Charge distribution Definition and 236 Threads

Homework Statement Hi! This is not really a problem. I'm just confused on how to express the charge distribution of a set of point charges in spherical coordinates. From our discussion, ρ(\vec{r})=\sum\limits_{i=1}^N q_i δ(\vec{r}-\vec{r}') where \vec{r} is the position of the point where...

So, I've got a charge distribution given by: \begin{equation} \rho(r,\phi,z)=\frac{q}{2\pi R}\delta(r-R)\delta(z)\cos(2\phi) \end{equation} This, if I'm not mistaken, translates into a circular charge distribution located in the z-plane, a distance R from origo. Thus \begin{equation}...

Consider two spherical hollow conductors, charged to Q1 and Q2 coulombs respectively. What happens when one is placed within the other, and they are connected by a thin metallic wire? I do know that if they were placed at a distance from each other, the charge is distributed in the ratio of the...

Homework Statement In fact, there are two problems, and I want to know whether my solutions are right or not. 1- Two charged line with density of 15 n c/m along the x and y axes (x\pm\infty, y\pm\infty), Find the Electric field at: (a) (0,0,4) (b) (0,5,4). 2- A cylinder with radius \rho=8cm...

Is the charge distribution of an electron uniform, or is there more charge concentrated near the center or perimeter?

Homework Statement Two line charges, of length L/2 and carrying equal and opposite charge density ±λ, are placed on the x-axis so that their ends just touch at the origin, as shown in Figure 1. They are separated by an insulating material with negligible width. a. Find the magnitude and...

Question: You’re 1.5 m from a charge distribution whose size is much less than 1 m. You measure an electric field strength of 282 N/C. You move to a distance of 2.0 m, and the field strength becomes 119 N/C. What’s the net charge of the distribution? (Hint: Don’t try to calculate the charge...

I want to derive this equation: V(r) = \frac{1}{\epsilon_0} [\frac{1}{r} \int_0^r \! r'^2 \rho(r') \, d r' + \int_r^{\infty} \! r' \rho(r') \, d r' ] of a spherical charge distribution. I can do it with the general integral definition of the electrostatic potential (which is basically...

As I mentioned, I want to know if the cahrge distribution of nuclei has any influence on electronic properties. And what can cause a change on the nuclear charge distribution!

Homework Statement suppose you have an 1-dimensional system with a charge distribution ##\rho(x)## (not given) moving with an speed ##v(x)##, calculate the potential ##\phi(x)## and the charge distribution ##\rho(x)## in the quasistatic limit ##\frac{d}{dt}=0##. Homework Equations...

Homework Statement Find the E produced by a spherical charge distribution with uniform charge density at a point inside the sphere, using triple integration. Homework Equations E = 1/4πε ∫f(x,y,z)/r^2 dV The Attempt at a Solution f(x,y,z) = p Radius of sphere = R Position of...

Hello, I've been trying to understand how the fact of grounding a conductor affects its charge distribution. So, for example, let's assume there are three spherical shells with radius R1 R2 and R3. Supose I charge the R1 shell with q and the R3 shell with -q , and I connect the R2 shell to...

Homework Statement I am to find the electric field for a charge distribution of $$ \rho(x)= e^{-\kappa \sqrt{x^2}} $$ Homework Equations I know that gauss law is $$ \int E \cdot da = \frac{q_{enc}}{\epsilon_0} $$ The Attempt at a Solution I am not sure what the charge...

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...

Homework Statement A conductor (wire) is folded into a square loop with each side having a length of a. Total charge of Q is transferred onto the conductor. Describe the line charge density of the square loop in equilibrium. (If I am interpreting this correctly what is required is...

First, this is not a homework question, just something I've been confused about for some time. I understand how to use Guass's law in many ways but one thing I have always stumbled with is whether the E-field of a charge distribution should involve little r or big R in such an example: In...

I was trying to calculate the the charge distribution (surface charge density = σ in function of r) in a very long circular metallic plate. I know σ not constant if we get closer to the rim of the plate Let's say we want to calculate the E field in point Q that is x distant from the center...

