Charge distribution Definition and 248 Threads

Homework Statement Design a charge distribution so that the resulting E is proportional to r^2. The Attempt at a Solution This is not really a homework problem just something our professor told us to think about at the end of our lecture. It made me really curious as to how you would do...

Here is the problem. I've been messing around with it for a while but I'm not sure if what I'm trying to do is the right way to approach this. The form factor F(q) = \int\rho(\vec{r})e^{i\vec{q}.\vec{r}/\hbar}d^{3}\vec{r} is the 3D Fourier Transform of the normalised charge distribution...

Hello everybody, I have to calculate the electric field and the potential for a charge q placed at distance d from an infinite plane charge distribution \sigma. For the electric field there's no problem, but how I can get the electric potential for an infinite charge distribution?

Claim: A charged sphere will have it's charges disperse (uniformly for symmetrical objects) on the outer surface. Proof: Consider a sphere charged to some amount q. If we take small gaussian surfaces within the sphere, it will have \vec{E} = 0 on the closed gaussian sphere [since it is an...

Homework Statement "A thin conducting spherical shell of radius a carries a charge q. Concentric with this is another spherical shell of radius b>a carrying a net charge Q. Describe how the charge is distributed between the inner and outer surfaces of the shells. What is te capacitance of the...

Homework Statement Two insulated metal spheres of equal sizes are given equal positive charges. The two spheres are brought very close to each other without touching. Draw the new charge distribution on the spheres if one sphere is much larger than the other. Homework Equations...

http://www.vias.org/physics/bk4_06_07.html This is a quote from the mentioned website, " For example, a charged metal ball will have charge spread nearly uniformly all over its surface, and in for most purposes it will make sense to ignore the fact that this uniformity is broken at the atomic...

In the Electric field of a Continuous Charge Distribution, what is "conti.." exactly? -I know its the "distribution"! but I`m asking about, like, how would the "distribution" be continuous? -I think the word "symmetry" should be used? -why is the word "continuous" used?

Homework Statement Show that any charge distribution in a conductor of conductivity σ and relative permittivity κ vanishes in time as ρ = ρ0exp(−t/ζ) where ζ = κǫ0 σ Homework Equations Maxwell's equation ∇ · D = ρfree equation of continuity for a free charge density ∇ · Jfree =...

The following is a worked example in my notes I am having difficulty with: A charge distribution with charge density \rho \neq 0 exist in the half space V:z>0 We can view this as a system with an earthed plate at the z=0 plane. So at z=0 we have the Dirichlet boundary condition...

Homework Statement Compute the form factor of rho(r) = rho0 * exp[-ln2*r^2/R^2] where rho0 and R are constants. Homework Equations F(q) = 4pi/q \intsin(q*r)rho(r)rdr where the limits of integration run from 0 to \infty The Attempt at a Solution This is probably more of a...

Homework Statement -------------------------------------------------------------------------------- Here is a problem I made up, in order to try to understand electrostatics of conductors better. Suppose two large square parallel conducting plates, are in space. One has a charge of Q, and...

This is just a quick conceptual question. If you have a charge on the surface of a conductor, and the gaussian surface within that has a cavity containing a positive charge... and you move that charge off-center, does that affect the charge distribution on the surface of the conductor?

Homework Statement A spherically symmetric charge distribution produces the electric field E = (5000r^2) N/C, where r is in m. a) What is the electric field strength at r = 20cm? b) What is the electric flux through a 40cm diameter spherical surface that is concentric with the charge...

Homework Statement A complicated distribution of 10 protron produces a radially symmetric electric field given by, E(r) = (10*charge_of_proton/4pi*epsilon_0)*(1/r^2 + 100/r^4)*r_hat Give an order of magnitude estimate for the size of the charge distribution. Homework Equations...

