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.
Solving the integral is the easiest part. Using spherical coordinates:
$$ \oint_{s} \frac{1}{|\vec{r}-\vec{r'}|}da' = \int_{0}^{\pi}\int_{0}^{2\pi} \frac{1}{|\vec{r}-\vec{r'}|}r_{0}^2 \hat r \sin{\theta}d\theta d\phi$$
then:
$$I = \dfrac{1}{|\vec{r}-\vec{r'}|}r_{0}^2(1+1)(2\pi)\hat...
The first image is for a conducting sheet (part of it anyway), the second is for a nonconducting sheet. Gauss' law seems to tell me that the electric field strength are different - they differ by a factor of two. Is this true?
The charge enclosed in both of them are the same, and my intuition...
Hi!
So my question is this, I have done measurements with an magnetic field meter around a transformer from 0.5 meter away (then measure some points around) and then I moved out 0.5 meters and so on until I reached a nearby building.
So my issue now is I want to visualize this to my customer...
I know the Gauss law for surface integral to calculate total charge by integrating the normal components of electric field around whole surface . but in above expression charge is calculated using line integration of normal components of electric field along line. i don't understand this...
I solved laplacian equation. and got the solution of V(r, phi) = a. +b.lnr + (summation) an r^n sin(n phi +alpha n ) + (summation) bn r ^-n sin( n phi +beta n)
Hi everyone!
I'm pretty new in this forum, I found the topics here very relevant to my physics course. And here is my question:
Given the following drawing, two infinite sheets (in y and z axis) of ideal conductive material. their thickness is infinitesimal (dx->0).
The electric field is...
When I try to derive Gauss's law with a straight line of charge with density ##\lambda## through a cylindrical surface of length L and radius R,
$$\vec E = \frac{\lambda*L}{4\pi\epsilon*r^2}$$
$$A = 2\pi*r*L$$
$$\vec E*A = \frac{\lambda *L^2}{2\epsilon*r} \neq \frac{q_{enc}}{\epsilon}$$
What am...
Draw a Gaussian pill box that starts from 0 (half way between the slab) and extends towards 2 cm.$$A \times \int_{0}^{0.02} \rho dz$$
I'm not sure if I should multiply the integral by A (area) or V (volume)
And if area would I multiply by 0.02^2?
I'm confused here. Thanks for your help.
First draw a gaussian shape outside of the sphere (a larger sphere) with radius R. The total charge from the (inner) sphere will be:
$$Q = \sigma A$$
$$A = 4\pi r^2$$
$$Q = \sigma 4\pi r^2$$
Use Gauss's Law to derive electric field magnitude
$$\oint_{}^{} E \cdot dA = \frac{q_e}{\epsilon_o}$$...
In the usual literature about analytical mechanics, I find very little about the Gauss principle of less constraints and the Gibbs-Apell equations. I think the only treatment I've seen on Gauss is given In Lanczos's The variational principle of mechanics".
So, I'm looking for introductory and...
Picture :
My answer :
I guess net electric flux is 0.
so electric flux passing through surface 1 = -(electric flux passing through surface 2)
and electric flux passing through surface 1 is EA = E(pi)(r^2)
Is it correct? Thank you ...
Gauss' law: $$\iint_{\partial A}\vec E\cdot d\vec A=\frac{Q}{\epsilon_0}$$
Suppose we have a unevenly charged non-conducting spherical shell, in which a Gaussian surface is placed. In this case, is the electrical field on A 0, given that there is no charge inside A? I came up with this example...
confused on part A/B when I look up they did E= Q/2e(0.8)^2.
But why not use the 0.100mm because that is the area of the enclosed.
Same with B why did they use 100m and not 0.8m because 0.8 is smaller so it enclosed the charge
Electric Flux = E*A = 5*6(0.05)^2.
when i look up at other sources they use Electric flux = q/ (8.854*10^-12 [this is e]) equation
but I am confused on why the E*A equation don't work. The answer is 0.02Nm^2/C
What am I missing?
