What is Gauss's law: Definition and 380 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. 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...
  2. P

    Gauss's Law problem involving a Cylinder

    Homework Statement The figure a shows a narrow charged solid cylinder that is coaxial with a larger charged cylindrical shell. Both are non-conducting and thin and have uniform surface charge densities on their outer surfaces. Figure b gives the radial component ##E## of the electric field...
  3. P

    Calculating Charge at the Center of a Spherical Shell has me stumped

    Edit: Forgot to type "stumped" at the end of the title 1. Homework Statement Instead of typing it out, a link to a scanned document of the problem is here: http://imgur.com/Be3jSLp. Homework Equations The equations to use are stated in the problem here: http://imgur.com/Be3jSLp The Attempt...
  4. K

    Derivation of Electric Field with Gauss's Law

    I did everything I could to solve the following problem: A solid ball of radius rb has a uniform charge density ρ. What is the magnitude of the electric field E(r) at a distance r>rb from the center of the ball? E(r) = My third attempt went like this: qencl=[ρ(4/3)(π)rb3]...
  5. C

    Gauss's law for a charged ring

    Hello physics world, I am having a hard time understanding a rather simple thing. Let's consider the electric field produced by a uniformly charged ring of radius R, at a position $z$ along the ring's axis. From Coulomb's law in every textbook, we know that E_z∝Qz/(R^2+z^2). That is, there...
  6. xSpartanCx

    Flux through a sphere due to a charge outside of it

    Homework Statement A point charge of +5.00 μC is located on the x-axis at x= 5.00 m , next to a spherical surface of radius x= 4.00 m centered at the origin. [/B] According to Gauss's law, the net flux through the sphere is zero because it contains no charge. Yet the field due to the external...
  7. gracy

    Understanding Gauss's Law: Electric Flux & Charge Enclosed by a Closed Surface"

    Electric flux through a closed surface S = q/ε0 (1.31) q = total charge enclosed by S In the situation when the surface is so chosen that there are some charges inside and some outside, the electric field [whose flux appears on the left side of Equation above is due to all the charges, both...
  8. P

    Electric Flux and Gauss's law

    Homework Statement 1) A large cube has its bottom face on the x-z plane and its back face on the x-y plane. The corners on the x-axis are at (3.39 m,0,0) and (12.3 m,0,0). The cube is immersed in an electric field pointing in the positive x-direction, and given by: E = (91.2x^2 - 2.9)i, x is...
  9. K

    Using the divergence theorem to prove Gauss's law?

    Hello, I've been struggling with this question: Let q be a constant, and let f(X) = f(x,y,z) = q/(4pi*r) where r = ||X||. Compute the integral of E = - grad f over a sphere centered at the origin to find q. I parametrized the sphere using phi and theta, crossed the partials, and got q, but I...
  10. A

    Heat energy dissipated between two conducting shells

    Homework Statement A conducting sphere of radius a is surrounded by a neutral conducting shell of radius b (b > a).Connections are provided as shown in diagram. Initially, the sphere has a charge Q. The switch S1 is opened and then closed. The switch S2 is then opened and closed. Finally, the...
  11. T

    Two touching neutral conductors in electric field separate?

    Homework Statement Given a situation like this: Where the two blocks are perfectly conducting materials and are touching, will they separate? If they do separate, will they have the net charge values you calculate in the initial setup using Gauss's Law? There are no numbers, it's just...
  12. yeshuamo

    Gauss's Law vs Coulomb's law problem

    Homework Statement A thin sheet in the shape of an annular semicircle has a positive surface charge density +σ as shown. What is the electric field at point P? Here is an illustration of the problem: http://postimg.org/image/630bpqwan/Homework Equations Gauss's Law: φ=Qenclosed/ε0 φ=∫E⋅dA...
  13. Z

    How Does Grounding Affect Charge Distribution on a Conductor?