I do not understand the following from Griffiths’ Electrodynamics – page 424 Equation 10.21. \nabla p = \dot{p} \nabla {tr} = … I’m not sure how much of this applies (I think my question is on the math) but p is the charge distribution, tr is the retarded time. Is this an...

Homework Statement A solid conducting sphere with radius of R1 and charge of 3Q, is placed in the center of a thin conducting spherical shell with inner radius of R2 and outer radius of R3, charged with -Q what is the field for r<R1, R2>r>R1, R3>r>R2, r>R3 and what is the charge...

Homework Statement In electrostatics it's useful to have ##\rho (\vec x )## written with Dirac's delta so that we can know the total charge by integrating the charge distribution over a region of space. Many problems/situations deal with point charges. In Cartesian coordinates for example...

Homework Statement A rod 16.0 cm long is uniformly charged and has a total charge of -21.0 µC. Determine the magnitude and direction of the electric field along the axis of the rod at a point 42.0 cm from its center.Homework Equations The Attempt at a Solution The equation I am advised to use...

I was watching a video on the internet about charge distributions over solid conductors. The solid conductor was heart shaped which was positively charged. The lecturer in the video said that when you touched this conductor, the charge would distribute itself non-uniformly over the surface of...

Homework Statement Homework Equations work = kqqq/(distance) The Attempt at a Solution http://i33.photobucket.com/albums/d86/warnexus/electrodiag.jpg

Homework Statement The electric potential for some charge distribution is given by the function V(x,y,z) = 1000z (Volts), for -10cm <= z <= +10cm, and zero otherwise (it does not depend on the x and y coordinates). Find the electric field corresponding to the given electric potential. Draw...

Homework Statement Show that, if a charge distribution  has cylindrical symmetry, then knowing the value of Qzz allows you to determine the entire quadrupole moment matrix. Homework Equations Tr Q=0, ie Qxx+Qyy+Qzz=0 The Attempt at a Solution Because of the cylindrical...

Homework Statement A total charge q is uniformly distributed throughout a sphere of radius a. Find the electric potential in the region where r1<a and r2>a. The potential is defined anywhere inside the sphere. Homework Equations letting ρ = volume charge density and ε = permittivity...

I recently had a problem set with two questions that seemed to give very similar answers. I'm not asking how to do this, so I don't think this post belongs in the homework section. Rather, I'm asking if the similarity I think I see has any deeper meaning in the physics of electric fields...

I am given a continuous charge problem in which there is a non-conducting wire of legnth L lying along the y-axis and I am required to calculate the electric field at any point along the x-axis. I know how to compute the electric field of a continuous charge distribution at a given point, but...

Homework Statement The thin plastic rod has length L, and a nonuniform linear charge density λ = cx. With V = 0 at infinity, find the electric potential (in V) at point P1 on the axis, at distance d from one end. c = 28.9 pC/m^2 L = 12.0cm d = 3.00 cm Now, from what I can tell the left...

Why is it that when you have an insulator, the charges are uniformly distributed but in a conductor, the charges are only at the surface?

Hey, I am helping out with a class and the students were given a question about an electroscope that is being charged by induction, and they have to label the charge distribution on a diagram. The diagram is drawn such that the conductive elements are separated - indicating a force between...

Recently I've been trying to understand this subject in more detail. I thought I'd post some of what I've learned here in case either (a) it's useful to others, or (b) others can add to what I've found out. Surprisingly, this seems to be a subject on which people are still publishing papers, and...

Hi experts, I still do not understand how positive charge is distributed inside a conductor. In case of extra electrons is it quite evident, as they are free to move and repel each other, so they go as far away as they can. But what exactly happens if electrons are removed from a conductor...

How do I calculate the charge distribution on the surface of any asymmetric closed conducting surface? Is it possible for me to calculate the surface charge density 'σ' as a function of '\bar{r}' the position vector in a spherical co-ordinate system in space, provided I know that the conductor...

