Gauss's law Definition and 381 Threads

Homework Statement Compare and contrast the electric field due to a uniform sheet of charge with charge density ## \sigma## for the conducting and non-conducting cases. Homework Equations Gauss's Law: $$\oint \mathbf{E}\cdot d\mathbf{A}=\frac{q_{\text{en}}}{\varepsilon_0}.$$ The...

I'm having trouble with the second part b) for this problem. I used Gauss's Law and for a I got r<R E = \frac{{r}^{2}}{4\varepsilon} and for r>R E = \frac{{R}^{4}}{4\varepsilon{r}^{2}} and then V = \int{E.dr} from r to infinity right? So for r>R I got V =...

Homework Statement So I was looking at this site reading up again on Gauss's Law and was a tad confused http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elecyl.html 1st thing on the page... Homework Equations The Attempt at a Solution It states that the electric flux will just be the...

I use Gauss's law to calculate: the net electric flux = flux through rounded portion + flux through the flat base = Q/ε. And the flux through the flat base is negative, the negative means?? Help me please, it is very confusing 2) Why they choose C, i think E is correct because Q doesnot...

Homework Statement find the field produced by a uniformly charged sheet carrying 87 pC/m2 Homework Equations \oint \vec{E}.d\vec{A} = qenclosed/\epsilon The Attempt at a Solution \Phi= \sigmaA/\epsilon \Phi=\oint E.dA = ## E(2A) ## 2EA= \sigmaA/\epsilon E =...

I'm running through the following problem in an EM text of mine: Calculate the flux of a point charge Q at the origin through a cube centered through the origin by both direct integration and Gauss's Law (essentially prove Gauss's Law for a point charge). Now I got the answer of Q/ε0 via...

My E&M professor brought up this problem of considering a uniform charge density, rho, that is infinite in volume and then using Gauss's Law to find the electric field at a point. It's resulted in a lot of head scratching and I'd appreciate some help/discussion to guide me towards a resolution...

Suppose you have a sphere (sphere A) with net positive charge 2Q. A conducting spherical shell (sphere B) of inner radius b and outer radius c is concentric with the solid sphere and carries a net charge -Q. When you calculate the flux between both spheres (gaussian surface with radius between...

Homework Statement The problem that inspired the upcoming question is: Find the magnitude of the electric field due to an infinite sheet of charge with uniform charge density σ using gauss's law. I have in fact arrived at the character answer σ/2ε...

I'm trying to build up some intuition with Gauss's law, calculating the flux through surfaces given certain charge configurations etc. For example, for any number of different charges enclosed in a box or sphere, if I move far away can I consider the object as a point source having the sum of...

https://www.physicsforums.com/showthread.php?t=479376 Looking at the above link, I was wondering how he found that electric field lost by removing the circular area from the sheet was proportional to ## \frac {z}{(z^2 + r^2)^{1/2}} ##? Why is it not just the ##πr^2##? I am fairly new to Gauss's...

Homework Statement Consider a spherical shell with inner radius r1=0.30 m and outer radius r2=1.00 m. The hollow inside the shell contains no charge; and charge is distributed on the inside surface of the shell and within the shell itself, such that the electrical field inside the shell itself...

I'm reading a book that deals with Gauss's law for electric fields in its differential form. I'm stuck now on a page that discusses taking deriviatives of the equation for a vector field: → A I'm familiar with the rules for deriviatives of products and quotients but unfortunately I cannot...

Just a quick general question in applying Gauss's law. Not exactly homework, more a general question so I can understand my other homeworks better. I have a spherical shell with inner radius R_1 and outer radius R_2 and a point charge Q in its center. It is NOT a conducting sphere. In the...

Hi, I have been trying to find out the derivation of Gauss's law but can't seem to find any derivations. May I know how the differential form of Gauss's law is derived and where does the epsilon come from? Does it have to do with the displacement field definition?

Homework Statement A proton is a distance d/2 directly above the center of a square of side d. What is the magnitude of the electric flux through the square?Homework Equations 1. Electric flux, \Phi_{net} = \oint \vec{E}\cdot d\vec{A} 2. \Phi_{net} = \frac{q_{enc}}{\epsilon_{0}} 3. \vec{E} =...

Hey everyone, I was wondering if someone could explain Gauss's law. For whatever reason, I just cannot grasp this idea (might be my teacher). I understand that the electric field through a surface can be represented as \oint \vec{E} d\vec{A} but every problem that we do ends up resulting in it...

