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.
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...
Homework Statement
Normally this style of question wouldn't be too bad, however the 2 different parts confused me. Surely once set to a potential V, it would stay at that potential - it doesn't need to stay connected
How are the 2 parts any different from each other?
Hi everyone, I am having problems figuring out how to solve a particular problem.
Because I was not able to access PhysicsForums recently, I typed everything about my issues into a pdf file that I have attached below.
I am grateful for your help in advance, and make it a great day...
Homework Statement
I want to derive the following equation. It is the potential energy of an electron inside a nucleus assumed to be a uniformly charged sphere of R.
Homework Equations
V'(r) =( -Ze2/4∏ε0R)(3/2 - (1/2)(r/R)^2)
The Attempt at a Solution
I get E = Ze2r/(4∏ε0R3)
But I am...
Hi.
Is it possible to derive the properties of a Faraday cage from Gauss' law alone? I found some "derivations" which I find rather unconvincing since they somehow conclude from a vanishing flux that the E field must vanish as well.
Some slightly more elaborate derivations use a combination of...
Homework Statement
What I basically want to do is to prove Gauss Law with a cylinder perpendicular to an infinite charged wire (I know I can do this simple, but I want to do it this way)
This is what I have done so far:
Homework Equations
$$\Phi=\int \frac{dq}{4\pi \varepsilon_0 r^2}...
At this point I was given rho, sigma and landa to hold value of these three different kinds of density
ρ = Charge/Volume -------------- Volume Density
σ = Charge/Area ----------------- Area Density
λ = Charge/Length ---------------- Length Density
How do I know which type of density to use over...
Homework Statement
An insulator is in the shape of a spherical shell. The insulator is defined by an inner radius a = 4 cm and an outer radius b = 6 cm and carries a total charge of Q = + 9 C (1 C = 10-6 C). You may assume that the charge is distributed uniformly throughout the volume of the...
As per the Gauss Law , Net Flux Electric Field through a closed Surface (Gaussian Surface) is zero if no charge is enclosed.
As per the definition of the Electrical Flux = Electrical Field Intensity dot product Area Vector i.e. Closed Integral of E.S
If Electrical Flux is zero then as per the...
Homework Statement
In the figure two large, thin metal plates are parallel and close to each other. On their inner faces, the plates have excess surface charge densities of opposite signs and magnitude 7.76 × 10-22 C/m2. What is the magnitude of the electric field at points (a) to the left of...
Homework Statement
Hi, I am studying gauss's law via this book below.[/B]
http://faculty.polytechnic.org/cfletcher/Phys%20With%20Calc_Vol_2_web_pdfs_2010/i-Ch14-PCALC--GAUSS'S%20LAW.pdf
On page 8, and 9, the book describes the shell method of finding the volume of the sphere and then using...
Homework Statement
The volume between two infinite plates located at x=L and x=-L respectively is filled with a uniform charge density ##\rho##. Calculate the electric field in the regions above, between and below the plates. Calculate the potential difference between the points x=-L and x=L...
Homework Statement
I just want to focus on the divergence outside the cylinder (r >R)
Homework Equations
The Attempt at a Solution
For r > R, I said ∇ * E = p/ε
But that's wrong. The answer is ∇ * E = 0
I'm confused because there is definitely an electric field outside the cylinder (r...
1. Homework Statement
I need to find the total charge inside the small metal sphere, inside the big metal sphere as well as outside the big metal sphere.
Homework Equations
What confuses me is the electric field vector. Since it's only poiting in one direction it can't originate from a...
1. The problem: A Geiger-Mueller tube is part of a Geiger counter, a device used to count the number of ionizing particles passing through it. It consists of a conducting outer cylinder held at zero electric potential with a thin central wire held at an electric potential of roughly 1000 volts...
hi, i still don't understand why infinite thin-walled cylindrical shell or conducting rod use lambda rather than sigma ?
lambda = C/m ,,, sigma = C/m^2
i mean when we look at conducting rod, the charges inside the conductor is zero, so the charges spread on the surface of conducting rod(have...
a long straight wire has fixed -ve charge density of 39nC/m. the wire is enclosed by thin wall non conducting coaxial cylinder of radius 1.7m. the shall has positive charge density and its Field is such as that it will cancel the field due to wire. what will be the surface charge density of...
