Charge density Definition and 439 Threads

Homework Statement We are given a two concentric spherical shells with small radius ## a ## and larger radius ## b ##. The inner and outer shells are made of conducting material and there is a volume charge density, ##\rho\left(r\right) ##, that exists between the shells,. The boundary...

Homework Statement Imagine a spherically symmetric charge density p(r)=Cr for r<=a, p(r)=0 for r>a. a) Find the electric field E(r) and potential V(r). Are they continuous at r=a? b) Suppose additional charge is placed uniformly on the surface at r=a with surface density sigma. Find E(r) and...

Homework Statement a parallel plate capacitor has 2 plates separated by a dielectric of rel. permittivity 5.0 are separated by 0.20mm and have area of 5.0 cm2. Potential difference between the plates is 500V. I need to be able to calculate the free surface charge density...

Homework Statement The electric field at a distance of 0.143m from the surface of a solid insulating sphere with radius 0.381m is 1630N/C . a) Assuming the sphere's charge is uniformly distributed, what is the charge density inside it? b) Calculate the electric field inside the sphere...

Homework Statement A 1.0 μA proton beam is accelerated across a potential difference of 1.0 kV. Assume the beam has uniform current density over a diameter of 2.0 mm, and zero outside. Find: volume charge density in the beam, (HINT use λ=I/v where λ= charge/ unit length) The radial...

Homework Statement A point charge +q is placed near a curved, charged, insulating rod as shown at the left below. (I'll just draw it, I don't have access to a camera at the moment) The charge is placed near the center of the curvature of the curved rod. For each of the five cases A-E, the...

Hey! I need to calculate the electric field on the axis of a circular plate of radius a with the following charge distribution: \sigma_0 \frac{r^2}{a^2} \delta (z), \; r\leq a0, \; r>a where \sigma_0 is a constant. I've already calculated the potential and taken its gradient to get the...

hello. The problem is : A metallic horizontal disk of radius R has been charged on its top surface with a total charge Q such that its surface charge density is "non uniform" and governed by the expression σ=q|cosθ|*r where r and θ are the polar coordinates measured from the center O of the...

What is the difference between complete and incomplete mode locking in charge density wave systems?

Hello everyone, I was wondering how one would calculate the three-dimensional charge density (per volume) in a capacitor plate with a given thickness. I know how to calculate the charge density on the surface based on the capacitance and voltage, but how would one calculate the comprehensive...

Homework Statement How to get equation ## \frac{d \theta}{dt}=-\omega_d+\omega_1\cos (\omega t)## where ##\omega_d## is the average drift frequency and ##\omega_1## is proportional to the amplitude of the ac current. from ## \frac{d \theta}{dt}=\omega_{co}(\frac{V(t)}{V_T}-\sin \theta) ##...

If I make a single, short (GHZ) negative voltage pulse propagate down a long, single wire which forms a closed circuit, will there be a corresponding negative charge density in the conductor (shown as bunched-up green electrons) which propagates with the pulse?

Hello I want to know surface charge density of the conductor in all part of that is same or not? for example in this shape ? if isn't why and how the surface charge density spread? Thanks

Homework Statement A long cylinder carries a volume charge density which is proportional to the distance from the axis, ρv=0.005r. Find the vector electric field inside the cylinder using Gauss’ Law in integral form. Homework Equations ∫E dot dA = Q/ε0 ∫vρv = Qenc The Attempt at...

I am creating a particle in cell simulation that models an electron plasma in a cylindrical container. Part of this process is assigning charge density to grid points based on the position of each particle. My question is this: for the examples of these simulations that I have seen, the charge...

This confusion is about the following problem: Suppose the entire region below the plane z=0 is filled with uniform linear dielectric material of susceptibility ##χ_e##. Calculate the force on a point charge q situated a distance d above the origin. Now, this problem is done in Griffiths'...

Homework Statement Determine the charge density due to the following electric flux density: \overrightarrow{D} = \hat{r}4rsin(\phi ) + \hat{\phi}2rcos(\phi)+\hat{z}2z^{2}Homework Equations \rho _{v} = \triangledown \cdot \vec{D} \rho _{v} = \frac{\partial }{\partial r} + \frac{\partial...

