# What is Gauss law: Definition and 180 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. ### I Problem with one of the premises in electrostatic pressure theory

I have the video linked with the time stamp. . Isn't Electric Field anywhere inside the conductor zero. So there will be no electric field inside the thickness of the conductor. But he managed to integrate it somehow? he considered electric field to be changing inside the conductor that has...
2. ### Electric field external to Conducting Hollow Sphere with charge inside

I have read Griffiths' Chapter 2 sections on Conductors. According to it, (if I understood it correctly) if the charge is put inside the cavity of a conductor, then the equal and opposite total charge will be induced surrounding the cavity. This charge and the total charge induced surrounding...
3. ### Determining field between oppositely charged conducting plates

I'm using a cylindrical gaussian surface that is right inside the positively charged conducting plate and has the other end in-between both plates. I'm having trouble discerning whether the charge density(##q_{in}##) should be ##\frac{\sigma}{2 \epsilon_0}## since the cylinder is only...
4. ### (Help) Surface charge density (σ) for particle to hit plate...

I don't know if i'm exactly right. But I started with x(time) = V cos θ t which = (6810 m/s) cos (69.1°) (11.4 * 10^-3 s) is ... 27.69 m & since Electric field due to uniformly charge surface is represented by... E = (q * σ)/(2 * ε_0 * m), and since acceleration (a) can be expressed as F/m...
5. ### E&M: Gauss' Law Surface Charge Density

In this question I need to find the inner and outer charge density of the shell I did part A just fine, I used the formula for an electric field due to a line charge, but parts B and C is what's really confusing me. I'm not really sure how to go about it, I placed a spherical gaussian surface...
6. ### I Do equipotential lines fall on the equiprobability contours?

For 2D charge distribution ρ(x,y)=Ne PDF(x,y), where PDF is the normalized probability density function with its peak on (0,0) and has standard deviations σ x. and σ y. Are the contours with the equal probability "PDF(x,y)=const" the same as the equipotiential contours?, I tend to think that...
7. ### Calculating Linear Charge Density of a Cylinder

For part a: I know that linear charge density is the amount of charge per unit length, and we are given the volume charge density. Since we are given the volume, we can obtain the length by multiplying the volume by the cross sectional area, so C/m^3 * m^2 = C/m. The cross sectional area of a...
8. ### Finding Constants: Potential and Field Analysis

I have wrote all feilds and potentials and I want to find the constants. My first question is " when we say in the a<x<2a the potential is V(x)" then the potential in the a is V(a) or V(0) ( cause it is 0 in our new area) ? Second one is " when I want to write the gausses law for the point x=a I...
9. ### I Question regarding the use of Electric flux and Field Lines

1)Field Lines is supposed to represent the electric field around a charge ,now we can draw infinite field lines around a charge and sinc Electric flux is No of Field Lines /area ,does it become infinite ,the whole concept of field lines is quite in the Gray Area for me ,I can in theory mark...
10. ### Calculating the Electric field inside an infinite planar slab using Gauss' Law

Draw a Gaussian pill box that starts from 0 (half way between the slab) and extends towards 2 cm.$$A \times \int_{0}^{0.02} \rho dz$$ I'm not sure if I should multiply the integral by A (area) or V (volume) And if area would I multiply by 0.02^2? I'm confused here. Thanks for your help.
11. ### Exam Prep: Electric Field - Is It Zero?

I'm having an exam soon so i want to make sure. Is the electric field here zero?? cause if i draw gauss surface covering both of them they should cancel out or am i wrong.
12. ### Quick question about which radius to use on Gauss' law problem

confused on part A/B when I look up they did E= Q/2e(0.8)^2. But why not use the 0.100mm because that is the area of the enclosed. Same with B why did they use 100m and not 0.8m because 0.8 is smaller so it enclosed the charge
13. ### Problem with differentiation

First I did drho/dr which is equal to 35.4*10^-12/R. Then I integrated drho by which I got rho=35.4*10^-12. And then the last eqn will be q=rhoV. But the answer was wrong. I have a doubt on the formula I am using for E because that formula is for a point charge or a charged shell.
14. ### I Another way of stating Gauss' law?

