What is Gauss law: Definition and 181 Discussions

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. Hijaz Aslam

    Gauss Law of Cube in non-uniform linear Electric Field.

    Gauss's Law states that if a Gaussian Surface encloses a charge ##q_{enc}## then the electric flux through the Gaussian Surface is given by ##\phi=q_{enc}/\varepsilon_{o}## . It also states that any external field does not contribute to the Electric Flux through the Gaussian Surface. I am bit...
  2. M

    Gauss Law: Proofs and Electromagnetism Resources

    about gauss law! is there any precise proof for gauss law? why ø=q/ε always regardless how the charge is distributed inside the surface and if anyone know a good book for electromagnetism please type its name for me.. thank u
  3. Sneakatone

    Line Charge and Charged Cylindrical Shell (Gauss law)

    Homework Statement An infinite line of charge with linear density λ1 = 6.2 μC/m is positioned along the axis of a thick insulating shell of inner radius a = 2.7 cm and outer radius b = 4.4 cm. The insulating shell is uniformly charged with a volume density of ρ = -552 μC/m3.1) What is λ2, the...
  4. H

    Gauss law and electric current

    According to the Gauss law, the extra charges gather on the surface of a conductor. When there is a current in a conducting wire, do the charges only move on the surface of the wire or we have current also inside the wire? If we also have current inside the wire how is it compatible with Gauss law?
  5. A

    Is Gauss's Law Valid for Moving Charges?

    I found in this forum an old thread regarding this topic, but as it didn't have (in my opinion) a satisfactory answer, I decided to open a new one. Usually when one begins to study Electromagnetism, Coulomb's law in introduced as an experimental result valid for static point charges. From...
  6. S

    Archived Gauss Law and the wrong Gaussian surface.

    Homework Statement The problem was to calculate the electric field inside an infinite length cylinder (with radius R) with a non uniform charge density. The charge density depended on r. Its easy enough to solve using a gaussian cylinder with r less than R. But what if I wanted to complicate...
  7. E

    How Does Gauss' Law Apply to Nested Spherical Surfaces with Varying Radii?

    Hi all, Lets suppose we have a sphere. This sphere has density of \rho(r) from 0 to the sphere's final radius R. Now, we all know that from Gauss law, the charge inside the sphere equals to the integral of the surface of the sphere. If we set our normal vector to be as usual out of the...
  8. N

    Gauss Law for non uniform spherical shell

    So i can see by symmetry arguments why The electric field inside a uniformly charged spherical shell would be zero inside. But what about a non uniformly charged spherical shell. Say most of the charge is located on one side, why is the electric field still zero? I can see that the flux...
  9. N

    Can You Help Me Solve the Infinitely Large Integral ∫|r|-3dV in Gauss Law?

    Hey. I want to use integrals-math to get from Gauss law in divergence form to the one in integral form. I know you can do it by simply accepting ∇*E dV = ρ/ε => ∫ ∇*E dV= ∫ρ/εdV = Q/ε = ∫E*dA, but I want to do it another way. I want to begin with ∫∇*E*dV and end up with Q/ε. So: E =...
  10. E

    Electric field and gauss law for different models of sphere

    Hello all! I actually have a few doubts regarding "gauss law" when applied "for different models of sphere" First, If we place a charge 'Q' inside a spherical shell at the center (somehow) then it should come out to its surface that means in no way can we do it. True or False? Next...
  11. Roodles01

    Gauss Law? Average charge density

    Homework Statement Hi. A cylinder of radius r & length L whose charge density distribution is given by ρ = C/2 * r3 where r = radial distance in cylindrical coordinates C = constant show that the average charge density ρbar = a3 C / 5Homework Equations Gauss differential law div E = ρ / ε0 div...
  12. L

    Need help with gauss law and charged ring AP Physics FRQ

    Homework Statement 1. 2. Homework Equations ∫E.dA = Qenc/\epsilon_{o} \lambda=Q/L \rho=Q/V V= q/4πε_{o}r The Attempt at a Solution these types of problems i suck at, i don't know how to do these at all independently, and is there any difference in question 2 if there is an insulator or...
  13. S

    Electric Field Direction at 14.1 cm from a Charged Cylinder and Conducting Shell

    Homework Statement A long non-conducting cylinder has a charge density ρ = αr, where α = 6.34 C/m4 and r is in meters. Concentric around it is a hollow metallic cylindrical shell. Diameter 1: 4.36 cm Diameter 2: 10.4 cm Diameter 3: 16 cm What is the direction of the electric field at...
  14. F

    Gauss law for semi-infinite sheet of charge

    We know that for an infinite sheet of charge, E = λ / 2ε, where λ is the surface charge density. This can be easily found using gauss law and a cylinder perpendicular to the sheet as a gaussian surface. We will end up with something like Qinc/ε = 2E ∫dS, from which we find E = λ / 2ε. Now say...
  15. D

    Gauss Law and Electric Field of a Dipole

    Hi, I don't understand this: You got a dipole, and a resulting electric field from it like this(hyperphysics): As z approaches infinity, the field becomes zero. But if you draw a gaussian surface round the charges, then the net enclosed charge is zero.So the electric field must be zero, no...
  16. Negi Magi

    How to justify the shell theory by using Gauss Law?

