Gauss law Definition and 184 Threads

In physics and electromagnetism , Gauss's law, also known as Gauss's flux theorem, (or sometimes simply called Gauss's theorem) is a law relating to the distribution of electric charge to the resulting electric field. In its integral form, it states that the flux of the electric field out of an arbitrary closed surface is proportional to the electric charge enclosed by the surface, irrespective of how that charge is distributed. Even though the law alone is insufficient to determine the electric field across a surface enclosing any charge distribution, this may be possible in cases where symmetry mandates uniformity of the field. Where no such symmetry exists, Gauss's law can be used in its differential form, which states that the divergence of the electric field is proportional to the local density of charge.
The law was first formulated by Joseph-Louis Lagrange in 1773, followed by Carl Friedrich Gauss in 1813, both in the context of the attraction of ellipsoids. It is one of Maxwell's four equations, which forms the basis of classical electrodynamics. Gauss's law can be used to derive Coulomb's law, and vice versa.

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  1. B

    Electric field of a charged nucleus (sphere) Gauss Law

    ok guys.. this question is regarding a spherical nucleus with radius R related to Gauss's Law... so where the electric field given as the following: E(r) = Q/4*pi*epsilon-nought(r^2+R^2) 1. the questions asks "why this model/behaviour for r>>R might be "reasonable" 2. what q(r) is needed...
  2. J

    Charge distribution (Gauss law)

    Claim: A charged sphere will have it's charges disperse (uniformly for symmetrical objects) on the outer surface. Proof: Consider a sphere charged to some amount q. If we take small gaussian surfaces within the sphere, it will have \vec{E} = 0 on the closed gaussian sphere [since it is an...
  3. S

    Gauss Law and Electrostatic Field

    Homework Statement Use Gauss' law and symmetry to find electrostatic as a function of position for an infinite plane of charge. Let the charge lie in the yz-plane and denote the charge per unit area by \rho=\alpha*e^{-abs(x/b)} Homework Equations Q=triple integral of density The Attempt at...
  4. A

    How Is Charge Distributed in a Conductor with an Internal Cavity?

    1. The Question An isolated conductor of arbitrary shape has a net charge of +10\times10^{-6}C. Inside the conductor is a cavity within which is a point charge q = +3\times10^{-6}C. What is the charge on the outer surface of the conductor? 2. The attempt at a solution On cavity wall...
  5. S

    Electrostatic field ( Gauss Law )

    Homework Statement Assuming that an infinitely long line charge of 50(pC/m) parallel to the y-axis at x=2(m) and z=1(m), determine the electric intensity at the point (-1, 5, -3). The answer given : -0.18(ax0.6 + az0.8)(V/m)Homework Equations Electric field intensity due to an infinite...
  6. B

    Finding Earth's Mass Using Gauss Law

    Is it possible to find the mass of the Earth based on the Earth's volume mass density, roe = A-Br=R, where A = 1.42 x 104 kg/m3, B = 1.16 x 104 kg/m3, and Earth’s radius R = 6.370 x 106 m I know that based on Gauss Law that (closed integral) g x da = -4Gmin, where g is the total electric...
  7. B

    Calculate Earth's Mass Using Gauss Law & Density

    Is it possible to find the mass of the Earth based on the Earth's volume mass density, roe = A-Br=R, where A = 1.42 x 104 kg/m3, B = 1.16 x 104 kg/m3, and Earth’s radius R = 6.370 x 106 m I know that based on Gauss Law that (closed integral) g x da = -4Gmin, where g is the total electric field...
  8. B

    How Do You Determine the Mass of Earth Using Gauss's Law for Gravitation?

    Homework Statement Problem 1. A block having mass m and charge +Q is connected to an insulating spring having force constant k. The block lies on a frictionless, insulating horizontal track, and the system is immersed in a uniform electric field of magnitude E directed as shown in Figure P25:7...
  9. 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
  10. 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...
  11. 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??
  12. 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...
  13. A

    Charge inside a charged sphere (Gauss law)

    Suppose we have a sphere with a uniform surface charge. According to Gauss law the electric field inside such a sphere is zero. So if I put a charge ( let me call it Q from here) in it, it wouldn't experience any force, would it? What I don't understand is this: the charge Q we actually put...
  14. 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...
  15. 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...
  16. 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...
  17. 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...
  18. 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...
  19. 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...
  20. 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 /...
  21. 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...
  22. 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...
  23. 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.
  24. 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...
  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. 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...
  27. 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...
  28. 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.
  29. P

    The Parallel Plate Capacitor and Gauss Law?

    The Parallel Plate Capacitor and Gauss Law? Hi I really do not understand these two things. I read like every single book on this things but still am a lot confused about these two concepts. Can anyone explain me in the most simplest terms of all? I would really appreciate that. What is this...
  30. R

    Electric Field Magnitude of Cylinder w/ Uniform Charge

    So question : We have cored cilynder. Inner radius 10 cm, outer radius 20 cm. In the walls of the cilynder uniformed charge 2nK/m^3. Find electric field magnitude at the points from axes 8cm 18cm 28cm. Sorry for my english.
  31. G

    What is the Physical Significance of Curl in Gauss Law?

    is gauss law (i.e surface integeral of E.ds is equal to charge enclosed upon epsilon not ) valid for charges in motion or is it just valid for electrostatic conditions ?
  32. M

    Solving Gauss Law Problem: Electric Field on Hollow Sphere

    Hi, I have this problem in my Physics Book: The electric field everywhere on the surface of a hollow sphere of radius 0.75m is found to be 890 N/C and points radially toward the center of the sphere, (a) What is the net charge within the sphere's surface? (b) What can you tell about the...
  33. S

    Damn Gauss law is so confusing

    Positive charge is uniformly distributed throughout a non conducting cylindrical shell of inner radius R and outer radius 2R. What radial depth beneath outer surface of the charge distribution is the elctric field strength equal to one half the surface value? errr e0 = epsilon 0 the...
  34. S

    Still more problems with Gauss Law

    Ok I'm realllly unsure about this! If a spherical cavity of radius 3.66cm in a piece of metal (kind of cube, but not a perfect cube) has a charge of +Q at it's centre and there is a point P1 located half way between the spherical cavity and it's surface and a point P2 located in the metal...
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