Gauss law relates the net flux phi of an electric field through a closed surface to the net charge q that is enclosed by that surface. It tells us that Phi = q/permittivity Can I say it like this : The gauss law states that the net flux of the surface depends upon the net charge enclosed by that...
15. ### I What is Electric Flux and How is it Calculated?

Gauss law relates between E at some point on guassian surface with the net charge enclosed by that surface. Using gauss law is like being able to tell what (ie charge)is inside a gift box by just looking at the wrapper(electric field). There are two types of problem. Sometimes we know the charge...
16. ### Solving Part e of the Electron Beam Problem

I am only asking about part e. If you are short on time, you can read through parts a - d, to get an idea of what is happening, and then attempt part e directly. I have solved parts a - d. If you would like to check your answers, the answer to part c is [rne^2 / 2e0] [ 1 - (v/c)^2], and the...
17. ### Electric potential inside a hollow sphere with non-uniform charge

I tried to find the charge distribution using the given potential but couldn't produce the correct result. Also, Gauss's Law doesn't help, as the electric flux is 0 but we don't have any symmetry. Can someone please shine a light on this? Thanks in advance..

19. ### Gauss' Law: Understand How to Calculate Flux

Hello everybody To calculate the flux for the electric field I need the gauss law. There are two formula one with the integration over some area and the other is Q/e0. When do I have to use which one?
20. ### Understanding the electric field of a sphere with a hole

Here's an image. O and O' are the respective centers, a is the distance between them, r is the distance from the center of the sphere to P, and r' = r - a, the distance from O' to P. The approach (which I don't understnad) given is to use Gauss' Law and superposition, so that we calculate the...
21. ### Electric field problem using Gauss' law: Point charge moving near a line charge

F = qE ma = (2*10^-6) * (λ / (2pi*r*ε0) ) ma = (2*10^-6) * (4*10^-6 / (2pi*4*ε0) ) => I am not certain what to put for r ( But I sub in 4 because dist is 4) a = ( (2*10^-6) * (4*10^-6 / (2pi*4*ε0) ) )/ 0.1 a = 0.35950 v^2 = U^2 + 2 a s v = 0 u^2 = -2 a s => Can't sqrt negative so...
22. ### Electric field at (0,0) for this charged square conductor

Can we assume that square charge resembles a sphere shell, and think like electric field at sphere shell's center is 0.
23. ### Modulus of the electric field created by a sphere

I think the right solution is c). I'll pass on my reasoning to you: R=6\, \textrm{cm}=0'06\, \textrm{m} \sigma =\dfrac{10}{\pi} \, \textrm{nC/m}^2=\dfrac{1\cdot 10^{-8}}{\pi}\, \textrm{C/m}^2 P=0'03\, \textrm{m} P'=10\, \textrm{cm}=0,1\, \textrm{m} Point P: \left. \phi =\oint E\cdot...
24. ### Capacitance of a spherical capacitor

When I try to do Gauss, the permeability is not always that of the free space, but it varies: up to a certain radius it is that of the void and then it is the relative one. How can I relate them? I'm trying to calculate the capacity of a spherical capacitor. The scheme looks like this: inside I...
25. ### Parameterize Radial Vector of Electric Field due to Spherical Shell

Homework statement: Find the electric field a distance z from the center of a spherical shell of radius R that carries a uniform charge density σ. Relevant Equations: Gauss' Law $$\vec{E}=k\int\frac{\sigma}{r^2}\hat{r}da$$ My Attempt: By using the spherical symmetry, it is fairly obvious...
26. ### Gauss Law Problem direction of Area

My attempt is ∅ = ∫E.dA. The direction of E is going out of the net towards +ve i axis. I am not clear on the direction of the Area, it can be either +ve i-axis or -ve i-axis. Which direction should i consider? ∅ = ∫3.dA = 3*∫dA ---->1 ∫dA is the area of the circle. A = π * (0.11)^2 = 0.038...
27. ### Gauss-Theorem on a solid dielectric sphere