Homework Statement 2 conducting spheres with radii 2 & 3m are connected with a conducting rod of thickness 0.1m & length 0.5m. 500C charge is put on the 2m radius sphere. Find the amount of charge on each sphere & on the rod. Homework Equations The Attempt at a Solution By...

Homework Statement A total charge Q is shared by two metal spheres of small radii R1 and R2, that are connected by a long thin wire of length L. Fin (a) the charge on each sphre and (b) the tension in the wire. Source: Haliday 4th edn chapter 26 q. 91, p. 738 The Attempt at a Solution...

I have been attempting to deduce the arrangement of electrons within a solid spherical conductor in different states of charge. I'd like to know which, if any, of my conclusions are correct; and of the incorrect, I'd like to understand where I went wrong. A cool conductive (metal) sphere is...

A small positively charged sphere is lowered by a nonconducting threead into a grounded metal cup without touching the inside surface of the cup.The grounding wire attached to the outside surface is disconnected and the charged sphere is then removed from cup.What is the distribution of excess...

Two metal spheres (r2 = 2 X r1) have the same charge q on each of them separately. Now they are brought in contact. What will be the new charge distribution? My extension : What are all the factors that determine the new charge distribution? What if they are connected by a metallic rod...

A 10.0 gram piece of styrofoam carries a net charge of -0.700\muC and floats 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 Equations \Phi = E\intdA =...

Hi everyone I am very new here so please don' be too harsh with me :shy: I hope I posted this in the right section. If I haven't, then please accept my apologies and can a mod please kindly move my post to the appropriate section? Im taking a very basic physics class atm and I was having...

1. A nonconducting rod of length L = 6cm and uniform linear charge density A = +3.68pC/M . Take V = 0 at infinity. What is V at point P at distance d = 8.0cm along the rod's perpendicular bisector? 2. V = S E * ds One half of the rod = L/2 1/4piEo = 9x10^9 R = sqrt((L/2)^2 +...

Homework Statement There is a charge density rho that exists in a spherical region of space defined by 0 < r < a. \rho (r) = Ke^{-br} How do you find the electric field if a charge density varies as such?The Attempt at a Solution I found Q total = \int \int \int \rho dV Now I need to find E...

Homework Statement A uniform charge (with density D) is distributed over a cone of radius R and height z. The axis of the cone is coincident with the x-axis. Find the total electric field due to the cone along the x axis.Homework Equations E = kqq/r^2The Attempt at a Solution This is really...

Homework Statement Find the energy required to add an additional charge to the chain in the limit where the total number of charges approaches infinity. So, I have a equidistant linear charge distribution like + - + - + -... where the total number of charges approaches infinity. The charges...

Homework Statement (Lead into question: "Assume that charges +q, -3q, 2q lie at positions -2a, 0, +2a along the x-axis respectively.") I've calculated dipole/quadrupole moments about the origin as well as the exact potential at x=+10a, however I'm confused by this next part to the...

Two identical, oppositely-charged, conducting plates of area 2.50cm² are separated by a dielectric 1.80 mm thick, with a dielectric constant of 3.60. The resultant electric field in the dielectric is 1.2*10^6 V/m. a)Compute the charge per unit area on the conducting plate. b)Compute the...

a long glass filament carries a charge density = -2.7nC/m. what is the magnitude of the electric field 0.67 mm from the filament?

A rod of length 80 cm has a uniform linear charge density of 5 mC/m. Determine the Electric Field at a point P located at a perpendicular distance 57 cm along a line of symmetry of the rod i don't know what i wrong..but here is what i am doing linecharge(change in lenght)= change in Q...

Hi, I have a random spherical distribution of N charges between radiuses R1 and R2. N is up to 10^9 or more.I want to calculate the electrostatic potential closed to the origin of the sphere. R1 and R2 are much bigger than the distance of this point to the origin. So I thought about using...

inside a sphere there is a cavity of an arbitrary shape . a chage q is kept inside the cavity . there will be a uniform distribution of charge on the outer surface of the sphere . how can i prove that ?

