Gauss law Definition and 182 Threads

We have learned the below formula for a plane sheet of charge with thickness. E=σ/ϵ and the one below for with no thickness (negligible) E=σ/2ϵ The problem, I am facing is digesting the derived equations. It is one thing for sure that these formulas must be right. But then the fact that E...

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...

Homework Statement We won't to find out the electric field at a point p due to a point charge q placed at o as shown in the figure [/B] Consider a sphere of radius r passing through the point p. Let the electric field at p be E then by Gauss law my problem is how we get the last step? I...

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...

about gauss law! is there any precise proof for gauss law? why ø=q/ε always regardless how the charge is distributed inside the surface and if anyone know a good book for electromagnetism please type its name for me.. thank u

Homework Statement An infinite line of charge with linear density λ1 = 6.2 μC/m is positioned along the axis of a thick insulating shell of inner radius a = 2.7 cm and outer radius b = 4.4 cm. The insulating shell is uniformly charged with a volume density of ρ = -552 μC/m3.1) What is λ2, the...

According to the Gauss law, the extra charges gather on the surface of a conductor. When there is a current in a conducting wire, do the charges only move on the surface of the wire or we have current also inside the wire? If we also have current inside the wire how is it compatible with Gauss law?

I found in this forum an old thread regarding this topic, but as it didn't have (in my opinion) a satisfactory answer, I decided to open a new one. Usually when one begins to study Electromagnetism, Coulomb's law in introduced as an experimental result valid for static point charges. From...

Homework Statement The problem was to calculate the electric field inside an infinite length cylinder (with radius R) with a non uniform charge density. The charge density depended on r. Its easy enough to solve using a gaussian cylinder with r less than R. But what if I wanted to complicate...

Hi all, Lets suppose we have a sphere. This sphere has density of \rho(r) from 0 to the sphere's final radius R. Now, we all know that from Gauss law, the charge inside the sphere equals to the integral of the surface of the sphere. If we set our normal vector to be as usual out of the...

So i can see by symmetry arguments why The electric field inside a uniformly charged spherical shell would be zero inside. But what about a non uniformly charged spherical shell. Say most of the charge is located on one side, why is the electric field still zero? I can see that the flux...

Hey. I want to use integrals-math to get from Gauss law in divergence form to the one in integral form. I know you can do it by simply accepting ∇*E dV = ρ/ε => ∫ ∇*E dV= ∫ρ/εdV = Q/ε = ∫E*dA, but I want to do it another way. I want to begin with ∫∇*E*dV and end up with Q/ε. So: E =...

Hello all! I actually have a few doubts regarding "gauss law" when applied "for different models of sphere" First, If we place a charge 'Q' inside a spherical shell at the center (somehow) then it should come out to its surface that means in no way can we do it. True or False? Next...

Homework Statement Hi. A cylinder of radius r & length L whose charge density distribution is given by ρ = C/2 * r3 where r = radial distance in cylindrical coordinates C = constant show that the average charge density ρbar = a3 C / 5Homework Equations Gauss differential law div E = ρ / ε0 div...

Homework Statement [SIZE="4"]1. [SIZE="4"]2. Homework Equations ∫E.dA = Qenc/\epsilon_{o} \lambda=Q/L \rho=Q/V V= q/4πε_{o}r The Attempt at a Solution these types of problems i suck at, i don't know how to do these at all independently, and is there any difference in question 2 if there...

Homework Statement A long non-conducting cylinder has a charge density ρ = αr, where α = 6.34 C/m4 and r is in meters. Concentric around it is a hollow metallic cylindrical shell. Diameter 1: 4.36 cm Diameter 2: 10.4 cm Diameter 3: 16 cm What is the direction of the electric field at...

We know that for an infinite sheet of charge, E = λ / 2ε, where λ is the surface charge density. This can be easily found using gauss law and a cylinder perpendicular to the sheet as a gaussian surface. We will end up with something like Qinc/ε = 2E ∫dS, from which we find E = λ / 2ε. Now say...

