Gauss' law Definition and 25 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. F

    Magnitude of the Line Charge Density of a Power Line

    Okay so I am a little confused as to where I made a mistake. I couldn't figure out how to program Latex into this website but I attached a file with the work I did and an explanation of my thought process along the way.
  2. A

    Electric field shielding: Does a hollow conductor shield its inside when a charge is brought near

    Hi. I was reading about conductors in electrostatic equilibrium and how it makes sense that they have zero electric field inside the material even when an external charge is brought near. The charge density of the material just rearranges itself to cancel. Then I searched for hollow conductors...
  3. solzonmars

    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...
  4. Const@ntine

    Gauss' Law: Sphere with an Opening

    Homework Statement An uncharged, unconductive, hollow sphere with a radius R of 10.0 cm, surrounds an electric charge of 10.0 μC, which is found at the beginning of the axises, in a standard cartesian system. Parallel to the z axis, a small drill with a radius r = 1.00 mm opens a hole in the...
  5. E

    Electric field outside conductor surface

    I'm confused as to how this expression E= (δ/εo) can't be used to calculate the electric field of a perfectly flat part of a surface even farther from just above the surface.If you just extend the same cylindrical Gaussian surface used for this proof, wouldn't the field stay the same no matter...
  6. AdrianMachin

    Confusion over electric field inside a charged shell

    I've got confused over a topic in my physics textbook (Fundamentals of Physics). The textbook says if a charged particle is enclosed by a shell of uniform charge, there is no electrostatic force on the particle from the shell. I don't firmly get this, as the book uses a confusing reasoning for...
  7. A

    B How to find the appropriate area in Gauss' law

    Knowing that Gauss' law states that the closed integral of e * dA = q(enclosed)/e naut, how would you find exactly what A is in any given problem? I know it varies from situation to situation depending on the geometry of the charge. For instance, I know that for an infinite wire/line of...
  8. J

    Electric field inside a sphere

    I'm confused with the electric field inside a sphere. The book said that E=keQr/a^3 While one of the properities of electrostatic equilibrium mentioned that the E-field is zero everywhere inside the conductor. Are there any exceptional cases? Thanks in advance.
  9. pesslovany

    Application of Gauss' law - point charge in hollow sphere

    Firstly I appologize, that I am not native english speaker and I don't study physics(but cybernetics we are getting just some general knowledge about physics), but hopeffuly I will write this right. Homework Statement We know that inside of a conductive object is protected from influence of...
  10. twist.1995

    Electric field discontinuity in a spherical shell?

    Homework Statement Lets say, there is a non-uniform charge distribution, given as in a spherical shell that has a cavity with radius a and the radius b to the outer surface. I am wondering if the field is discontinuous just on the surface of this sphere. Homework Equations...
  11. G

    Uniform E field for spherical shell.

    Homework Statement In the figure a nonconducting spherical shell of inner radius a = 2.07 cm and outer radius b = 2.51 cm has (within its thickness) a positive volume charge density ρ = A/r, where A is a constant and r is the distance from the center of the shell. In addition, a small ball of...
  12. A

    Calculating the electric flux

    Homework Statement Hello, A 3.60cm x 4.50cm rectangle lies in the xy-plane. What is the electric flux through the rectangle if E=(80.0i + 50k) N/C ? Homework Equations Φ = E * A =EAcos(θ) The Attempt at a Solution My attempt: First convert the rectangle units from cm to m. 4.50cm =...
  13. A

    Calculating the Electric FLux

    Hello, The problem: A 3.60cm x 4.50cm rectangle lies in the xy-plane. What is the electric flux through the rectangle if E=(80.0i + 50k) N/C ? My attempt: First convert the rectangle units from cm to m. 4.50cm = 0.045m 3.60cm = 0.036m Find the area of the rectangle. A = 0.036m x 0.045m =...
  14. J

    Gauss' Law for a coaxial cable

    Homework Statement I have attached the problem Homework Equations E*A = Qenc/ E0 The Attempt at a Solution At the moment I am looking at the problem more conceptually and seeing what is happening at each point and I wanted to know If I was on the right track. r<a As all charge would...
  15. Idyia

    B Shape of a Gaussian surface

    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?
  16. S

    I Properties of body with spherical symmetry

    I'm studing Gauss law for gravitational field flux for a mass that has spherical symmetry. Maybe it is an obvious question but what are exactly the propreties of a spherical simmetric body? Firstly does this imply that the body in question must be a sphere? Secondly is it correct to...
  17. erick rocha

    Using Gauss's Law on two separated, and infinite plates

    Homework Statement The figure shows cross-sections through two large, parallel, nonconducting sheets with identical distributions of positive charge with surface charge density σ = 1.06 × 10-22 C/m2. What is the y component of the electric field at points (a) above the sheets, (b) between them...
  18. B

    Gauss' Law question

    Homework Statement Consider two balls of equal radii and masses but opposite charges, distributed uniformly over their volumes. Initially, the balls are at rest and far away from one another. Due to the Coulomb attraction, the balls start moving towards each other. The balls can be treated as...
  19. A

    Does Gauss' Law use line integrals or surface integrals?

    In my physics textbook, I see Gauss' Law as\ointE [Broken] dA but in other places I see it as...
  20. J

    An insulating sphere inside a conducting sphere questions

    I've been given a copy of my friend's midterm exam from this same class from last term, and decided to take a crack at it to help study. One question type in particular really messes me up and it looks like the following. How would I go about solving these in the future? A solid insulating...
  21. Elvis 123456789

    Applications of Gauss' law

    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. Let the charge...
  22. V

    Divergence Theorem Question (Gauss' Law?)

    If F(x,y,z) is continuous and for all (x,y,z), show that R3 dot F dV = 0 I have been working on this problem all day, and I'm honestly not sure how to proceed. The hint given on this problem is, "Take Br to be a ball of radius r centered at the origin, apply divergence theorem, and let the...
  23. Shreyansh

    Electric field inside a closed conductor.

    I recently studied Gauss' theorum according to which there is no electric field inside a closed conductor. But an isolated chage emits field lines in all possible directions. So why is it that there are no electric lines from the surface of the closed conductor inside it?
  24. H

    Pointlike charge - electric potential

    This is my first time using a website like this, so I sincerely apologize if I'm posting in the wrong spot, I'm just in a bind/frustrated with this seemingly easy problem. Homework Statement What is the electric potential at a point 0.80 m away from a point charge of 3.5m C? Homework...
  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...