Find the electric field for a non-conducting sphere of radius R = 1 meter that is surrounded by air in the region r > 1. The interior of the sphere has a charge density of ρ(r) = r. The answer is k(pi)/r^2, but I can't seem to get that. My problem is with finding the enclosed charge. I've tried...

Homework Statement A charged paint is spread in a very thin uniform layer over the surface of a plastic sphere of diameter 10.5 cm, giving it a charge of -22.3 µC. (a) Find the magnitude of the electric field just inside the paint layer. (b) Find the magnitude of the electric field just...

Homework Statement The three small spheres shown in the figure below carry charges q1 = 4.30 nC, q2 = -7.70 nC, and q3 = 3.40 nC. Find the net electric flux through each of the following closed surfaces shown in cross section in the figure. Homework Equations...

Homework Statement A 10.0 g piece of Styrofoam carries a net charge of -0.700 \muC and is suspended in equilibrium above the center of a large, horizontal sheet of plastic that has a uniform charge density on its surface. What is the charge per unit area on the plastic sheet? Homework...

The diagram I've attached shows a cross-section view of a very long straight metal cylinder of radius r1 within a coaxial hollow metal cylinder of inner radius r2 and outer radius r3. The inner cylinder has a positive charge per unit length λ, whereas the outer cylinder has negative charge per...

Hi, could anyone help me understand the permittivity of free space in Gauss's Law: \Phi = q/\epsilon0 If you consider a point charge in a box then I think it tells you how easy it is to establish an electric field in free space. But what happens if the medium is not free space - say you...

Homework Statement For my physics assignment I need show how Gauss's Law has been used in a modern technology, such as antennae's or telecommunications of some form. I need to be able to show some worked example equations and link it back to Gauss's Law and explain how the technology would...

hi all, gauss's law states that for any surface, the total electric flux coming through an open surface is always q/ε0. okay.. i understand this... so for a sphere.. the simplest case... http://imgur.com/bwJzf7t,2KFO8Xw,O9Mgafg \Phi=\int\vec{E}\bullet\hat{n}dA=EA= \frac{q}{4(pi)ε}...

I'm familiar with the differential form of Gauss's Law, which reads that ##\nabla\cdot\vec{E}=\frac{\rho}{\epsilon_0}##, where E is the electric field, ρ is the charge density, and ##\epsilon_0## is the permittivity of free space. We can take the volume integral of both sides, and then use the...

Homework Statement When is the net flux for a cube 0 and when is it not? Homework Equations ∫EdA= Q/8.85E-12 The Attempt at a Solution if you have no test charge then the flux of a cube is zero. but if you have a test charge then the net flux is the charge divided by 8.85E-12...

I was reading here https://www.physicsforums.com/library.php?do=view_item&itemid=294 gauss law's for magnetism says ∮B⋅dA = 0 but then faraday's law has d/dt ∮B⋅dA in it. Well if its 0 then d/dt of 0 is 0.

For the configuration shown in the figure below, suppose a = 5.00 cm, b = 20.0 cm, and c = 25.0 cm. Furthermore, suppose the electric field at a point 10.5 cm from the center is measured to be 3.25 × 10^3 N/C radially inward and the electric field at a point 50.0 cm from the center is of...

Consider the interface between two materials with different electrical permitivities ε1 and ε2; Let's say we know the surface charge density on this surface γ(Let's say the only charge is on the interface). How do you apply Gauss's Law here. Or, How do you find the elecrtic field at a random...

Homework Statement Use Gauss's Law to calculate the field of an infinite plane sheet of surface charge density σ0. Homework Equations The Attempt at a Solution The solution is, where A=area: 2EA=(σ/ ϵ0)A E=σ/2ϵ0 Why is there a '2' in the solution? I know it's...

Homework Statement A spherical drop of water has radius R = 5 * 10^-4 cm. The drop has an even surface charge distribution. Consider an element dA of the surface. This element is exposed to a force from the rest of the surface elements. The effective field in the surface is equal to...

Homework Statement A conducting spherical shell with inner radius a and outer radius b has a positive point charge Q located at its center. The total charge on the shell is -3Q, and it is insulated form it surroundings. What is the surface charge density on the inner surface of the...