    So I am extremely confused at the moment. We had a hollow ring in physics lab today. There was a positive charge (30V) inside the sphere that was no centered and then the ground was attached to the ring itself (0 V). So, I understand that the negative charges unevenly distribute to cancel the...
  14. M

    A 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...
  15. eifphysics

    Insights A Partial "Derivation" of Gauss's Law - Comments

    eifphysics submitted a new PF Insights post A Partial "Derivation" of Gauss's Law Continue reading the Original PF Insights Post.
  16. 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...
  17. binbagsss

    Gauss's law, nucleus, potential proton due to other protons

    I'm a little out of touch with this stuff , but I'm really not getting it.. So my book is considering: in a nucleus of ##z## protons, consider one proton in spherical charge distribution to other protons. So ## \rho = (z-1)e/(4/3) \pi R^{3}##, where ##R## is the radius of the nucleus, is the...
  18. B

    Derivation of coloumbs law without Gauss's law

    Whenever I try searching on how coloumbs law is derived Gauss's law is always used,for this reason when I search for Gauss's law it is always derived from coloumbs law :frown:.could you guys guys help me out by telling me which camfirst and how it was derived Coloumbs law- F=Q1Q2/r2ε Gauss's...
  19. R

    Electric Displacement (Gauss's Law)

    Homework Statement Two long, conducting cylinders of thin metal with radii ##R## and ##5R##, respectively, are arranged concentrically so that their axes coincide. The smaller cylinder is placed inside the larger one and the space between them is filled with a dielectric whose relative...
  20. R

    Gauss's Law (Differential Form)

    Homework Statement Find the electric field inside and outside a sphere of radius R using the differential form of Gauss's law. Then find the electrostatic potential using Poisson's equation. Charge density of the sphere varies as ##\rho (r) = \alpha r^2 \ (r<R)## and ##\rho(r)=0 \...
  21. patrickbotros

    Why does a Charge Outside a Surface Produce No Net Flux?

    My textbook says "the net flux is zero through a closed surface that does not contain any net charge," and justifies it by saying that everything flowing in has an equal thing flowing out. This makes ABSOLUTELY NO sense to me.
  22. L

    Gauss's law: Why does q=0 if E is uniform?

    Homework Statement [/B] a) In a certain region of space, the volume charge density p has a uniform positive value. Can E be uniform in this region? Explain. b) Suppose that in this region of uniform positive p there is a "bubble" within which p=0. Can E be uniform within this bubble? Explain...
  23. J

    Why Gauss's law works when charge enclosed is not uniform?

    This problem has charge that is not uniform in the inside, but it is still possible to find the electric field as a function of distance outside the slab using Gauss's law. How is this possible if the electric field is not uniform in the slab and plane? Wouldn't the electric field from the...
  24. J

    Why doesn't Gaus's law count for charges outside the area?

    In Gaus's law when the integral is set up, we don't account for the charge outside the closed area. Why is this? How does this law work when the charges outside are not accounted for and only the charges enclosed is in the equation? I need an explanation why Gaus's law still works for...
  25. B

    Surface Integrals and Gauss's Law

    When I learned Integrals in Calc III, the formula looked like this ∫∫ F(r(s,t))⋅(rs x rt)*dA but in physics for Gauss's law it is ∫∫E⋅nhat dA How are these the same basic formula? I know that nhat is a unit vector, so it is n/|n|, but in the actual equation, it is a dot between the cross...
  26. H

    Coulomb's Law and Gauss's law

    Two electric charges q1 = 2 microC and q2 = -2 microC are located at \vec{r_1}=(1,0,0)m and \vec{r_2}=(0,0,-1)m respectively. Calculate the force on q1 in vector form. \vec{F_{12}} = \frac {1}{4\pi\epsilon_0}\frac{q_1q_2}{|\vec{r_1}-\vec{r_2}|^3}(\vec{r_1}-\vec{r_2}) is the formula I am...
  27. little neutrino

