What is Gaussian surface: Definition and 54 Discussions

A Gaussian surface (sometimes abbreviated as G.S.) is a closed surface in three-dimensional space through which the flux of a vector field is calculated; usually the gravitational field, the electric field, or magnetic field. It is an arbitrary closed surface S = ∂V (the boundary of a 3-dimensional region V) used in conjunction with Gauss's law for the corresponding field (Gauss's law, Gauss's law for magnetism, or Gauss's law for gravity) by performing a surface integral, in order to calculate the total amount of the source quantity enclosed; e.g., amount of gravitational mass as the source of the gravitational field or amount of electric charge as the source of the electrostatic field, or vice versa: calculate the fields for the source distribution.
For concreteness, the electric field is considered in this article, as this is the most frequent type of field the surface concept is used for.
Gaussian surfaces are usually carefully chosen to exploit symmetries of a situation to simplify the calculation of the surface integral. If the Gaussian surface is chosen such that for every point on the surface the component of the electric field along the normal vector is constant, then the calculation will not require difficult integration as the constants which arise can be taken out of the integral. It is defined as the closed surface in three dimensional space by which the flux of vector field be calculated.

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  1. J

    Electric Field Inside a Gaussian Surface with Point Charge q

    If I have a point charge q right outside of a gaussian surface, it makes sense that the flux is zero inside the surface because the electric field going in equals the electric field going out. However, how would the electric field be zero inside? Wouldn't it just take on the electric field of...
  2. NoahCygnus

    Electric field on Gaussian surface due to external charge

    There's something I need to confirm about Gauss' law. If I have to determine the electric field at point P due to charge +q, I take a Gaussian sphere enclosing the charge with the point on the surface of the sphere. So Gauss law doesn't care about the charge +Q because the flux do to this charge...
  3. A

    Flux Through a Gaussian Surface

    Homework Statement A metal sphere of radius a is surrounded by a metal shell of inner radius b and outer radius R, as shown in the diagram below. The flux through a spherical Gaussian surface located between a and b is 1.20Q/εo and the flux through a spherical Gaussian surface just outside R is...
  4. K

    Grounded conductor and Electric field potential question ?

    Homework Statement [/B]Homework Equations V= kq/r.[/B]The Attempt at a Solution For 8-8, I do not really know how to approach it. For 8-14 , I think that q2=-q1 and q3=q1+q2. I can now use V=kq/r and then find the equations for r>R3 , r=R3 , R2<r<R3 , r=R2 and R1<r<R2 and then graph...
  5. math4everyone

    Proving Gauss Law using a "bad" Gaussian surface

    Homework Statement What I basically want to do is to prove Gauss Law with a cylinder perpendicular to an infinite charged wire (I know I can do this simple, but I want to do it this way) This is what I have done so far: Homework Equations $$\Phi=\int \frac{dq}{4\pi \varepsilon_0 r^2} \hat{r}...
  6. R

    Electric Potential of Two Spherical Shells: Gaussian Surface Homework

    Homework Statement A thin spherical shell with radius R1 = 2.00 cm is concentric with a larger thin spherical shell with radius 6.00 cm . Both shells are made of insulating material. The smaller shell has charge q1=+6.00nC distributed uniformly over its surface, and the larger shell has charge...
  7. Ryaners

    Electric field in two concentric conducting cylinders

    Homework Statement Two concentric cylindrical conducting shells of length L are separated by a vacuum. The inner shell has surface charge density +σ and radius ra. The outer shell has radius rb. Using Gauss’ Law, as a function of radius r find: The direction and magnitude of electric field...
  8. Idyia

    B Why doesn't the flux through a Gaussian surface change with a change in shape?