Homework Statement
If ##\vec{E}=k\frac{x\hat i +y\hat j}{x^2+y^2}##, find flux through a sphere of radius R centered at origin.
Homework Equations
##\int E.da=\int(\nabla\cdot E)\cdot da##
The Attempt at a Solution
I was able to solve this problem without finding divergence of electric field...
Hi everyone,
I am wondering if anybody could help me out. For my study I got the following question but I got stuck in part C (see image below).
I Found at A that due to symmetry all components which are not in Ar direction will get canceled out
I found at B that there is only charge density at...
Homework Statement
a) and b) are no problem.
I need help to solve c) and d)
Homework Equations
c) Delta dirac function
Gauss' law
d) Gauss' law
## \int_V {\rho \, d\tau} = Q_{enclosed} ##
The Attempt at a Solution
By taking laplace on the potential I get:
## \rho(\mathbf{r}) =...
Homework Statement
1)
A large cube has its bottom face on the x-z plane and its back face on the x-y plane. The corners on the x-axis are at (3.39 m,0,0) and (12.3 m,0,0). The cube is immersed in an electric field pointing in the positive x-direction, and given by:
E = (91.2x^2 - 2.9)i, x is...
I was just wondering why the strength of the electric fields of insulating surface charges like sheets and shells aren't dependent on the distance from the charge according to Gauss's Law?
Homework Statement
Spherical capacitor with two linear and uniform dielectrics with relative permitivitty Ɛr1 and Ɛr2 is connected to constant voltage U. When second dielectric is removed, intensity of electric field by inner electrode is reduced by 1/3, and electric field by outer electrode...
Homework Statement
Given a situation like this:
Where the two blocks are perfectly conducting materials and are touching, will they separate? If they do separate, will they have the net charge values you calculate in the initial setup using Gauss's Law?
There are no numbers, it's just...
I'm currently writing my EP on various physical equations including Maxwell's equations, and I had to justify using the dot product of the normal unit vector and the electric field in the integral version. However, I can't think of a reason for not using trigonometry as opposed to the...
Homework Statement
Three very long (theoretically infinite long) hollow cylindrical conductors, with radius a,b,c (c>b>a) are in vacuum. Inner and central conductor are charged, and outer conductor is grounded. Potentials of inner and central conductors with reference point relative to outer...
Hi! I have trouble with solving this problem and would be really thankful for some help. :)
1. Homework Statement
Inside a thin, spherical metal-shell with a radius of 50 cm, a smaller homogenous metal-sphere with a radius of 20 cm is placed concentrically. The smal sphere is grounded through...
Homework Statement
The total electric flux from a cubical box 34.0 cm on a side is 1.29 x 103 N·m2/C. What charge is enclosed by the box?
----and----
Three charged particles are placed at the corners of an equilateral triangle of side d = 1.00 m (Fig. 16-53). The charges are Q1 = +4.0 µC, Q2...
Homework Statement :
[/B]
Co-axial cable, relative permittivity, capacitance, internal energy
A long straight co-axial cable of length 1 consists of an inner conductor of radius r1 and a thin outer conductor or radius r2. The dielectric between the conductors has a relative permittivity εr...
Homework Statement
Assume I want to calculate the electric flux through a spherical surface centred at point P with radius R which contains a point charge Q, that is not concentric with the spherical surface.
Here, I can no longer assume that ∫∫sEdA = E.A, and I have to calculate the value of...
Gauss's Law states that if a Gaussian Surface encloses a charge ##q_{enc}## then the electric flux through the Gaussian Surface is given by ##\phi=q_{enc}/\varepsilon_{o}## .
It also states that any external field does not contribute to the Electric Flux through the Gaussian Surface.
I am bit...