. D

    How to Solve a Gauss' Law Problem in a Spherical Region?

    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...
  2. 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...
  3. B

    Electrostatic energy with gauss' law

    Homework Statement A solid sphere contains a uniform volume charge density (charge Q, radius R). (a) Use Gauss’s law to find the electric field inside the sphere. (b) Integrate E^2 over spherical shells over the volumes inside and outside the sphere. (c) What fraction of the total electrostatic...
  4. Saladsamurai

    Solve Gauss' Law for Electric Field - Help Here!

    ! AHH Gauss' Law! Homework Statement Figure 23-27 is a section of a conducting rod of radius R1 = 1.30 mm and length L = 11.00 m inside a thick-walled coaxial conducting cylindrical shell of radius R2 = 10.0R1 and the (same) length L. The net charge on the rod is Q1 = +3.40 × 10^-12 C; that...
  5. M

    Does Gauss' Law Hold for Non-Conservative Electric Fields?

    the electric field produced due to a time varying magnetic field is non-conservative in nature. does it follow gauss law?
  6. J

    How Does Gauss's Law Apply to Electric Fields at Points P2 and P3?

    [SOLVED] Gauss and E-Field Homework Statement http://img443.imageshack.us/img443/9452/eletroof9.th.png My main problem with this problem is finding the electric field at Point 2 (P2) Homework Equations The Attempt at a Solution I derived the electric field using Gauss's Law for a...
  7. tony873004

    How Does Gauss' Law Apply to Infinite Planes with Different Charge Densities?

    I'm still not confident with these kinds of problems. Hopefully I got it right, but can someone double check my work? Thanks! Two parallel, infinite planes are separated by a distance d. Find the electric field everywhere (a) if both planes carry a surface charge density \sigma and (b)...
  8. P

    Explaining Gauss Law: Easy Guide

    hi, i hav read gauss law chapter from my textbook but still i m facing problems based on it. please explain me GAuss law in an easy language.
  9. M

    Gauss Sphere Surface / U = -W / f=ma=qE

    Homework Statement What is the escape speed for an electron initially at rest on the surface of a sphere with a radius of 1.0 cm and a uniformly distrubted charge of 1.6 X 10^-15 C? That is, what initial speed must the electron have in order to reach an infinite distance from the sphere and...
  10. J

    How Does the Electric Field Vary with Distance in a Cylindrical Shell?

    Homework Statement Consider an infinitely long cylindrical metallic shell with a line of charge within and coincides with the axis of the cylindrical shell as shown in Figure . How does E field vary with r? Homework Equations E.A=q/\epsilon E=E field, A = surface area The...
  11. G

    Gauss' law (1/r^3 instead of 1/r^2)

    Homework Statement If the electric field of a point charge were proportional to 1/(r^3) instead of 1/(r^2), would Gauss's law still be valid? Explain reasoning. Homework Equations The Attempt at a Solution Considered a spherical Gaussian surface centered on a single point charge.
  12. M

    Solve Gauss Curvature for Ruled Surface: A(s)+tB(s)

    I'm reviewing for my final and there is a question I can't seem to solve. If anyone could help me with it I would appreciate it very much. A ruled surface has the parameterization of the form: x(s,t) = A(s) + tB(s) where A(s) is unit speed, |B(s)| = 1. Show that: K<or= to 0. So...
  13. G

    Is the Electric Field Always Zero on an Imaginary Surface Containing No Charge?

    Homework Statement A certain region of space bounded by an imaginary closed surface contains no charge. Is the electric field always zero on the surface? If not, under what circumstances is it zero on the surface? Homework Equations Φ = Qenclosed÷εo = EA The Attempt at a Solution...
  14. marcus

    Sydney Coleman (1937-2007) was a descendant of Gauss

    Sidney Coleman (1937-2007) was a descendant of Gauss Arivero informed us of this back in 2005, about the time a celebration for the much beloved and admired Sidney Coleman was held at Harvard---the "Sidneyfest". Attended by a who's who of Nobel laureates and the like. Anyway Arivero came up...
  15. T

    Gauss Row Operations: Solving by Hand?