    Why doesn't the flux through a Gaussian surface change, when the shape is changed? (while keeping the net charge inside it the same) Flux is the dot product of electric field and surface area, so wouldn't it change if surface area is changed?
  9. K

    Gaussian surface (infinitely long cylindrical conductor)

    Homework Statement An infinitely long, cylindrical, conducting shell of inner radius b and outer radius c has a total charge Q. A line of uniform charge distribution Λ is placed along the axis of the shell. Using Gauss's Law and justifying each step, determine. A) The Electric Field for r>a...
  10. I

    Electric field outside a gaussian surface

    Hello If we have a gaussian surface that is placed in a uniform electric field E and encloses 0 charge, what would the E-field at the gaussian surface be? I have assumed the gaussian surface to be cubic surface, and then I have found from Gauss's law that the electric field is zero at the...
  11. Mnemonic

    Cylindrical Gaussian Surface around charged rod

    Homework Statement a) 21.4-nC of charge is placed on a 4.8-m long steel tube with a d = 5.9-cm diameter. What is the magnitude of the electric field as a radial distance of r = d / 3? b) What is the magnitude of the electric field as a radial distance of r = 20 d? I was able to determine the...
  12. P

    How much charge inside a Gaussian surface?

    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 = 80 V/m, and all over the right, slanting, side of the box E2 = 400 V/m. On the top the average field is E3 = 260...
  13. H

    Where to place Gaussian surface

    Homework Statement I'm trying to calculate the electric field through two oppositely charged plates with the same magnitude: http://imgur.com/uXCQqtW Homework Equations Flux = ∫E⋅dA = Qenclosed/ε0 The Attempt at a Solution I understand how the electric field is calculated using S1 and S4...
  14. G

    Can a Gaussian Surface Confirm Zero Electric Field Between Two Charges?

    1. We have two positive point charges (+q) at a distance from each other 2. Goal is to Find electric field at point A halfway between the point charges 3.By logic and summation of fields we should get ZERO 4. But how would I use a gaussian surface (sphere i assume ) to prove at point A...
  15. R

    Gaussian surface surrounding only a proton inside a conductor

    Homework Statement I understand why, using Gauss's law, the net charge within a conductor should be zero at any point. However, when I try making a Gaussian surface that is so small so as to enclose a single proton, I cannot see why the enclosed charge should be zero for that situation as...
  16. M

    Electric Field of a charged sphere with cylindrical gaussian surface

    So the problem statement is: A conducting solid sphere (R = 0.167 m, q = 6.63·10–6 C) is shown in the figure. Using Gauss’s Law and two different Gaussian surfaces, determine the electric field (magnitude and direction) at point A, which is 0.00000100 m outside the conducting sphere. (Hint: One...
  17. W

    Gaussian Surface Electric Field Problem

    Homework Statement An uncharged spherical thin metallic shell has a point charge q at its center. Find expressions for the electric field Inside the shell Outside the shell has the shell any effect on the field due to q? has the presence of q any effect on the shell? if a second point charge...
  18. A

    Gaussian surface - which charges contribute to the electric field

    Homework Statement in the following figure, the dashed line denotes a Gaussian surface enclosing part of a distribution of four positive charges. a) which charges contribute to the electric field at P? b) is the value of the flux though the surface, calculated using only the...
  19. 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...
  20. W

    Gaussian Surface and Charge Density

    1. A solid dielectric sphere of radius 10 cm has an electric charge uniformly distributed throughout its volume. The electric field at 5 cm from the center of the sphere is 8.6 x 10^4 N/C, pointing radially outward. Calculate the magnitude and direction of the electric field at a point 15 cm...
  21. P

    Is a Gaussian surface truly arbitrary ?

    Consider a point charge q at the vertex of an arbitrary cube. If asked to consider the flux the cube experiences, q/8epsilon seems a natural answer, by constructing seven more such cubes to create an overall cube of 8 times the volume with q at its center. But, this doesn't make sense to me...
  22. P

    How to choose Gaussian surface

    1 Why do we choose a spherical surface as gaussian surface for a point charge to calculate electric field? In my view, the reason may be i. If we take the point charge at centre, each point of spherical surface will be at same distance from the...
  23. B

    Top view of a Gaussian surface in a uniform electric field

    The field makes an angle θ with side 1 and the area of each face is A. In symbolic form, find the electric flux through (a) face 1, (b) face 2, (c) face 3, (d) face 4 and (e) top and bottom. My professor got: a=EAcosθ b=-EAsinθ c=-EAcosθ d=EAsinθ e= 0 I understant why e=0 but for the...
  24. B

    Net electrical flux on a cylindrical Gaussian Surface

    Homework Statement a cylindrical solid of charge q, radius R, and length H. The Gaussian surface S is a cylindrical shell of radius r and length h, with r < R. Determine the net electric flux given that q = -48Q, R = 4L, H = 3L, r = 2L, and h = 2L (type the integer value, along with the sign...
  25. C

    What is the total flux flowing through a spherical Gaussian surface?