Homework Statement three concnetric conducting spherical shells are there with charges +4Q on innermost shell,-2Q on middle shell and -5Q on outermost shell. what is the charge distribution and charge on inner side of outermost shell? Homework Equations The Attempt at a Solution...

I need the electric potential generate by an hemuspherical constant charge density along the axis normal to the plane surface of the distribution an passing for the center of the hemisphere. In practice i have to solve the integral: ∫1/|x-x'| d^3x' over the volume occupied by the distribution...

The problem is stated: The preceding problem was an artificial model for the charging capacitor, designed to avoid complications associated with the current spreading out over the surface of the plates. For a more realistic model, imagine thin wires that connect to the centers of the plates...

good evening! i am trying to calculate the electric field of a spherical charge distribution ρ=ρ_{0}e^{-kr}, where r is the radial distance. i am a little bit embarressed,but i have to say that i am not comfortable with spherical coordinates in practical calculations. i would appreciate if...

The page here mentions about the charge distribution inside the electron but I do not know how this assumption is made. It will be nice if some one can help me out with this. http://www.electronspin.org/2.htm

I am currently doing a past paper question for my electromagnetism exam and I can't seem to figure out this problem, it is probably quite simple but I can't see a solutionHomework Statement Consider a spherically symmetric charge distribution: ρ(r) = ρ0(r/r0)-n for r>r0 ρ(r) = ρ0 for r≤r0...

Homework Statement two infinite conducting plates 1 and 2(both grounded or connected by a wire so that their potential is same) are separated by a distance l. A point charge q is located between the plates at a distance x from plate 1. find the charges induced on each plate. Homework...

Homework Statement In the exercise 8.4 from Quarks and Leptons. An Introductory Course in Modern Particle Physics - F.Halzem,A.Martin we can see: if the charge distribution \rho(r) has an exponential form e^{-mr}, then: F(q) \propto (1 - \frac{q^2}{m^2})^{-2} where...

Suppose everywhere in space charge is distributed with uniform and constant volume charge density. What will be Electric field at any point in space?? 1>..Symmetry demands it to be zero, 2>..if I consider the space to be a sphere of infinite radius with constant charge density on its volume...

Homework Statement Consider a spherically symmetric charge distribution \rho = \rho (r) Homework Equations By dividing the charge distribution into spherical shells, find the potential \phi and the electric field strength \bf{E} in terms of \rho (r) The Attempt at a Solution The...

Homework Statement A cigar-shaped static charge distribution is situated at the origin of coordinates. The long dimension of the "cigar" extends along the z-axis. The total charge is q. The field at point P on the z-axis outside the charge distribution will be called E. If q were...

Homework Statement We have a infinite plate on the yz plane from x=-d/2 to x=d/2. The plate has a uniform volume charge distribution ρ_{0}. Parallel to the z axis at y=y_{0} we have a cylindrical hole with a radius a. At the center of the hole (paralle to the z-axis) we have an infinite line...

Homework Statement Hey guys. As you can see, there are 5 questions to answer regarding this question. I'm working through it and need some help regarding a few of the questions. I have A.) The electric potential at the center of the circle is Zero. B.) The value of the electric...

Homework Statement The problem can be found in Jackson's book, I think in chapter 1 problem 3 or something like this. I must determine the charge distribution of a uniformly charged disk of radius R in spherical coordinates (I've done it in cylindrical coordinates and had no problem). The...

Homework Statement I am having trouble understanding how \textit{Δ}\vec{E}\textit{ = k}_{e}\frac{Δq}{{r}^{2}} (where ΔE is the electric field of the small piece of charge Δq) turns into \vec{E}\textit{ = k}_{e}\sum_{i}\frac{{Δq}_{i}}{{{r}_{i}}^{2}} then into \vec{E}\textit{ =...

Homework Statement 1st terms = -e and positive e separated by d. 2nd terms = Two units of charge e form a system of 3 point charges -e, 2e, and e (all d apart). The next terms are formed by changing the sign of the charge and then moving by one unit length. Homework Equations E=q(1)q(2)/d^2...