    I am just interested is there anyway to solve these through a specific method by hand. I know that you can produce an algorithm so that you can solve these into upper triangle form but is there a way to do it by hand other than by inspection.
  16. P

    Gauss' Law With an Infinite Cylinder of Charge

    [SOLVED] Gauss' Law With an Infinite Cylinder of Charge Homework Statement The test question was to find the potential difference between a point S above a cylinder of charger per length lambda, and a point on the surface of the cylinder having radius R and infinite length. Homework...
  17. M

    Solve Gauss' Law Problem: Electric Field at P on Spherical Shell

    Homework Statement An insulator in the shape of a spherical shell is shown in cross-section above. (see attached .gif) The insulator is defined by an inner radius a = 4 cm and an outer radius b = 6 cm and carries a total charge of Q = + 9 mC (1 mC = 10-6 C). (You may assume that the charge...
  18. R

    Electric Flux and Gauss' Law of point charges

    Homework Statement A point charge q_{1} = 4.15 \times 10^-6 is located on the x-axis at x = 1.80 m, and a second point charge q_{2} = -5.80 \times 10^-6 C is on the y-axis at y = 1.10 m. What is the total electric flux due to these two point charges through a spherical surface centered at...
  19. P

    Gauss' Law (Why the opposite sign?)

    Homework Statement 4. In Fig. 23-28, a butterfly net is in a uniform electric field of magnitude {E = 3.0} mN/C. The rim, a circle of radius a = 11 cm, is aligned perpendicular to the field. The net contains no net charge. Find the electric flux through the netting...
  20. B

    Use Gauss' Law to find the magnitude of E in a sphere

    Problem Problem 27.56 A sphere of radius R_0 has total charge Q. The volume charge density (C\m^3) within the sphere is \rho(r) = C/(r^2), where C is a constant to be determined. Part A The charge within a small volume dV is dq = \rhodV. The integral of \rhodV over the entire volume of...
  21. E

    Solve Gauss' Law: Volume Charge Density in Region r > a

    Homework Statement An electric field in the region r > a is given by E,r = 2*A*cos(theda)/r^3 E,theda = A*sin(theda)/r^3 E,phi = 0 A = constant Find the volume charge density in this region. E,r and E,theda and E,phi are the components of E in the r, theda, and phi directions...
  22. M

    How Does Gauss' Theorem Explain Tension in a Wire Connecting Charged Spheres?

    Two identical conducting spheres each having a radius of 0.460 cm are connected by a light 1.20 m long conducting wire. Determine the tension in the wire if 69.2 (micro)C is placed on one of the conductors. (Hint: Assume that the surface distribution of charge on each sphere is uniform.)...
  23. F

    Electric field between two wires and gauss law

    I'm not entirely sure how to word this without a diagram, but please bare with me! In an ideal case, the charge on a wire is evenly distributed. According to Gauss' Law, an electric field from a charged wire decays with 1/r where r is the distance from the centre of the wire. Say two...
  24. F

    Solving Gauss' Law for a VDG Dome: Electric Field at 25cm

    Homework Statement Use Gauss' law to find the charge density on a Van Der Graff dome (r=40cm) if it is charged to 100kV. What is the electric field strength at r=25cm? I understand gauss's law and I know that I need to use it to find the total charge enclosed on the dome. I can then work out...
  25. N

    Can Gauss' Law Determine Intensity in Complex Spherical Charge Distributions?