    Homework Statement Consider a uniformly charged sphere (an insulating sphere of radius R,) and a spherical Gaussian surface with radius R/2 concentric to the sphere. What is the total flux flowing through the Gaussian surface? Homework Equations Vsphere= (4∏R^3)/3 Asphere= 4∏R^2 Gauss' Law...
  26. C

    How Does Moving a Charge Affect Electric Flux in a Cubic Gaussian Surface?

    Homework Statement A point charge of negative polarity is located at the centre of a cubic Gaussian surface with edges of length ##0.5m##. Calculate the electric flux through one of the faces of the surface. What would happen if the charge was moved 10cm to the right? Homework Equations...
  27. A

    Using a cube as a Gaussian surface

    Homework Statement Suppose there is a uniformly charged cube with known side length. I then imagine a larger, closed cube surface surrounding it. This larger cube has double the side length and is symmetrical to the smaller cube. Is is practical to use this Gaussian surface to compute the...
  28. K

    Time-retarded E-field and Gaussian surface integral

    If I have an oscillating charge inside of a sphere, will the integral of E(t), where t=proper time of the sphere, over the sphere's surface area result in a value of electric flux equal to the value of the charge?
  29. K

    Relativistic corrections to E-fields of charges bounded inside a Gaussian surface

    If I have a spread of electrical charges contained inside a Gaussian surface, and if I cause those electrical charges to move at relativistic speeds, the electric fields of those charges should be subject to relativistic contraction. What happens then to electric flux that cuts through that...
  30. A

    Integration limits for Gaussian surface

    Homework Statement Say you have a nonconducting spherical shell. A is the inner radius and B is the outer radius. If you wanted to set up an integral to find the flux, would the gaussian surface include B, or be just inside it? That is, would the limits of integration go from A to B? If...
  31. J

    Gaussian surface line charge

    Homework Statement A uniformly charged, straight filament 7.00 m in length has a total positive charge of 2.00 \muC. An uncharged cardboard cylinder 2.00 cm in length and 10.0 cm in radius surrounds the filament at its center, with the filament as the axis of the cylinder. Using reasonable...
  32. T

    Flux Through Gaussian Surface

    Homework Statement A metal sphere of radius a is surrounded by a metal shell of inner radius b and outer radius R, as shown in the diagram below. The flux through a spherical Gaussian surface located between a and b is 1.20Q/εo and the flux through a spherical Gaussian surface just outside R...
  33. M

    Gaussian Surface, Coaxial Cable

    Homework Statement A long coaxial cable consists of an inner cylindrical conductor with radius a and an outer coaxial cylinder with inner radius b and outer radius c. The outer cylinder is mounted on insulating supports and has no net charge. The inner cylinder has a uniform positive charge per...
  34. F

    Basic Gaussian Surface Conceptual Problem

    So I'm pretty sure I have the right answer I just want to make sure I am getting the idea. There is a large solid copper cube. At the center of the cube there is a hollow sphere of radius a. At the center of the hollow sphere there is a charge Q. What is the total charge induced on the...
  35. P

    Electric Flux through a Gaussian Surface

    Hi all, I need your help with a question. Here goes, Homework Statement There is a hollow conducting sphere with a uniform surface charge density of +\sigma. A charge -q, is placed inside the cavity of the hollow sphere. What is the electric flux through a spherical surface just inside...
  36. E

    Gauss' Law and gaussian surface

    Hey there, just had a question about Gauss' law, should be relativity simple however the explanation we were given was quite poor and only seems to apply well to the examples we were given. (This isn't homework). I (think I ) know the equation for Gauss' Law and what it means, that basically...
  37. M