If you have a charged solid sphere with uniform volume charge density ρ, then the total charge on the sphere is Q = ρ*4/3*∏*R^3 , where R is the radius of the sphere. Now...

Homework Statement I have a function for an E-field E(x,y,z,t)=E_o\cos(k(x-ct))\hat j and I need to find the charge density... Homework Equations \vec \nabla \cdot\vec E=\frac{\rho}{\epsilon_o} The Attempt at a Solution When I compute the dot product of gradient operator with...

Im confused by a concept i have run across in Griffiths electrodynamics. E_{out} - E_{in} = \frac{\sigma_{free}}{\epsilon_0} However, in the case of a uniform, circular charge density, \vec{E_{in}} = \frac{\rho r}{3\epsilon_0}\hat{r} \vec{E_{out}} = \frac{\rho R^3}{3\epsilon_0...

To write the uniform charge density of a disk with radius a in cylindrical coordinates, If we do this form: \rho (x)=\frac{A\delta(z)\Theta (a-\rho)}{\rho} (A is constant that sholud be determined and \theta is step function), we get A=\frac{Q}{2\pi a} and so: \rho (x)=\frac{\frac{Q}{2\pi...

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...

Homework Statement Figure 23-37a shows a narrow charged solid cylinder that is coaxial with a larger charged cylindrical shell. Both are noncon-ducting and thin and have uniform surface charge densities on their outer surfaces. Figure 23-37b gives the radial component E of the electric field...

I was studying Density functional theory, the premise of whose reasoning needs one to accept the phenomenon that when we place electrons into a potential, they "arrange" themselves into an unique wave function/charge density. Are there any forces that oppose this arrangement? (other than the...

Homework Statement Let the electric field in a certain region of space be given by E(\vec{}r)=C\vec{}r/ε0a3, where a has dimension length and C is a constant. The charge density is given by? Homework Equations ∇.E=ρ/ε The Attempt at a Solution I've been searching this on the net...

Rather than try to explain what I am talking about, I am going to link to an image of it below. My question is in regards to the negative value I marked in the answer (the one for the surface charge density for the inside of the outer shell). While I get the concept that it would be negative...

Suppose that we have the potential V=\frac{exp(-\lambda r)}{r} that \lambda is a constant. To calculate the charge density we have to calculate the \nabla^2V. We can calculate directly by the formula \nabla^2 V =1/r^2 \frac{\partial (r^2 \frac{\partial V}{\partial r})}{\partial r}without...

Homework Statement Hey guys, So the title pretty much says it. I have to find the total charge density produced by all the electrons in a closed subshell where n = 3 and l = 2. The charge density produced by a single electron is (-e)|R_{32}(r)Y_{2,m}(\theta , \phi)|^{2}Homework Equations So he...

For example, let's say there was an block infinitely long in the x and y direction and in the z direction bounded by positive and negative a. I am trying to find the charge of a imaginary partition infinitely long in the x and y direction and in the z direction bounded by positive and...

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!

I want to exchange my Au-citrate nanoparticle with two kinds of ligands :PEG-COOH and PEG-OH. Which one is suppose to have more anionic charge density.

I want to find ##\Phi## and ##\vec{E}## for the general case of a Spherical Ball with uniform Charge Density centered at the origin radius d. ##\Phi = \frac{\rho}{4*\pi*\epsilon_0}\int\int\int\frac{r^2*sin\theta}{|r-r'|}dr d\theta d\phi## ##E =...

Homework Statement Consider a right circular cylinder with radius R and height L oriented along the z-axis. The center of the cylinder coincides with the origin. Inside the cylinder the volume charge density is given by \rho(z)=\rho_0+\beta z. Find the electric field at the origin (in terms...

Homework Statement Given a volume charge density function defined as follows: \rho=\frac{dQ}{d\tau}= \begin{cases}z-z^{2} & 0<z<1\\ z+z^{2} & -1<z<0\\ 0 & \text{everywhere else} \end{cases} and is independent of x...