    Homework Statement Is it possible to use Gauss' law to find intensity of a spherical charge distribution where the charge distribution (i)is non-homogeneous in general...i.e. dependent on (r,theta,phi) (ii)can be thought of as a made up of concentric spherical shells of different...
  26. D

    Gauss' law to calculate electric potential

    I would appreciate hints on how one can calculate the dependence of the electric potential as a function of distance r from an isolated charge Q in 5-dimensions
  27. A

    Harmonic Functions and Gauss' Theorem

    Homework Statement Let f be an element of C^2 (R^3=> R) be harmonic in the ball |x|< 1 (i.e. the laplace of f would be 0). Prove that f = 0 inside if it vanishes on the surface |x|=1. What if the dF/dn=0 (partial derivative) on the surface |x|=1 [What is div(f grad f)]? Also think of heat...
  28. S

    Solving "If the Photon Had Mass m" Problem with Gauss' Law

    hi I have this question, I need your help: If the photon had mass "m" , show that the Gauss' law would no longer be true. Note that the electric poential for a point charge would then have a form V(r) = e/r exp ( -mc/h * r ) Thank you
  29. S

    .Showing Gauss' Law is False with Photon Mass "m"

    hi I have this question, I need your help: If the photon had mass "m" , show that the Gauss' law would no longer be true. Note that the electric poential for a point charge would then have a form V(r) = e/r exp ( -mc/h * r ) Thank you
  30. S

    Solving Gauss' Law: E Field & Volume Charge Density

    Homework Statement 1.)Two large metal plates of area 1.0m^2 face each other. They are 5 cm apart and have equal but opposite charges on their inner surfaces. If the magnitude E of the electric field between the plates is 55N/C, what is the magnitude of the charge on each plate?Neglect edge...
  31. R

    Electric dipole and Gauss' Law

    We have an electric dipole. Now, let us draw a Gaussian surface around our electric dipole. Now, the total charge enclosed by our Gaussian surface is zero, so according the Gauss' Law the flux through the Gaussian surface is zero, and so is the electric field intensity due the electric dipole...
  32. Y

    Gauss' Law - Planar Symmetry HELP

    Homework Statement A square plate of edge length 9.0 cm and negligible thickness has a total charge of 6.3 x 10-6 C. (a) Estimate the magnitude E of the electric field just off the center of the plate (at, say, a distance of 0.50 mm) by assuming that the charge is spread uniformly over the...
  33. M

    Discovering Ceres: Gauss and the Least Square Approach

    I've been reading 'Measuring the World' by D. Kehlmann, i have reached to the part when Gauss using the least square approach (¿? still not 100% sure) discovered the orbit of 'Ceres' but my question is How did he get it??.. assuming the orbit is elliptic and using some possible meditions how...
  34. B

    Using Gauss Law to Solve a Planar Slab of Charge Problem

    Hey, I need help to use the Gauss law in this problem: We have A planar slab of charge with a charge density ρv=ρvosin(2*pi/(2*a)),for -a<x<a the thickness of the stab is 2*a. the horizontal y-axis passes through the middle of the stab. the x-axis is vertical a) Find the electric field...
  35. S

    Cylindrical Shells and Gauss' Law

    Homework Statement An infinitely long cylindrical shell of radius 6.0 cm carries a uniform surface charge density sigma = 12 nC/m^2. The electric field at r = 5.9 cm is approximately a.0.81 kN/C b.zero. c.1.3 kN/C. d.12 kN/C. e.0.56 kN/C...
  36. S

    Spheres, Plates, and Gauss' Law

    Homework Statement A sphere of radius 8.0 cm carries a uniform volume charge density rho = 500*10^-9 C/m^3. What is the electric field at r = 3.0 cm? a.36.0 N/C b.230 N/C c.140 N/C d.565 N/C e.450 N/C Homework Equations E = (k*Q*r)/(R^3), where...
  37. S

    Spherical Shells and Gauss' Law

    Homework Statement A small, insulating, spherical shell with inner radius a and outer radius b is concentric with a larger insulating spherical shell with inner radius c and outer radius d. The inner shell has total charge q distributed uniformly over its volume, and the outer shell has...
  38. A

    Using Gauss (Divergence) theorem to find charge distribution on a conductor

    Hi, I hope this is advanced enough to warrant being in this section: I'm supposed to use the Gauss theorem (and presumably his law) to show: 1)The charge on a conductor is on the surface. 2)A closed hollow conductor shields its interior from fields due to charges outside, but doesn't...
  39. I

