# Gauss law Definition and 81 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. ### Solving linear charge density from volume charge density using Gauss' Law

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...
2. ### A nice electrostatics problem -- Find the E-field for these 2 charged planes

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...
3. ### 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...
4. ### 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.
5. ### Gauss' law question -- Two infinite plane sheets with uniform surface charge densities

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.
6. ### 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
7. ### 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.
8. ### 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...
9. ### I Problem with electric flux

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...
10. ### Gauss's Law and Ampere's Law -- Force on an ion in a plasma due to a nearby electron beam

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...
11. ### 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..

13. ### Gauss' Law for 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?
14. ### 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...
15. ### 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...
16. ### 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.
17. ### 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...
18. ### 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...
19. ### 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...
20. ### 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...
21. ### 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...
22. ### 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...
23. ### 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...
24. ### 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...
25. ### 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...
26. ### 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...
27. ### 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 Equations The Attempt at a Solution I...
28. ### 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...
29. ### 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...
30. ### 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...
31. ### Capacitance of a sphere

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...
32. ### 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...
33. ### 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...
34. ### 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...
35. ### 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...
36. ### 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...
37. ### Application of Gauss' Law

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...
38. ### 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...
39. ### 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...
40. ### 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...
41. ### 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}##...
42. ### 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...
43. ### Elec. flux through the top side of a cube with q at a corner

Homework Statement Find the electrix flux through the top side of a cube. The cube's corner is on the origin, and is 'a' units on length. The charge 'q' is located at the origin, with the corner of the cube. Homework Equations Gauss's law and symmetry The Attempt at a Solution I take 8 cubes...
44. ### Gauss' Law for electromagnetic radiation?

For the proof I've read that verifies transverse electromagnetic waves are consistent with Gauss' Law, there seems to be the suggestion that the magnetic and electric field at a given small length c(dt), along which the waves travel, propagate infinitely backwards and forwards in their...
45. ### Electric potential related to electric field question

Homework Statement (i) Consider a non-conducting sphere of radius R with non-homogeneous charge density ρ = ρ(r) = r, where r is the radial co-ordinate. (a) Find the electric field inside and outside of the sphere (b) Find and plot the electric potential inside and outside of the sphere...
46. ### Electric potential of charged concentric spheres

Homework Statement Two conducting concentric spheres of negligible thickness. The radii of the spheres are R_1 and R_2, respectively, with R_2>R_1. A charge q_2 is placed on the external sphere. A charge q_1 is placed on the internal sphere. Assume that the electric potential is zero...
47. ### Capacitance capacitor parallel plate with dielectric (Gauss)

Homework Statement I have an elementary doubt with the calculation of the capacitance of a capacitor of parallel plates that has a dielectric in the middle. https://ibb.co/b0W4BQ Homework Equations ∫D⋅ds=Q D=E+γP C=Q/V The Attempt at a Solution Suppose the top plate has a positive charge...
48. ### Gauss' Law - electric field

Homework Statement An infinite metal plate has a surface density of charge σL=-6μC/m² , Left side and a surface density Of load σR=+4μC/m² , in the right side. A Gaussian surface In the form of a circular cylinder, with area A 12 cm², is Located with the left side inside the plaque and a thin...
49. ### Capacitor with uniform space charge between them

Homework Statement 2 large plates are separated by a distance d and a space charge of uniform charge density p is placed between them and a potential difference V is applied accross the plates. Find the electric field stength at a distance x fromt the positive plate The answer is -V/d...
50. ### Electric field of a washer (hollow disk)

Homework Statement A washer made of nonconducting material lies in the x − y plane, with the center at the coordinate origin. The washer has an inner radius a and an outer radius b (so it looks like a disk of radius b with a concentric circular cut-out of radius a). The surface of the washer is...