I also don't get the title of the section: "Charge distributions with enough symmetry for Gauss's Law".
I thought Gauss's Law was valid for any closed surface enclosing a charge. I don't understand what "enough symmetry" means in the title above. I get that with symmetry...
Hi guys i have some concept issues about flux. My book says flux is proportional to the number of lines passing through that area. so my question is: first i am thinking that a 2D circle which has a 2r diameter and it is enclosing a 2q charge so its flux should be 2q/Epsilon.then i am thinking a...
Gauss law relates the net flux phi of an electric field through a closed surface to the net charge q that is enclosed by that surface. It tells us that
Phi = q/permittivity
Can I say it like this : The gauss law states that the net flux of the surface depends upon the net charge enclosed by that...
My book claims that the diff. form of Gauss' law is
$$\nabla\cdot\mathbf E=4\pi\rho$$
Can someone tell me why it isn't ##\nabla\cdot\mathbf E=\rho/\epsilon_0##?
Hello everyone. I have been recently working in an optimization model in the presence of uncertainty. I have read https://www.researchgate.net/publication/310742108_Efficient_Simulation_of_Stationary_Multivariate_Gaussian_Random_Fields_with_Given_Cross-Covariance in which, a methodology for...
##\nabla \cdot \vec{E} = \frac{\rho}{\epsilon_0}##
##\vec{E}_0 k cos(kr -\omega t) = \frac{\rho}{\epsilon_0}##
##E_0 = \frac{\rho}{\epsilon_0} / k cos(kr -\omega t)##
and
##k^2 = (\arccos{\frac{\rho}{E_0 \epsilon_0}} + \omega t)/r##
I don't think it makes sense since I found ##k = \pm...
Hello everybody
To calculate the flux for the electric field I need the gauss law. There are two formula one with the integration over some area and the other is Q/e0. When do I have to use which one?
Hey! :giggle:
Calculate the node $x_0$ and the weight $a_0$ of Gauss Quadrature so that $$\int_0^1w(x)f(x)\, dx\approx I_0(f)=a_0f(x_0)$$ where $w(x)=1+\sqrt{x}$.
I have done the following:
The Gauss quadrature formula with $(n + 1)=1$ node (i.e. $n=0$) integrates polynomials of degree $2n +...
I get a nonsensical result. I am unable to understand where I go wrong.
Let's consider a material with a temperature independent Seebeck coefficient, thermal conductivity and electrochemical potential to keep things simple. Let's assume that this material is sandwiched between 2 other materials...
I am trying to derive that
$$\nabla \times B=\mu_0 J$$
First the derivation starts with the electric field
$$dS=rsin\varphi d\theta r d\varphi $$
$$ \iint\limits_S E \cdot dS = \frac{q}{4 \pi \varepsilon_0} \iint\limits_S \frac{r}{|r|^3} \cdot dS $$...
If I understand correctly, Gauss’ Law is (roughly) derived as follows:
Part A
Electric Flux = EA
E = q / (∈4πr^2)
A of the surface of a sphere is 4πr^2
They cancel out and therefore EA =q/∈
Line 4 seems to only apply to a sphere, as it is based on line 3.
Now, Gauss’ Law is applied to...
I'm a bit confused on the derivation above. I understand what the goal of the derivation is, as it derives Gauss's Law using the solid angle, but i was wondering if someone could kind of fill in the steps the author skipped and explain the use of the solid angle.
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...
Attached is problem 23.03 from Halliday and Resnick.
We have a sphere of uniform negative charge Q = -16e and radius R = 10cm. at the center of the sphere is a positively charged particle with charge q = +5e. We are supposed to use Gauss' law to find the magnitude of the electric field at...