Does anyone know how to find the actual charge dustribution on a conductor? More like the alignment of all the charges on a conductor? I know that the electric field should be zero everywhere on the conductor and that on pointy edges there is more charge buildup, but I have no idea how to find...

I am trying to correctly understand the following problem: Here is the setup: I have two conducting spherical shells. We will call them S-Left and S-Right. Both spherical shells are initially grounded, therefore, they have no net charge w.r.t. Earth. S-Right is hanging from a string. S-Left...

Hi, I hope this is advanced enough to warrant being in this section: I'm supposed to use the Gauss theorem (and presumably his law) to show: 1)The charge on a conductor is on the surface. 2)A closed hollow conductor shields its interior from fields due to charges outside, but doesn't...

Consider a uniform charge distribution occupying all of (flat) spacetime, \rho(t,x,y,z) = \text{constant} \;\;\;\;\; ,\; (t,x,y,z) \in R^{1,3} Because this charge distribution is translationally invariant, it seems reasonable to expect that the electric field arising from the charge...

Of the charge Q initially on a tiny sphere, a portion q is to be transferred to a second, nearby sphere. Both spheres can be treated a particles. For what value of q/Q will the electrostatic force between the two parts have 1/4 of the maximum possible value? q1=Q when the charge is...

There's a problem in Electricity I can't seem to figure out: A charged ring of radius 40 cm has a gap of 4 cm. Determine the electric field, at the center of the ring, when it carries a charge of 2 coulombs. I think that the linear charge density doesn't change much because of the small...

How exactly does one find the potential energy of a charge distribution? More precisely, how does one get over the 1/r term in the integral goes crazy near r=0? Purcell says it is possible, but I'm not seeing how for an continuous distribution this is possible. Consider for a line of length L...

The question says that charges are distributed with uniform charge lambda along a semicircle of radius R, centered at the origin of a coordinate system. What is the potential at the origin? I am not sure how to approach this one. Can anyone help me set this up and solve it? Thanks!

Hi, I have a problem with finding charge distribution. If anyone could provide help or any tips as to how to solve it, I would greatly appreciate it. I have already solved half of the problem. The potential V(r) of a spherically symmetric charge distribution is given by V(r) =...

I'm having trouble with this problem: Consider a thin spherical shell of radius 14.5 cm with a total charge of +38.9 microCloumbs distributed uniformly on its surface. (Take radially outward as the positive direction.) So I need to find the field at 35.6cm from the center of the charge...

Take two charged, moderately thick conducting plates. Suppose one has a charge +Q and the other -Q. Arrange the plates facing each other as in a capacitor. So why don't the outer surfaces of the plates have any charge? (The charge +Q, for instance, is wholly on the inner surface, the surface...

Finite Number of Charges around a regular Polygon I know this is probably an easy one, but I'm just unsure... There are 13 equal charges, q, that are placed at the corners of a regular 13-sided polygon. a) What is the Force on a test charge Q at the centre? What I've been donig is...

Hello, Question again. If we have a conductor, then according to Gauss, all the charged particles will migrate to the surface where they are furthest away from each other. This seems to make logical sense. But what if I have a charged sphere and now every particle on the surface of the...

Hey, this is from "Foundations of Electromagnetic Theory" by Reitz, et al. Problem 2-15. I have had a really hard time trying to learn from this book as there are no examples to apply the equations they prove throughout the chapters. Anyhow, I don't really have anything down for this problem...

Hello, I am new to this forums but i think you are doing a wonderfull job in helping us students trough our physics learning :redface: Here is my q. I have a conductor sphere moving at constant velocity trough a constant perpendicular magnetic field and i need to find the induced...

I have a new question: "In applying Gauss's Law describe the types(s) of charge distribution for which (a) a spherical gaussian surface is useful and (b) a cylindrical gaussian surface is useful" please help!