    Solving Electric Field of an 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. Homework...
  28. K

    Gauss's law in cgs unit system

    Homework Statement Is there a constant parrallel to the ε0 permittivity in the Gauss law in c.g.s? Homework Equations Coulomb force in m.k.s: ##F=\frac{1}{4\pi\varepsilon_0}\frac{qq'}{r^2}## Coulomb force in c.g.s: ##F=\frac{qq'}{r^2}## Gauss's law in m.k.s: ##\frac{N}{A}=\varepsilon_0 E##...
  29. QuantumCurt

    Why does Gauss's Law for Magnetism prohibit monopoles?

    I'm currently in an introductory electricity and magnetism course, and I've been pondering magnetic monopoles. We didn't go in depth with them at all, but the professor made a comment when discussing Gauss's Law for Magnetism, ##\oint \vec B \cdot d \vec A=0## (can't figure out how to type a...
  30. G

    A sphere of linear dielectric material surrounded by another dieletric material

    Homework Statement A sphere of linear dielectric material with permittivity ##\epsilon_1## and radius ##a## is surrounded by an infinite region of linear permittivity ##\epsilon_2##. In the spherical region, there is free charge embedded given by ##\rho_{free}=\beta r^2##, ##0<r<a##, where...
  31. beer

    Gauss's Law - deducing lamda

    Given the following information: An infinite line of charge lies long the z-axis. The electric field a perpendicular distance 0.490m from the charge is 770N/C . We're asked to do the following: How much charge is contained in a section of the line of length 1.20cm ? The answer is 2.52*10^-10...
  32. Godparicle

    Can an electron exist at many places at the same time?

    If I am not wrong, the Michio says that an electron (not the parts of an electron) can be found in many places at the same time. Is that right? If that is the case, consider a gaussian surface enclosing the electron at many places at the same time, then the charge inside the surface will be...
  33. baby_1

    Some question about gauss's law in Catesian Coordinate

    Hello I have some questions to understand much more better the Gauss's law in Cartesian coordinate. 1-when can we use Gauss's law and it's integral to solve a question easier in Cartesian coordinate? 2-Is it difference to use a cylindrical or cube shape for a plane that disturbed some...
  34. B

    Differential form of gauss's law.

    I don't understand what charge density is meant in the equation: div E = constant times charge density. I have the derivation in front of me and the last step follows from accepting that the rate of change of the integral of the field divergence per change in volume is the same as the rate of...
  35. G

    Find the total electrostatic energy stored in the configuration

    Homework Statement A spherical conductor of radius ##a## carries a charge ##q## and also there is a jelly of constant charge density ##\rho## per unit volume extending from radius a out to radius ##b##. Find the electrostatic energy stored in the configuration. Homework Equations ##\oint...
  36. G

    Is this the correct set up for the electric field?

    Homework Statement A spherical conductor of radius ##a## carries a charge q and also there is a jelly of constant charge ##rho## per unit volume extending from radius ##a## out to radius ##b##. I'm looking to see if I got the correct set up for the electric field of this spherical conductor for...
  37. M

    How Does Electron Shape Affect Electric Field Energy?

    Homework Statement a. Calculate the energy density of the electric field at a distance r from an electron (presumed to be a particle) at rest. b. Assume now that the electron is not a point but a sphere of radius R over whose surface the electron charge is uniformly distributed. Determine the...
  38. EnchantedEggs

    How Does Decreased Amplitude Compensate for Field Line Spread in Gauss's Law?

    Has anyone read the book by Daniel Fleisch, 'A Student's Guide to Maxwell's Equations'? I'm having some trouble with Chapter 1, page 36. He's talking about the divergence of an electric field originating from a point charge. Apparently, the divergence of the vector electric field is zero...
  39. P

    Gauss's law to solve for electric field.

