What is Gauss: Definition and 645 Discussions

Johann Carl Friedrich Gauss (; German: Gauß [kaʁl ˈfʁiːdʁɪç ˈɡaʊs] (listen); Latin: Carolus Fridericus Gauss; 30 April 1777 – 23 February 1855) was a German mathematician and physicist who made significant contributions to many fields in mathematics and science. Sometimes referred to as the Princeps mathematicorum (Latin for '"the foremost of mathematicians"') and "the greatest mathematician since antiquity", Gauss had an exceptional influence in many fields of mathematics and science, and is ranked among history's most influential mathematicians.

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  1. Hawkingo

    What is the effect of the dielectric material on Gauss' law?

    [PAGE 1] [PAGE 2] [PAGE 3] so in the 2nd page,when the dielectric material is introduced the gauss's law becomes $$\oint _ { S } \vec { E } \cdot \vec { d S } = \frac { ( q - q _ { i } ) } { \epsilon _ { 0 } }$$.But my question is why the ##{ \epsilon _ { 0 } }## is in the equation.Shouldn't...
  2. cianfa72

    I Gaussian elimination for homogeneous linear systems

    Hi, I ask for a clarification about the following: consider for instance a 10 x 12 homogeneous linear system and perform Gauss elimination for the first 8 unknowns. Suppose you end up with 5 equations in the remaining 12-8 = 4 unknowns (because in the process of the first 8 unknowns elimination...
  3. N

    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...
  4. adamaero

    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
  5. Ssnow

    I Strange formulation of Gauss' Theorem

    Hi to all! The ordinary Gauss theorem states that ##\Phi\left(\vec{E}\right)\,=\, \frac{\sum_{i=1}^{n}q_{i}}{\varepsilon_{0}}## where ##\sum_{i=1}^{n}q_{i}## is the sum of all charges internal of a closed surface and ##\varepsilon_{0}## is the dielectric constant in the empty. Now I ask to the...
  6. M

    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...
  7. S

    Numerical integration - Gauss Lobatto

    Homework Statement I need calculate the points (##x_i##) and weights (##w_i##) with Gauss Lobatto seven points on the interval [a,b]. With the points and the weights I am going to approximate any integral at this interval.Homework Equations I have found the relevant points and weights at the...
  8. ubergewehr273

    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...
  9. yohanes vianei

    Applying Gauss' Law: Solving Electric Field Problems

    Homework Statement Homework Equations ∮E.dA = qencl/ϵ0 The Attempt at a Solution (a) magnitude E we use∮E.dA = qencl/ϵ0For a cylinder:∮E.dA = E(2πrL), thenqencl/ϵ0 = E(2πrL)E = qencl/(2πrLϵ0) E = λ/(2πrϵ0); WITH λ = qencl/L (a) the magnitude E, qencl = Q1 + Q2 , thenE = (Q1 +...
  10. Clara Chung

    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...
  11. C

    Exploring Electrostatics with Gauss Theorem

    Having come experimentally to an interesting electrostatic effect, I have returned, aged 47, to my old books in physics. It turns out that my books delight in using Gauss theorem etc. in rather ideal geometrical surface charge distribution, but never gave me the tools to answer to this simple...
  12. B

    I The integral form of Gauss' theorem

    In many texts I have seen, Gauss theorem has the form of$$\frac{q}{\epsilon_0}=\oint\vec{E}d\vec{A}$$ Why a line integral symbol was used for this surface integral everywhere? The more I see it the more I believe there is something wrong with my understanding about this. I didn't think too much...
  13. B

    Electric Field and Potential in a conductor

    So in my textbook (Introduction to Electrodynamics by Griffiths) it said that inside a conductor, the electric field E would have to zero, since if it wasn't the free charges would move accordingly and create a electric field that cancels the original field. But in a question that soon followed...
  14. Silentwhale

    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...
  15. E

    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...
  16. cookiemnstr510510

    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...
  17. cookiemnstr510510

    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...
  18. sams

    I Gauss' Theorem -- Why two different notations are used?