    Fundamental Theorems for Vector Fields

    Please check my work for the following problem: Homework Statement By subsituting A(r) = c \phi(r) in Gauss's and Stokes theorems, where c is an arbitrary constant vector, find these two other "fundamental theorems": a) \int_{\tau} \nabla \phi d \tau = \int_{S} \phi ds b) - \int_{S} \nabla...
  40. R

    Solve Gauss' Law Problem: Electric Flux Hemisphere

    Hello, everyone. I hope that you can help me get started on one of the problems I have due this week. Homework Statement Find the electric flux through the hemisphere z = (square root of a^2 - x^2 - y^2). - The Attempt at a Solution I'm fairly certain I need Gauss' law to help...
  41. J

    How Does Gauss' Law Apply to Non-Zero Electric Flux in a Rectangular Box?

    Homework Statement A charge Q is located inside a rectangular box. The electric flux through each of the six surfaces of the box is: Φ1=+1500 Φ2=+2200 Φ3=+4600 Φ4=-1800 Φ5=-3500 Φ6=-5400. (unit: N x m^2/C) What is Q?Homework Equations ΦE =Q/ε The Attempt at a Solution Add up all the Φ's to...
  42. H

    C/C++ Would you mind if you give me code for gauss elimination by C++

    H e l p m e I want code for gauss elimination by C++ for solving my homework
  43. L

    Confirm/Deny Vector Surface of z=e^(1-x^2-y^2) using Gauss' Theorem

    I have a problem that involves computing the vector surface of z=e^(1-x^2-y^2) where z is greater then or equal to 1, for a Vector Field F=xi+yj+(2-2*z)k. This is to be done using Gauss' theorem. I got an answer of 0, which doesn't seem right I just want to ask if anyone can confirm or deny the...
  44. C

    What factors affect the electric field around a charged conduction sphere?

    Ok for example, if a solid conduction sphere was charged to 500volts and had radius of 1cm. Then charge, Q = VR = 5? So the E field just outside the sphere would be E = (1/4pi epsilon) x charge/R^2 = 4.5 x 10^14? Or am i getting confused?
  45. C

    How to Derive Gauss's Law from the Divergence Theorem?

    Can anyone help me with how to derive Gauss's law (differential form) from the Divergance theorem?
  46. S

    How Do Gauss' and Stokes' Theorems Apply to These Integral Problems?

    Hi guys, I am having trouble with this "simple" problem involving these two theorems: Find the value of the integral (A dot da) over the surface s, where A = xi - yj + zk and S is the closed surface defined by the cylinder c^2 = x^2 + y^2. The top and bottom of the cylinder are z= 0 and...
  47. S

    Easy gauss' law question that I wanna make sure I didn't make too easy

    A sphere of radius a has its center at the origin, and has charge density p=Ar^2 another sphere of radius = 2a is concentric with the first. Find the flux SE*da through the larger sphere, where that's the surface integral of E dot da, like usual. It'd just be Qin/e where e is that constant...
  48. S

    Gauss Law and a hollow spherical shell

    A hollow spherical shell carries a charge density \rho = \frac{k}{r^2} in the region a<= r <= b. As in the figure Find the elctric field in these three regions i) r <a ii) a<r<b iii) r>b SOlution: for r<a it simple.. no exclosed charge for any gaussian sphere within that region...
  49. S

    Gauss' Law and a uniform surface charge

    Use Gauss' Law to find the field inside and outside a long hollow cylindrical tube which carries a uniform surface charge sigma. It has been a few months since i did this so i may be a bit rusty As i can recall if there is a point inside a holow cylindrical tube there is no enclosed charge...
  50. P

    The Parallel Plate Capacitor and Gauss Law

    Hi Can anyone please explain Gauss Law in simple terms for me? I really don't understand the electric flux and formulas in this law. My book is very short on explaining this law.
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