Stokes theorem relates a closed line integral to surface integrals on any arbitrary surface bounded by the same curve. Gauss theorem relates a closed surface integral to the volume integral within a unique volume bounded by the same surface. What causes this asymmetry in these 2 theorems, in the...
Summary:: For finding the electric field at P in the photo below, may I select a gaussian surface circular?
[Mentor Note -- thread moved to the schoolwork forums, so no Homework Template is shown]
I don't know the terms so I'm sorry if the informations at summary above is unclear. But I add a detailed photo of my calculations below. I use Gauss' Elimination laws.
Gauss' law dictates that charge will only appear on the outer surface of a conductor. But if there's charge in a conducting cavity, the inner surface of the conductor will accumulate induced charge. So what's outer or inner should be redefined?
In derivations of capacitance it is standard to consider two oppositely charged, infinitely thin sheets. If we construct a Gaussian cylinder across one sheet, we obtain ##E_{1} = \frac{\sigma}{2\epsilon_{0}}## for one sheet, and then we can superpose this field with that from the other at an...
This is my attempt, i am confused at some points
a. r = 0; The Electric field is 0
b. At r = a/2.00; I verified the answer and it is non zero, but my understanding is that the net charge should be on the surface of the conductor. Hence the charge q1=5*10^-15 C, should go to the surface of the...
Hi,
I just have a quick question about a problem involving Gauss' Theorem.
Question: Vector field F = \begin{pmatrix} x^2 \\ 2y^2 \\ 3z \end{pmatrix} has net out flux of 4 \pi for a unit sphere centred at the origin (calculated in earlier part of question). If we are now given a vector...
I really don't understand the theory of the above kind of questions. But from the little theory i understand the Electric field is 0 inside the conductor and all the charge goes to the surface and distributes equally.
a. Since the E=0 inside the conductor the point charge distributes outside...
My attempt is
∅ = ∫E.dA.
The direction of E is going out of the net towards +ve i axis.
I am not clear on the direction of the Area, it can be either +ve i-axis or -ve i-axis. Which direction should i consider?
∅ = ∫3.dA = 3*∫dA ---->1
∫dA is the area of the circle.
A = π * (0.11)^2 = 0.038...
i have little experience with the differential form of Gauss's Law, and I've tried three times now to arrive at it for a point mass M (spherically symmetric classical gravitational field) but instead of getting an answer proportional to the mass density I keep getting zero. Is the divergence...
The first time I saw this question I had no idea how to do it (as you can see in the figure, I lost a lot of points :s) because I was confused on how to even approach it with area of the slab from all sides being infinity. Right? That's problematic, no?
Today, I just tried the problem again for...
I need a citeable source that gives the formula for the Gaussian curvature at a single point of an intrinsically defined Riemannian or Semi-Riemannian manifold given the intrinsic metric tensor and/or Riemann tensor.
I've got sources for this already, but I'm not "allowed" to use them for this...
I have read multiple threads on Physics Forums, Stackexchange and Quora, as well as the explanation of Gauss Law, but still don't understand the most fundamental aspect of it: its applicability for any kind of surface. More precisely, I don't get how this follows from the fact that...
I've just been learning about Gauss' law which as far as I can tell states that the net electric flux through a surface equals the enclosed charge divided by the permittivity of free space, and is often expressed as the integral $$\int_S {\bf{E} \cdot d \bf{A}} = \frac{Q}{\epsilon_0}$$In some...
Hi,
I'm trying to prove Gauss's Law by using a cubical surface with a point charge located at its center, and I'm running up against some difficult integration. I've worked through the first integral of the surface integral, but I can't seem to figure out a proper integration technique. Here is...
So the first problem stated is to show that for a charge distribution between two spherical shells of radii r1<r2, the total charge inside is described by:
This is rather trivial using Gauss' law in integral form, so I regard this as completed.
I have used the gradient to find the electrical...
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so in the 2nd page,when the dielectric material is introduced the gauss's law becomes $$\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...