    In Mathematical Methods for Physicists, Sixth Edition, Page 60, Section 1.11, the Gauss' theorem is written as: In Mathematical Methods for Physicists, Fifth Edition, Page 61, Section 1.11, the Gauss' theorem is written as: Kindly I would like to know please: 1. What is the difference between...
  19. T

    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...
  20. cookiemnstr510510

    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...
  21. cookiemnstr510510

    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...
  22. cookiemnstr510510

    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...
  23. Jenab2

    I How to get state vector in 4-observation method of Gauss

    In the four-observation method of Gauss for orbit determination, the right ascension and declination of an asteroid is observed at specified times, and the heliocentric position of Earth is obtained from tables (or JPL Horizons) for those same times. I can follow the procedure to the point...
  24. H

    I Gauss' law applied on a four-dimensional surface

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

    A few questions regarding Neutral Objects

    1. Homework Statement Hello, I'm learning electricity and I'm having a few conceptual questions regarding the subject ( especially about neutral objects ) which I'm unsure of the answers and I'd be happy if someone could help me:1. Is the charge density of a neutral object ( doesn't matter if...
  26. A

    Gauss' law: find the electric field

    Homework Statement A long, thin, straight wire of length 1.3 m has a positive charge 4.1 × 10-8 C distributed uniformly along it. The electric field created by this wire at a radial distance 3.2 cm has a magnitude of ε= 8.85E-12 Homework Equations I think I need to use E= q/(4πr^2ε) but I...
  27. Wrichik Basu

    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...
  28. Samnolan1031

    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...
  29. Wrichik Basu

    B A question about Gauss' Theorem

    I was reading the book "Mathematical Methods for Physicists", and in the first chapter, under Gauss's Theorem, the statement given was: The surface integral of a vector over a closed surface equals the volume integral of the divergence of the vector over the entire closed surface. But the in...
  30. Conductivity

    Permittivity in Gauss' law and Ampere's law

    In the derivation of the electric field inside a non conducting sphere, We still use the permittivity of free space even though we are in a medium. The same applies for ampere's law in a solid wire. http://physics.bu.edu/~duffy/semester2/c15_inside.html...
  31. G

    Potential of an undefinided cylinder

    Homework Statement Determine the potential that creates an undefined cylinder of radius $R$ and density density $\rho$ that is uniformly charged. Homework Equations Gauss's law. The Attempt at a Solution I know that for this problem I can use gauss because it is a cylinder, now I do not get...
  32. G

    Using Gauss's Law to Calculate Electric Field of a Charged Thread

    Hello, Can not Gauss's Law be used to calculate the electric field generated by a uniformly charged finite thread? I suppose it is because I can not consider the electric field constant (always going to the same direction), and for this I would have to do it by parts (the lateral flow, and the...
  33. F

    Gauss’ law and Enclosed Charges

    What exactly does the electric field as solved for by Gauss’s law tell us? If you use a Gaussian surface that encloses no charge you find that the electric field is equal to 0. But if there is a charge outside of that Gaussian surface, it is not true that the electric field is 0 on the Gaussian...
  34. SothSogi

    I Is my attempt to derive Gauss' law correct?

    Hi there. I am trying to derive Gauss's law from the divergence. I would like to know if it is correct: The divergence is defined as (I saw this on Fuller & Byron "Mathematics of classical and quantum physics") ##...
  35. S

    Apparent disagreement between Coulomb's Law and Gauss' Law

    This is probably my misunderstanding, so please clarify. In a region of empty space, there are two point charges with the charges+Q and -Q. Exactly in the middle of the two charges (distance r from both charges) is point P, colinear with the centers of both charges. A Gaussian surface that...
  36. Conductivity

    Is Gauss' Law for Magnetism Proven by Magnetic Field Lines?