Homework Statement Imagine that you've been invited to try out a new "hoversuit," and here's how it works: Someone has set up a large flat sheet, many kilometers across, somewhere on the Earth, and they've charged the sheet up to a uniform charge density σ = +2 x 10^-6 C/m^2. You are...

Hi folks, I am having trouble generalizing a well-known problem. Let's say we have a cylindrical cavity inside a conductor, and in this cavity runs a line charge λ. I would now like to know the surface charge density on the inside wall of the cavity, but with the line charge not in the center of...

Homework Statement A point charge +Q is placed at the center of a spherical insulator of radius a. The insulator completely fills three cavity of a spherical conducting shell of radius b. Find the inner and outer surface charge density of the conductor and the bound surface charge density of...

Homework Statement A charge is located a distance 'a' above a sheet of metal. The charge density induced on the sheet of metal is (-2aQ)/(4pi(ρ^2+a^2)^(3/2)). Since there are no dimensions indicated for this plate, would it be plausible to assume that we are integrating from zero to...

Problem: In a neutral He atom consisting of a positively charged nucleus of charge ##2q## and two electrons each of charge ##-q##, the volume charge density for the nucleus and for the single electron cloud are respectively given by \rho_n(\vec{r})=2q\delta^3(\vec{r}) and...

1. Homework Statement A long coaxial cable consists of an inner solid cylinder, radius a, and an outer thin coaxial cylindrical shell, radius b. The outer shell carries a uniform surface charge density σ. Find the uniform volume charge density ρ that the inner cylinder must have in order...

Homework Statement The electric field intensity in polystyrene (relative permittivity 2.55) filling the space between the plates of a parallel plate capacitor is 10kV/m. The distance between the plates is 1.5mm. Calculate the surface charge density of free charge on the plates, and the surface...

Hello, Homework Statement We use an accelerator to uniformly implant electrons in a block of lucite, its surface is 25 cm², thickness 12mm. The current of the electron beam is 0,1 µA and the implantation takes 1s. The electrons are "trapped" in a layer of uniform density of 2mm thickness...

Homework Statement In some region of space, the electric field is \vec{E} =k r^2 \hat{r} , in spherical coordinates, where k is a constant. (a) Use Gauss' law (differential form) to find the charge density \rho (\vec{r}) . (b) Use Gauss' law (integral form) to find the total charge...

Homework Statement Upload Problem 2.3 and I uploaded the question in a reply belowHomework Equations D/2ε E=KQ/R^2 E=E1+E2+E3 The Attempt at a Solution I would upload my work but I am in a location where I can't right now but I can type what I did hopefully it will be clear enough. When r is...

1. A solid dielectric sphere of radius 10 cm has an electric charge uniformly distributed throughout its volume. The electric field at 5 cm from the center of the sphere is 8.6 x 10^4 N/C, pointing radially outward. Calculate the magnitude and direction of the electric field at a point 15 cm...

Homework Statement A point charge ##Q## is embedded in a dielectric medium with relative permittivity ##\epsilon_r##. What is the free charge enclosed by a sphere of radius ##R## centered at ##Q##. Homework Equations ##\nabla \cdot \mathbf D = \rho_f## ##\oint \mathbf D \cdot d...

Homework Statement Given a solid hemisphere with radius R and uniform charge density ##/rho##, find the electric field at the center. Homework Equations ##E = \frac{1}{4 \pi \epsilon_{0}} \frac{Q}{r^{2}}## ##E = \frac{1}{4 \pi \epsilon_{0}} \int \frac{\rho (x',y',z') \hat{r} dx' dy'...

I've been studying electric fields in class for some time and one thing is seemingly contradictory and really confuses me. The charge density ρ is related to the electric field E and the permiativity ε and the potential \Phi by the following equation ρ/ε=∇\cdotE=-∇2\Phi if we examine...

We have a spherical shell. We want to find the electric potential everywhere. Given charge density σ=k*sinθ, k is constant. Also it is wanted from direct integration. V=1/4piε ∫σ/r da. How can we do this, please help? I thought because it is sphere da is in the direction of r so da=r^2sinθ dθ...

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...