    Magnet with negative charge in gaussian surface?

    i would really appreciate if someone could help me out with this one. i m preparing for an exam and this question is a question from papers of previous years and its bugging me because it seems very specific in that i can't seem to find anything like it in textbooks. what i m mainly stuck on...
  38. M

    Magnet with negative charge in gaussian surface?

    i would really appreciate if someone could help me out with this one. i m preparing for an exam and this question is a question from papers of previous years and its bugging me because it seems very specific in that i can't seem to find anything like it in textbooks. what i m mainly stuck on...
  39. C

    Calculating Electric Flux Φ w/o typical Gaussian surface

    Hello all, new here. In the past few weeks, I have been trying to gain a basic understanding of classical electricity and magnetism through the fantastic lectures at http://ocw.mit.edu, specifically the physics course...
  40. M

    Understanding Gauss' Law in Cases with Charges Outside Gaussian Surface

    Gauss' Law only figures out the the total charge enclosed by the Gaussian surface and on it, I treid this in a few cases where charges were placed only inside the surface, and my answers were correct. But, when I tried imagining how to do this if there were charges present outside...
  41. Q

    How Does Flux Distribute in a Gaussian Cube with a Corner Charge?

    Homework Statement A particle charge of q is placed at one corner of a Gaussian cube. What multiple of q/\epsilon_0 gives the flux though each cube face not making up that corner? The solution is amazing - stack up eight cubes around the corner and find the flux through each individual cube...
  42. L

    Why Can't I Use My Indicated Vector ds on a Gaussian Surface?

    folks, in my attached image, why can't i take the vector ds as indicated by me in pencil. i am confused. help will be greatly appreciated.
  43. L

    Gaussian Surface: Electric Field & dA Visualization

    Homework Statement In the case of calculating electric field due to an infinitely long line charge, we assume cylinder to be a gaussian surface and electric field and small area element of the cylinder acts along the same direction at the curved surface and they act perpendicular direction at...
  44. P

    Finding total flux on Gaussian surface

    Homework Statement Consider the uniformly charged sphere with radius R. Q is the total charge inside the sphere. Find the total flux passing through the Gaussian surface (spherical shell) with radius r. (r<R) Homework Equations I I tried solving for the Electric Flux by simply...
  45. M

    Gaussian surface and net flux

    In the figure below, the charge on a neutral isolated conductor is separated by a nearby positively charged rod. What is the net flux through each of the five Gaussian surfaces shown in cross section? Assume that the charges enclosed by S1, S2, and S3 are equal in magnitude. Surface 1...
  46. J

    Electric Field Inside a Cylindrical Gaussian Surface: Exploiting Symmetry

    What is the electric field inside a cylindrical Gaussian surface in terms of volume charge density?
  47. P

    Cylindrical Gaussian surface

    Homework Statement A long cylindrical insulator has a uniformcharge density of 1.46uC/m3 and a radius of 6cm.a-What is the electric field inside the insulator at a distance of 2cm and 12cm? Answer should be in N/C. b-How much work must you do to bring a q=0.086uC test charge from 12cm to 2cm...
  48. A

    Does Gauss' Law Hold for Infinite Gaussian Surfaces?

    Hi, From what I understand the proof of Gauss' law applies only to finite surfaces. Can anyone give an example of a charge distribution and an infinite Gaussian surface, where the total flux on it is not proportional to the enclosed charge? Thanks!
  49. M

    Cant understand Gaussian surface

    Homework Statement Can someone please explain what use gaussian surfaces have, in really simple terms? I don't really understnd the point of wrapping an imaginary surface around a charge, when we can just do the calcs without the imaginary surface. Also if there are preset gaussian surfaces...
  50. N

    Gaussian Surface Derivations

    For the following Eo is epsillon zero Homework Statement 41. A solid nonconducting spere of radius R has a uniform charge distribution of volume charge density p = kr/R where k is constant and r is the distance from the center. Show the (a) the total charge on the sphere is Q =...
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