    An infinitely long line charge with a linear density +λ inside an infinitely long cylinder of radius R and area density -λ/(2pi*R). So if I set up a cylindrical Gaussian surface with length L, the positive charge inside the surface would be λL and negative charge inside the surface would be...
  40. S

    Gauss's Law with a sphere on and charge on z-axis

    I have a question for E&M and I feel like I am over complicating it. As the title says, the is a positive charge on the x-axis and I must prove that flux = q/εo. Since the charge is on the z-axis, could I just add in a term (z-z') to account for the charge not being at the origin into...
  41. A

    Solving Gauss's Law Problem: Excess Electrons in Plastic Sphere

    Homework Statement How many excess electrons must be distributed uniformly within the volume of an isolated plastic sphere 23.0cm in diameter to produce an electric field of 1250N/C just outside the surface of the sphere? Homework Equations E=Q/4*pi*ε*r^2 The Attempt at a Solution...
  42. P

    Gauss's Law with a Insulating Shell

    Homework Statement An insulator in the shape of a spherical shell is shown in cross-section above. 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 μC(You may assume that the charge is distributed uniformly throughout the...
  43. F

    Solve Gauss's Law for D: Electric Displacement of Sphere with Polarization kr

    Homework Statement We have a sphere with a polarization kr. I need to show that the electric displacement D=0 everywhere. Homework Equations ∫closed surfaceD.dS=qfree The Attempt at a Solution qfree=0 everywhere so the flux of D is zero everywhere. Clearly D=0 everywhere does solve...
  44. A

    Gauss's Law and conservative fields

    1) Do all conservative fields follow Gauss's Law? For all laws of the nature 1/R^n the field would be conservative but would follow Gauss's Law only when n=2. So a field may be conservative but would not follow Gauss's law? 2) Do all field that follow Gauss's Law conservative in nature? Are...
  45. L

    Finding electric field vector given charge density, using Gauss's Law

    Homework Statement A long cylinder carries a volume charge density which is proportional to the distance from the axis, ρv=0.005r. Find the vector electric field inside the cylinder using Gauss’ Law in integral form. Homework Equations ∫E dot dA = Q/ε0 ∫vρv = Qenc The Attempt at...
  46. Ackbach

    Gauss's Law: Cond. versus Non-cond. Sheets: Conflicting Results

    Homework Statement Compare and contrast the electric field due to a uniform sheet of charge with charge density ## \sigma## for the conducting and non-conducting cases. Homework Equations Gauss's Law: $$\oint \mathbf{E}\cdot d\mathbf{A}=\frac{q_{\text{en}}}{\varepsilon_0}.$$ The...
  47. applestrudle

    Question about Gauss's law, finding electric field and potential field

    I'm having trouble with the second part b) for this problem. I used Gauss's Law and for a I got r<R E = \frac{{r}^{2}}{4\varepsilon} and for r>R E = \frac{{R}^{4}}{4\varepsilon{r}^{2}} and then V = \int{E.dr} from r to infinity right? So for r>R I got V =...
  48. C

    Why Does Gauss's Law Use Cylinder Circumference Instead of Area?

    Homework Statement So I was looking at this site reading up again on Gauss's Law and was a tad confused http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elecyl.html 1st thing on the page... Homework Equations The Attempt at a Solution It states that the electric flux will just be the...
  49. C

    Calculate: the net electric flux = flux through rounded portion + flux

    I use Gauss's law to calculate: the net electric flux = flux through rounded portion + flux through the flat base = Q/ε. And the flux through the flat base is negative, the negative means?? Help me please, it is very confusing 2) Why they choose C, i think E is correct because Q doesnot...
  50. P

    Gauss's law on a charged sheet.

    Homework Statement find the field produced by a uniformly charged sheet carrying 87 pC/m2 Homework Equations \oint \vec{E}.d\vec{A} = qenclosed/\epsilon The Attempt at a Solution \Phi= \sigmaA/\epsilon \Phi=\oint E.dA = ## E(2A) ## 2EA= \sigmaA/\epsilon E =...
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