Hi, I don't understand this: You got a dipole, and a resulting electric field from it like this(hyperphysics): As z approaches infinity, the field becomes zero. But if you draw a gaussian surface round the charges, then the net enclosed charge is zero.So the electric field must be zero, no...

"As the ball gets deeper under the surface of the Earth, the layers above it stop exerting gravitational force, and all that matters is the mass underneath." How to justify this sentence is true?

Homework Statement A spherical charged ball of radius a has total charge Q; there is no charge outside the ball and no sheet-charge on its surface. The (radial) field inside the ball has the form Er(r) = constant x r2 for r between 0 and a. Use Gauss's Law in integral form to evaluate the...

Hi guys, this is more of a conceptual question, so I hope you guys can give me a detailed explanation if possible. Homework Statement Find the Electric Field inside a Charged Sphere (charge only on the surface) and between two Parallel Plates (oppositely charged) separated by some distance d...

hi all, im new at electromagnetics and vector calculus, so facing these trivial problems. The differential form of gauss's law for empty space states ∇E = ρ/ε .The right side refers to charge density at the point of calculation of divergence? If a point charge(or a small uniformly charged...

Homework Statement Attached Homework Equations Gauss' Law The Attempt at a Solution \epsilon_{0} E(4\pi r^{2}) = q_{enc} = -1.738x10^{-19}

Given a symmetric Charge distribution where Gauss Law can be applied which method will one select to obtain Electric field. Potential or Gauss Law. I feel that Gauss law must be used because using Gauss law one can calculate electric field easily as compared to Potential. Which is advantageous...

Homework Statement Homework Equations Just to clarify the question, the value given for R2 is the overall radius of Earth, it isn't R1-R2. (At least, that's my interpretation given that the R2 value is approx. the Earth's radius) The Attempt at a Solution Don't really know how...

Why use k = 1/[4(pi)(epislon)] and epsilon = 8.8 * 10^(-12) and subsequently, k = 9 * 10^9 It could simply be k = 9 * 10^9, and different k for different medium instead of different permittivity for different medium. What I mean is why does Pi, (I can handle the 4) comes into the...

Homework Statement Space distribution of electric charge is limited by to planes. Charge has the same intensity in planes parallel to these planes, but in dependence of the x coordinate, charge density is being distributed like: \rho (x)=A\cdot x\cdot (d-x) d is distance between those to...

You are a hollow metallic sphere of inner radius r1, and outer radius r2. Inside is a charge of magnitude Q and a distance d<r1 from the centre. First I need to draw the electric field lines for regions r<r1, r1<r<r2, and r2<r Since the sphere is a conductor the only place where there is...

Homework Statement The problem is given in the attachment belowHomework Equations (i)EA= Q/epsilon naught (ii)Area of cylinder used = 2pi*r*L (iii)The integral of E*dA =Q/4pi*epsilon naught (iv) Llamda= Q/LThe Attempt at a Solution Well I know I needed to choose a suitable Gaussian surface...

Homework Statement A hollow conducting sphere carries a charge of 72nC and has an inner radius of 44cm and an outer radius of 68cm. At the center of the hollow sphere is a point charge (-89)nC, insulated from the sphere. What is the magnitude of the electric field inside the sphere at a...

imagine a charge placed inside a closed conducting shell (a hollow metal box or sphere) Feynman says: - no static distribution of charges inside a closed conductor can produce any fields outside. The fields on the two sides of a closed conducting shell are completely independent. but...

For electrostatic fields gauss law depends on three factors viz inverse square nature ,central character and principle of linear superposition of electrostatic force.Now,within the Newton's framework of gravitation the gravitational force has all of the above properties.Then why does one does...

