Gauss law Definition and 182 Threads

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...

A solid sphere has surface charge density, Rho (r) Rho(r) = k 1 ( 0 < r < a) k2 x ( a < r < R) 2) Find the electric field in all region i.e 1) r < a and 2) a < r < R and 3 ) R < The attempted solution and the question with the diagram is attached below Could the answer be verified...

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...

If the coulomb's law instead of following an inverse square relationship, follows an inverse cube relationship, How would it affect an isolated charged conducting sphere? How would it's field vary within the volume and how would the volumetric charge density be affected? Please give in some...

Homework Statement A static charge distribution has a radial electric field of magnitude ##E = \alpha \frac{e^{-\lambda r}}{r} ## where λ and α are positive constants. Calculate the total charge of the distribution. Homework Equations Gauss's law ##Q/\epsilon_0 = \int \vec{E} \cdot d\vec{S}##...

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...

Homework Statement Find the electrix flux through the top side of a cube. The cube's corner is on the origin, and is 'a' units on length. The charge 'q' is located at the origin, with the corner of the cube. Homework Equations Gauss's law and symmetry The Attempt at a Solution I take 8 cubes...

For the proof I've read that verifies transverse electromagnetic waves are consistent with Gauss' Law, there seems to be the suggestion that the magnetic and electric field at a given small length c(dt), along which the waves travel, propagate infinitely backwards and forwards in their...

Homework Statement (i) Consider a non-conducting sphere of radius R with non-homogeneous charge density ρ = ρ(r) = r, where r is the radial co-ordinate. (a) Find the electric field inside and outside of the sphere(b) Find and plot the electric potential inside and outside of the sphere...

Homework Statement Two conducting concentric spheres of negligible thickness. The radii of the spheres are R_1 and R_2, respectively, with R_2>R_1. A charge q_2 is placed on the external sphere. A charge q_1 is placed on the internal sphere. Assume that the electric potential is zero...

Homework Statement I have an elementary doubt with the calculation of the capacitance of a capacitor of parallel plates that has a dielectric in the middle. https://ibb.co/b0W4BQ Homework Equations ∫D⋅ds=Q D=E+γP C=Q/V The Attempt at a Solution Suppose the top plate has a positive charge...

Homework Statement An infinite metal plate has a surface density of charge σL=-6μC/m² , Left side and a surface density Of load σR=+4μC/m² , in the right side. A Gaussian surface In the form of a circular cylinder, with area A 12 cm², is Located with the left side inside the plaque and a thin...

Homework Statement Theres a cylinder rod inner radius a outer raidus b.we want to find electric field between a and b,like point r (or radius r) a<r<b. Homework Equations Gauss Law The Attempt at a Solution [/B]I am trying to find Q enclosed but something make me confused.I am...

Homework Statement Uniform Slab: Consider an infinite slab of charge with thickness 2a. We choose the origin inside the slab at an equal distance from both faces (so that the faces of the slab are at z = +a and z = −a). The charge density ρ inside the slab is uniform (i.e., ρ =const). Consider a...

Homework Statement 2 large plates are separated by a distance d and a space charge of uniform charge density p is placed between them and a potential difference V is applied across the plates. Find the electric field stength at a distance x fromt the positive plate The answer is -V/d...

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 having...

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...

Hey guys can we derive the formula of Electric Field Intensity around a uniformly charged ring if yes please share the derivation thanks

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} \hat{r}...

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...

Which one is correct?? 1) electric field calculated by gauss law is the field due to charges inside the closed surface. 2) the flux of the electric field through a closed surface due to all charges is equal to the flux due to charges enclosed by the surface

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...

Divergence theorem states that $\int \int\vec{E}\cdot\vec{ds}=\int\int\int div(\vec{E})dV$ And Gauss law states that $\int \int\vec{E}\cdot\vec{ds}=\int\int\int \rho(x,y,z)dV$ If $\vec{E}$ to be electric field vector then i could say that $div(\vec{E})=\rho(x,y,z)$ However i can't see any...

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...

I need to prove that the field charge of 2 infinite, oppositely charged plates is 0 using Gauss' law. I know that the sum of E=4PiK(Sum of q) but I don't know how to prove the charge is 0.

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 Two concentric spheres have radii a and b with b>a. The region between them is filled with charge of constant density. The charge density is zero everywhere else. Find E at all points and express it in terms of the total charge Q. Do your results reduce to the correct values...

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 A line charge exists in air along the z-axis between z=0 and z=5 cm. It has a uniform charge density given by: ρl = 4(uC/m) Determine E at (0,10 cm, 0) Homework EquationsThe Attempt at a Solution [/B] I am using gauss law so I draw a cylinder around the wire Qenc = ρl *...

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...

A thin metallic spherical shell contains a charge Q over it. point charge +q is placed in side the shell at point T separated from the centre by a distance a. Another point charge q1 is placed outside the shell at a distance b from the centre find the electric field at the centre due to the...

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 I just noticed that whenever I'm doing a problem involving Gauss Law, it always involves an infinite line/plate. I can't seem to figure out why it must be infinite large/long. Here is an explanation I read, but don't quite understand...