    "As the ball gets deeper under the surface of the Earth, the layers above it stop exerting gravitational force, and all that matters is the mass underneath." How to justify this sentence is true?
  17. H

    Spherical Charge Ball, Gauss law

    Homework Statement A spherical charged ball of radius a has total charge Q; there is no charge outside the ball and no sheet-charge on its surface. The (radial) field inside the ball has the form Er(r) = constant x r2 for r between 0 and a. Use Gauss's Law in integral form to evaluate the...
  18. P

    Gauss Law with Charged Sphere and Infinite Parallel Plates

    Hi guys, this is more of a conceptual question, so I hope you guys can give me a detailed explanation if possible. Homework Statement Find the Electric Field inside a Charged Sphere (charge only on the surface) and between two Parallel Plates (oppositely charged) separated by some distance d...
  19. 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...
  20. 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}
  21. 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...
  22. M

    Gravitational Acceleration (Gauss law)

    Homework Statement Homework Equations Just to clarify the question, the value given for R2 is the overall radius of Earth, it isn't R1-R2. (At least, that's my interpretation given that the R2 value is approx. the Earth's radius) The Attempt at a Solution Don't really know how...
  23. 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...
  24. 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...
  25. B

    Gauss law differential form.

    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...
  26. 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...
  27. 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...
  28. 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...
  29. 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...
  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. 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...
  32. 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...
  33. 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...
  34. 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...
  35. H

    Understanding the Contradiction in Gauss Law for Planar Capacitors

    we know that the electric field between the planes of planar capacitor is σ/ε (according to gauss law) however we have two conducting plate that each plate produe this electric field that are in the same direction therefore we must have E=2σ/ε what is the reason for this contradiction.
  36. P

    Gauss Law Problem with Cylinders

    Homework Statement An infinitely long, non-conducting cylinder of radius R carries a uniform volume charge density ρ. Find the magnitude of the electric field for 0 < r < R Homework Equations EA=Qin/εo The Attempt at a Solution I am debating whether the answer should be ρr^2/2εoR...
  37. M

    Gauss's Law for Electric Field Components in a Charged Sphere

    An infinite line of charge with linear density λ = 7.6 μC/m is positioned along the axis of a thick insulating shell of inner radius a = 3 cm and outer radius b = 5 cm. The insulating shell is uniformly charged with a volume density of ρ = -611 μC/m3. (see attachment) What is Ex(R), the value...
  38. N

    Can Gauss's Law Be Applied to a Charged Circular Ring?

    Homework Statement A circular ring of radius a carries a uniform charge q C/m and is placed on x-y plane with axis same as z axis. To determine E at P(0,0,h). My ques is can't we apply gauss theorem? if yes then what will be the gaussian surface? if no then why not? Homework Equations...
  39. C

    Solving Gauss Law Question: Q/(πR^4)

    Hi Im getting a slightly different answer to the one that is needed for the following question: 2) A positive charge Q is distributed throughout a spherical volume of radius R in vacuum. The charge density rho varies with the radius according to the linear law rho = a r. Show that the...
  40. E

    Flux & Gauss Law: Electric Field Lines & Types of Areas

    I know that electric flux is defined as the number of electric field lines passing through an area but what kinda area are we talking about. Does it have to be perpendicular to the field lines like this or could it be at an angle like this does it have to be a flat area on 1 plane like the...
  41. G

    Why is the Electric Field Constant Along a Charged Cylinder's Surface?

    Am really suprised when deriving electric field due to a uniform charged thin long rod! It was suprising to have a cylinder as a gausian surface! actualy is that posible, that all along the surface of the cylinder has same field intensity and why? also why are there no electric flux along...
  42. M

    Gauss Law Problem to determine F/A

    Three large but thin charged sheets are parallel to each other as shown in the figure . Sheet I has a total surface charge density of 7.9 nC/m^2, sheet II a charge of -3.3 nC/m^2, and sheet III a charge of 5.4 nC/m^2. Figure: ----------------(I) ----------------(II)----------------(III)...
  43. N

    Charge Distribution on Concentric Spheres: Exploring Gauss's Law

    Homework Statement Consider two concentric conducting spheres. The outer sphere is hollow and initially has a charge Q1 = -6Q deposited on it. The inner sphere is solid and has a charge Q2 = +1Q on it. (a) How much charge is on the outer surface? How much charge is on the inner surface...
  44. L

    Electricity, Gauss law concept question

    A certain region bounded by an imaginary closed surface contains no charge. Is the electric field always zero everywhere on the surface? If not, under what circumstances is it zero on the surface. I think it is zero everywhere because as the electric field is entering the closed surface, it...
  45. K

    Gauss law, having problem with spherical load distribution, me

    A region in space containing cargo which is distributed spherically so that the stocking load ρ is given by the equotations: ρ = a for r<=R/2 ρ = 2a(1-r/R) for R/2<=r<=R ρ=0 for r>=R The total charge Q is 3*10^-17 C, the radius R of the overall distribution is 2*10^-14 m and a is a constant...
  46. C

    How to get zero electric field inside spherical shell without using Gauss law

    Now, i am trying to prove that electric field inside spherical shell whose constant surface charge density \rho is zero. Usually, it is proved by using Gauss law (there is no charge enclosed inside gaussian surface so there is no electric field inside the sphere). But, whe i am trying to solve...
  47. N

    Gauss law and nonconducting spherical shells

    Homework Statement there are two nonconducting spherical shells fixed in place. shell 1 has uniform surface charge density 6.0 uC/m^2 on its outer surface and radius 3.0cm. shell 2 has uniform surface charge density 4.0 uC/m^2 on its outer surface and radius 2.0cm. the shell centers are...
  48. 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...
  49. 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...
  50. 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...
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