1. The problem statement Consider an infinite spherical charge distribution with constant charge density. According to symmetry of the problem, I expect the electric field at any point to be zero. But if you construct a Gaussian sphere and apply Gauss theorem, it will give you some finite field...

if i have a current carrying straight long wire, I = I0sin(wt) why is gauss law ∇.E = 0? i thought only for steady currents , then the charges reside on surface, that's why 0 charge enclosed, and hence gauss law gives 0 right? so now since i have a time varying current, what should...

Homework Statement The electric field has been measured to be horizontal and to the right everywhere on the closed box shown in the figure. All over the left side of the box E1 = 90 V/m, and all over the right, slanting, side of the box E2 = 400 V/m. On the top the average field is E3 = 120...

we know that the electric field between the planes of planar capacitor is σ/ε (according to gauss law) however we have two conducting plate that each plate produe this electric field that are in the same direction therefore we must have E=2σ/ε what is the reason for this contradiction.

Homework Statement An infinitely long, non-conducting cylinder of radius R carries a uniform volume charge density ρ. Find the magnitude of the electric field for 0 < r < R Homework Equations EA=Qin/εo The Attempt at a Solution I am debating whether the answer should be ρr^2/2εoR...

An infinite line of charge with linear density λ = 7.6 μC/m is positioned along the axis of a thick insulating shell of inner radius a = 3 cm and outer radius b = 5 cm. The insulating shell is uniformly charged with a volume density of ρ = -611 μC/m3. (see attachment) What is Ex(R), the value...

Homework Statement A circular ring of radius a carries a uniform charge q C/m and is placed on x-y plane with axis same as z axis. To determine E at P(0,0,h). My ques is can't we apply gauss theorem? if yes then what will be the gaussian surface? if no then why not? Homework Equations...

Hi Im getting a slightly different answer to the one that is needed for the following question: 2) A positive charge Q is distributed throughout a spherical volume of radius R in vacuum. The charge density rho varies with the radius according to the linear law rho = a r. Show that the...

I know that electric flux is defined as the number of electric field lines passing through an area but what kinda area are we talking about. Does it have to be perpendicular to the field lines like this or could it be at an angle like this does it have to be a flat area on 1 plane like the...

Am really suprised when deriving electric field due to a uniform charged thin long rod! It was suprising to have a cylinder as a gausian surface! actualy is that posible, that all along the surface of the cylinder has same field intensity and why? also why are there no electric flux along...

Three large but thin charged sheets are parallel to each other as shown in the figure . Sheet I has a total surface charge density of 7.9 nC/m^2, sheet II a charge of -3.3 nC/m^2, and sheet III a charge of 5.4 nC/m^2. Figure: ----------------(I) ----------------(II)----------------(III)...

A certain region bounded by an imaginary closed surface contains no charge. Is the electric field always zero everywhere on the surface? If not, under what circumstances is it zero on the surface. I think it is zero everywhere because as the electric field is entering the closed surface, it...

A region in space containing cargo which is distributed spherically so that the stocking load ρ is given by the equotations: ρ = a for r<=R/2 ρ = 2a(1-r/R) for R/2<=r<=R ρ=0 for r>=R The total charge Q is 3*10^-17 C, the radius R of the overall distribution is 2*10^-14 m and a is a constant...

Now, i am trying to prove that electric field inside spherical shell whose constant surface charge density \rho is zero. Usually, it is proved by using Gauss law (there is no charge enclosed inside gaussian surface so there is no electric field inside the sphere). But, whe i am trying to solve...

Homework Statement there are two nonconducting spherical shells fixed in place. shell 1 has uniform surface charge density 6.0 uC/m^2 on its outer surface and radius 3.0cm. shell 2 has uniform surface charge density 4.0 uC/m^2 on its outer surface and radius 2.0cm. the shell centers are...

ok guys.. this question is regarding a spherical nucleus with radius R related to Gauss's Law... so where the electric field given as the following: E(r) = Q/4*pi*epsilon-nought(r^2+R^2) 1. the questions asks "why this model/behaviour for r>>R might be "reasonable" 2. what q(r) is needed...