The load system formed by the point load and the load distribution generates two regions in space corresponding to r<1m and r>1m, i.e. inside and outside the sphere. Given the symmetry of the distribution, by means of the Gaussian theorem we can find the modulus of the field at a distance r from...
28. ### Electric Flux through a circle

Hi! My main problem is that I don't understand what the problem is telling me. What does it mean that the surface is a flast disc bounded by the circle? Is the Gauss surface the disc? Does that mean that inside the circle in the figure, there is a disc? Can you give me some guidance on how to...
29. ### Find the Electric Field E using Gauss' Law

I tried to work out both a) and b), but I am not sure if I am correct. I drew a picture with a sphere around q first with radius r and then with radius 3r. For a) ##E.A=\frac {q}{ε_°}## (when using Gauss' Law) Since ##A=4πr^2##, I substituted this in the equation and solved for E giving me...
30. ### B Doubt on an EM problem regarding gauss law

There's this problem 2.18 in the book "Introduction to electrodynamics" by Griffith. The problem says the following, "Two spheres, each of radius R and carrying uniform charge densities ##+\rho## and ##-\rho##, respectively, are placed so that they partially overlap (Image_01). Call the vector...
31. ### Potential across a conducting sphere surrounded by an insulator

Homework Statement A conducting sphere has a radius of 2.25 m and carries a positive surplus charge of 35.0 mC. A protective layer of barium titanate is applied to the surface of the sphere to make it safe for laboratory workers nearby. Safety considerations dictate that the potential...
32. ### Gauss law two infinite plane question

Homework Statement Homework EquationsThe Attempt at a Solution How do you know the left plate (or the right plane) produces a field (1/2ε) σ to the left and right? How do you apply Gauss Law? For one infinite plane, we can use Gauss law because of symmetry, so we can assume the electric flux...
33. ### Flux linked with lower face of a cube

Homework Statement A point charge q is placed inside a cube of side 2a. What will be the flux associated with the lower surface ABCD? Homework Equations I think I can apply Gauss Law here, but can't think of something connecting it with the lower surface. ∫B.dl = 1/ε° X Charge Enclosed The...
34. ### Find the electric field at an arbitrary point

Homework Statement A distribution of charge with spherical symmetry has volumetric density given by: $$\rho(r) = \rho_0 e^{ \frac {-r} {a} }, \left( 0 \leq r < \infty \right);$$ where ##\rho_0## and ##a## is constant. a) Find the total charge b) Find ##\vec E## in an arbitrary point...
35. ### Gauss' Law problem: determine the electric flow through a square surface due to a nearby charge

Homework Statement determine the electric flow through a square surface of side 2l due to a load + Q located at a perpendicular distance l from the center of the plane I really don't know how to answer this question .i need help guys Thanks Homework EquationsThe Attempt at a Solution I ended...
36. ### Flux of a vector and parametric equation

Homework Statement Compute the flux of a vector field ##\vec{v}## through the unit sphere, where $$\vec{v} = 3xy i + x z^2 j + y^3 k$$ Homework Equations Gauss Law: $$\int (\nabla \cdot \vec{B}) dV = \int \vec{B} \cdot d\vec{a}$$ The Attempt at a Solution Ok so after applying Gauss Law...
37. ### Electric Flux through the Face of a Cube

Homework Statement Griffiths' Introduction to Electrodynamics problem 2.10, Homework Equations Gauss' Law, ##\int_{S} \textbf{E}\cdot \textbf{dS} = \frac{Q_{\text{enc}}}{\epsilon_0}##[/B]The Attempt at a Solution It seems reasonable that the flux through the shaded surface and the front...
38. ### Finding electric flux using Gauss' Law

Say you have a hollow cylinder, whose one side is open. Now, you pace a positive charge ##Q## at the centre of this open end (such that it is just inside the cylinder). How much should be the flux coming out from the closed end? I just thought of this problem. In order to use Gauss' Law, we...
39. ### How Do You Calculate the Capacitance of a Sphere Using Only Charge or Potential?

