# What is Gauss' law: Definition and 338 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. ### 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...
2. ### Gauss' law for a cavity in an insulator

This is a problem from Yale OCW (Shankar). The solution he gives is as follows: Sure, this makes sense. However... Superimposed rho and negative rho with radius R/2 means there is no charge enclosed in the cavity... therefore no charge -> no flux -> no electric field.
3. ### I Gauss' law, method of images, and force induced on conductor plates

Hi, I would very much appreciate some guidance on the below. Consider a one-dimensional world as depicted in the attached figure. We have two (lets say positively charged particles enclosed by two conductor plates. One plate is at ##x=0##, the other at ##x=L##. The particles are at ##x_1## and...

38. ### 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...
39. ### By using Gauss' law, can the electric field be p/(pi*ε*r^2)

Which is better to use? The equation for the area or the circumference of a circle? Schaum's Electromagnetics (4 ed) by Edminister vs http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elecyl.html
40. ### I Determining continuity using Gauss' law

I know how Gauss law helps us to calculate the discontinuity at a point on the surface of a surface charge. Similarly using Gauss law, is there a way to determine the continuity at other points of electric field due to a surface charge or the continuity at all points of electric field due to a...
41. ### Why does a Faraday Cage work?

Why does a Faraday Cage work? (or more generally, why does the inside of a conducting shell have no electric field if there are charges placed outside it?) I understand that this is the result of polarisation, but why does the polarisation happen to exactly cancel out the field? Could there be...
42. ### Electricity and magnetism (Gauss' law)

Homework Statement Given two things spherical shells radii r1 and r2 with r2 > r1. The inner she'll is charged uniformly with a total charge Q1, while the outer shell with Q2. A) use gauss law to computer the electric field everywhere B) Use any method to calculate the potential everywhere...
43. ### 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...
44. ### Use Gauss' Law to find E-field, tricky problem

Homework Statement A) use gauss's Law to determine the electric field at all values of radial distance (0<r<infinity) from the center of a non-uniformly charged cylinder that is very very long and lies along the x-axis. The cylinder carries excess charge per volume ρ=[a]r^2 (the [] are supposed...
45. ### Determining net force using Gauss' Law

Homework Statement We have a uniformly charged, non-conducting sphere (charge per volume,ρ, and radius, R). Then a uniformly charged ruler (charge per length,λ, and length, d) is aligned radially almost touching the surface of the sphere. Determine the net force experienced by the ruler...
46. ### I Why do the signs alternate when using Gauss' law for gravity?

"Gauss's theorem can be established as follows. consider an attracting particle of mass m at the point P, and let a cone of small solid angle ω be generated by radii through P. This cone cuts the surface at the points Q1, Q2, ... taken in order from P; the parts of the surface cut off by the...
47. ### Conducting Sphere With Cavity E-field / Gauss' law

Homework Statement You have a conducting sphere that is in equilibrium, it has a cavity in it with positive charge +q. If you bring another charge +q2 near the outer edge of the conductor does the total surface charge on the wall of the cavity, q(int) change? There is an image attached that...
48. ### Electric field sphere calculations with a hollow cavity using Gauss' law

Homework Statement A spherical cavity is hollowed out of the interior of a neutral conducting sphere. At the center of the cavity is a point charge, of positive charge q. (picture attached) a)What is the total surface charge q(int) on the interior surface of the conductor (i.e., on the wall of...
49. ### Electric field using Gauss' Law

Homework Statement Two small insulating spheres with radius 9.00×10−2m are separated by a large center-to-center distance of 0.545 m . One sphere is negatively charged, with net charge -2.35 μC , and the other sphere is positively charged, with net charge 4.35 μC . The charge is uniformly...
50. ### I Gauss' law applied on a four-dimensional surface

in a 4D plane or on a four-dimensional surface can gauss law be used?