Consider a point charge on the x-axis at x=4. And a sphere with radius 3cm is kept beside the point charge centered at the origin. Consider the near end (x=3) and the far end (x=-3) ... We will find that E from the point charge is much bigger in the close end than E at the far end. So if we...

It is asked to find the electric flux through a "gaussian" sphere which has a point charge (-3 microcoloumbs) enclosed with the radius of 0.2 m ... I can shortcut this and use Flux= q Enclosed / e0.. However, i want the other approach using the formula Flux = ∫ E da... I know that E is constant...

Consider a point charge surrounded by a gaussian sphere. In the derivation of the formula, we said that E is constant everywhere on the sphere. Hence, we used Flux= EA.. However, isn't the E created on the surface is due to one field line out of the pint charge. I mean the formula kQ/r^2 is the...

Hello, So I had been studying Gauss's Law yesterday, and I still don't feel like I have an excellent grasp of it. I wonder, why is it when there is cylindrical symmetry, sometimes it seems you need to calculate the E coming from both ends of the gaussian surface, but other times only out of...

What if Gauss' Law was div(E)=q2/eps0 Then if we had two point charges, how could we calculate the resultant E field at an arbitrarily point? Obviously superposition would not work anymore, so how could it be done mathematically? This is essentially a math question

Homework Statement Homework Equations The Attempt at a Solution I'm not sure if I am doing part a,b,e, and f correctly

Homework Statement I am working on a problem that is similar to this one: https://www.physicsforums.com/showthread.php?t=598914 Homework Equations The Attempt at a Solution When r < a, why doesn't the electric fields generated by the concentric conducting, hollow sphere affect the Gaussian...

Homework Statement Consider a sphere centered at origin with radius R > z0. By calculating the total flux ϕ = ∫E . da through the sphere, explicitly show that ϕ = q/ϵ0 Homework Equations Gauss's Law The Attempt at a Solution I have a general idea of what to do, but I just want...

Homework Statement "A cylindrical shell of length 230 m and radius 6 cm carries a uniform surface charge density of σ = 14 nC/m^2. What is the total charge on the shell? Find the electric field at the end of a radial distance of 3 cm from the long axis of the cylinder." Homework Equations...

Homework Statement A hollow metal sphere has 7cm and 9cm inner and outer radii, respectively. The surface charge density on the inside surface is - 300nC/m^2</units> . The surface charge density on the exterior surface is + 300nC/m^2</units> . What is the strength of the Electric Field at...

Homework Statement Suppose that the electric field in the Earth's atmosphere is E = 1.50 x 10^2 N/C, pointing downward. Determine the electric charge in the Earth. (The radius of the Earth is 6371 km, and the Coulomb's constant, ke, is 8.99 x 10^9 N · m2/C2.) Homework Equations E=kQr/a^3...

Homework Statement Provide a proof of Gauss’s law starting from Coulomb’s law for a point charge Homework Equations F=kq1.q2/r^2 (closed)s∫E.n.da=qenc/ε0 The Attempt at a Solution My starting point is: F21=1/(4∏.ε0).(q2.q1)/r21^2.r(unit vector)21 *Note, the 21 terms after...

Gauss's law can be proved qualitatively by proving that the field inside a charged closed surface is zero. However Maxwells' equations says that gauss's law holds true even for electrodynamics. how can this be verified experimentally? Thanks in advance !

Homework Statement I'm basically just wondering why the given diagram wouldn't violate Gauss's law of magnetism...there are two B-field lines exiting, but none entering the red box. So the net flux isn't zero. I vaguely remember the lecturer addressing this when we were studying the topic, but...

1. Homework Statement A nonconducting spherical shell of inner radius R1 and outer radius R2 contains a uniform volume charge density ρ throughout the shell. Use Gauss's law to derive an equation for the magnitude of the electric field at the following radial distances r from the center of...

Homework Statement A nonconducting spherical shell of inner radius R1 and outer radius R2 contains a uniform volume charge density ρ throughout the shell. Use Gauss's law to derive an equation for the magnitude of the electric field at the following radial distances r from the center of the...

Consider the integral form of gauss's law \oint \vec{E}.\vec{d \sigma}=\frac{q}{\epsilon_0} Then let's write q in terms of the volume and surface charge densities \rho and \delta and let's assume that the surface charge is distributed over the gaussian surface of the above integral \oint...