Homework Statement Assume a conducting sphere has a radius of 3400km with an electric field of 100 V/m at it's surface. a) Calculate total charge of sphere. b)Calculate potential at the surface using infinity at reference point c) Calculate capacitance of the sphere using the result of a or b...
40. ### Gauss Law- Conducting and Non-conducting cylindrical shells

Homework Statement Below is a diagram of an infinitely long non-conducting rod of radius, R, with a uniform continuous charge distribution. The uniform linear charge density of this line is lamba1. The rod is at the center of an infinitely long, conducting pipe. The linear charge density of...
41. ### Electric field inside/outside (uniformly charged sphere)

A sphere of radius a carries a total charge q which is uniformly distributed over the volume of the sphere. I'm trying to find the electric field distribution both inside and outside the sphere using Gauss Law. We know that on the closed gaussian surface with spherically symmetric charge...
42. ### Classical Book(s) with problems on classical electromagnetism

I started studying the book "A Student's Guide to Maxwell's Equations" by Daniel Fleisch some time back. It is an excellent book, giving a very good idea about the main laws of electromagnetism. I will soon finish the book. Now I need some book(s) which has problems on all the laws in classical...
43. ### Electrostatic force between a Half Cylinder and a Plate

Homework Statement (This is not a HW problem, but HW-type problem.) A half cylinder of radius R and length L>>R is formed by cutting a cylindrical pipe made of an insulating material along a plane containing its axis. The rectangular base of the half cylinder is closed by a dielectric plate of...
44. ### Finding the gravitational force over a flat infinite sheet

Homework Statement Homework Equations F=ma F=Gm1m2/r2 Gauss' Law? The Attempt at a Solution I'm not sure if I should be using Gauss' Law for this question, because I've never heard of it or learned about it. I'm currently taking multi-variable calculus (gradients, vectors, etc.). From what I...
45. ### How Does Gauss' Law Apply to an Insulated Cylindrical Shell and Rod System?

Homework Statement Question ==== An infinitely long insulating cylindrical rod with a positive charge ##\lambda## per unit length and of radius ##R_1## is surrounded by a thin conducting cylindrical shell (which is also infinitely long) with a charge per unit length of ##-2\lambda## and radius...
46. ### Electric Field of a solid sphere of non-uniform surface density

A solid sphere has surface charge density, Rho (r) Rho(r) = k 1 ( 0 < r < a) k2 x ( a < r < R) 2) Find the electric field in all region i.e 1) r < a and 2) a < r < R and 3 ) R < The attempted solution and the question with the diagram is attached below Could the answer be verified...
47. ### Gauss' law for uniformly charged space

the problem: Say we have the entire space uniformly charged. Then, the E field experienced by any point is zero, from symmetry.* But, it means that for any Gaussian surface, the flux though it is zero even though the charge enclosed is clearly not. Gauss' law seems to disagree with symmetry, but...
48. ### Modification in Coulomb's Law and its implications

If the coulomb's law instead of following an inverse square relationship, follows an inverse cube relationship, How would it affect an isolated charged conducting sphere? How would it's field vary within the volume and how would the volumetric charge density be affected? Please give in some...
49. ### Finding Total Charge from E-field

Homework Statement A static charge distribution has a radial electric field of magnitude ##E = \alpha \frac{e^{-\lambda r}}{r} ## where λ and α are positive constants. Calculate the total charge of the distribution. Homework Equations Gauss's law ##Q/\epsilon_0 = \int \vec{E} \cdot d\vec{S}##...
50. ### Gauss' Law: Charged Rod & Sphere (Electric Flux)

Homework Statement A charged, straight line/rod of infinite length has a Discrete uniform distribution of charge, has a linear density of λ and is at a distance d from a sphere with a radius of R. Find the entirety of the Electrical Flux that is caused by this charged rod, which passes...