    We took today in a lecture gauss' law for magnetism which states that the net magnetic flux though a closed shape is always zero (Monopoles don't exist). The professor explained/proved it as following (Since it needs math theorems): Draw any shape. From the fact that any magnetic field line that...
  37. F

    I Gauss’ law and an infinite rod

    To find the electric field from an infinitely long charged rod you can use gauss’s law with a cylinder as your Gaussian surface. I don’t quite understand by this works. Wouldn’t the electric field given by the equation only be the electric field cause by the charge within the cylinder? And if...
  38. Ignitia

    How Does Gauss' Law Apply to a Spherical Conducting Shell with a Central Charge?

    Homework Statement A point charge q=−5.0×10−12 C is placed at the center of a spherical conducting shell of inner radius 3.5cm and outer radius 4.0 cm. The electric field just above the surface of the conductor is directed radially outward and has magnitude 8.0 N/C. (a) What is the charge...
  39. F

    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...
  40. Ben2

    A Proving the Last Gauss Lemma for Real Numbers Using Induction

    Modified from Disquisitiones Arithmeticae, p. 10: Let "*" indicate multiplication and "^" indicate "to the power." For real numbers a, b, c,..., let [a] = a, [a,b] = b*a+1, [a,b,c] = c*[a,b]+[a], [a,b,c,d] = d*[a,b,c]+[a,b], etc. Prove that [a,b,...,l,m]*[b,c,...,l] - [a,b,...,l]*[b,c,...,m]...
  41. G

    Gauss's Law and Parallel Line Charges

    Homework Statement Find an equation for the net electric field at a point, above and between, two infinite line charges, one with line charge density λ and the second with line charge density -λ. The point is a distance R from both line charges, a distance y above the midpoint between charges...
  42. M

    MHB Understanding Gauss Quadrature for Approximating Integrals

    Hey! :o I am looking at the Gauss Quadrature to approximate integrals. I haven;t really understood the meaning of the weighting function. Could you explain that to me? At each case, the points that we need depend on what weighting function we have, so which polynomials we consider or not...
  43. lawsonfurther

    Applying Gauss' Law for Calculating Work Req'd to Move Charge

    Homework Statement A capacitor has two square plates that are d apart. Each plate is L×L. The capacitor is initially uncharged. (a)Calculate the work required to move q of charge from one plate to the other. (b)Calculate the work required to move an additional q of charge from one plate to the...
  44. Likith D

    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...
  45. Lucas Silva

    Gauss' Law: Charge of a Hydrogen Atom

    Suppose the hydrogen atom consists of a positive point charge (+e), located in the center of the atom, which is surrounded by a negative charge (-e), distributed in the space around it. The space distribution of the negative charge changes according to the law p=Ce^(−2r/R), where C is a...
  46. Const@ntine

    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...
  47. 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...
  48. M

    MHB Gauss theorem: Prove equalities

    Hey! :o With appropriate conditions, I want to show that $$\iiint_{\Omega}(\nabla \phi)\cdot \textbf{f}\ dV=\iint_{\Sigma}\phi\textbf{f}\cdot \textbf{N}\ dA-\iiint_{\Omega}\phi\nabla\cdot \textbf{f}\ dV$$ With appropriate conditions, I want to prove Green's identities...
  49. M

    MHB What is the application of Gauss theorem on a pyramid?

    Hey! :o Using Gauss theorem I want to calculate $\iint_{\Sigma}f\cdot NdA$, where $\Sigma$ is the closed boundary surface of the pyramid with vertices $(0,0,0), (1,0,0), (0,1,0), (0,0,1), (1,1,0)$ and $f(x,y,z)=(x^2y, 3y^2z, 9xz^2)$ and the perpendicular vectors $N$ to the inside of the...
  50. Tom MS

    Why Does Diatomic Hydrogen Form Despite Zero Net Electric Field?

    Say you had two isolated hydrogen atoms. Because of the spherical distribution of electronic charge on each hydrogen and the net charge of 0 outside each atom, wouldn't Gauss's law dictate a 0 net electric field outside each atom? If this is the case, why does diatomic hydrogen so readily form...
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