Charge density Definition and 419 Threads

Homework Statement A large plane having uniform charge density has an electric field just outside the plane that points directly toward the plane with magnitude 1.50×10^4 N/C . What is the surface charge density? Express your answer with the appropriate unit Homework Equations I am...

Homework Statement "Consider a charge density distribution in space given by [rho] = [rho]_0 * e^(-r/a), where [rho]_0 and a are constants. Using Gauss' Law, derive an expression for the electric field as a function of radial distance, r. Sketch the E vs. r graph. Was a question on a quiz...

Homework Statement If the Earth's surface was charged to QTOTAL = 13548.3 [C] by removing all of the electrons from a volume of soil, how large would this volume be? Assume electron density of soil = 7e23 [cm-3]. Homework Equations Volumetric charge density pv = QTOTAL/volume of soil...

Homework Statement A point charge, Q, is located @ (0,0,d) above infinite conducting plane that lies in xy plane and is maintained at ground potential. Find: a.) surface charge density as a function of x and y on conducting plane, and b.) total charge induced on conducting plane...

Homework Statement You are informed that the charge density is: $\rho \left( r \right)=k{{r}^{-n}},r<a$, where k is a constant and n is a whole number. Determine n. Homework Equations Besides that, I know that: \[E=\frac{Q}{4\pi {{\varepsilon }_{0}}}\frac{1}{{{r}^{2}}},r<a\] (E is...

1. A spark occurs at the tip of a metal needle if the electric field strength exceeds 4.00×106 N/C, the field strength at which air breaks down. What is the minimum surface charge density for producing a spark? 2. surface charge density = Q/A 3. The answer is 3.54*10-5 C/m2. How was this...

Homework Statement A sphere with excess charge of 1.5 x10 -7 Coulombs, An outer radius of 2.5cm and inner radius of 1.5 cm ( a cavity ). The question is to find the surface charge density on the inside surface. I'm totally at a loss on this one and couldn't find how to solve it...

Homework Statement The electric field produced by a static electric charge Pe(R) at a point R in free space is give by, E(R) = (R3+AR2) R\hat{} , R<a E(R) = B(a5+Aa4)R-2 R\hat{}, R>a Where a, A and B are arbitrary constants and R spherical coordinate system radial vector (R locates...

Homework Statement a 5 cm radius conducting sphere has a charge density of 2x10^-6 C/m^2 on its surface. Its electric potential, relative to the potential far away is? Homework Equations I used V= K(q/r) The Attempt at a Solution Using the above equation I got 1.12 x 10^4. This...

Homework Statement In the atmosphere and at an altitude of 250 m, you measure the electric field to be 150 N/C directed downward, and you measure the electric field to be 170N/C directed downward at an altitude of 400 m. Calculate the volume charge density of the atmosphere in the region...

A small, nonconducting ball of mass 1.4E-6 kg and charge 1.9E-8 C hangs from an insulating thread that makes an angle of 32 degrees with a vertical, uniformly charged nonconducting sheet. Considering the gravitational force on the ball and assuming the sheet extends far vertically and into and...

Homework Statement An air-filled capacitor consists of two parallel plates, each with an area of 7.60 cm2, separated by a distance of 1.60 mm. 1. If a 25.0 V potential difference is applied to these plates, calculate the electric field between the plates. 2. What is the surface charge density...

Homework Statement An infinite cylinder of radius \textbf{R} has a linear charge density \lambda. The volume charge density \frac{C}{m^{3}} within the cylinder (r\leq R) is \rho(r)=\frac{r\rho_{0}}{R} where \rho_{0} is a contant to be determined. The charge within a small volume...

Homework Statement A square plate of copper with 50.0-cm sides has no net charge and is placed in a region of uniform electric field of 80.0 kN/C directed perpendicularly to the plate. Find: (a) the charge density of each face of the plate and (b) the total charge on each face Homework...

Is my procedure/result correct? Are these equations relevant for the problem? Many thanks! Homework Statement - blue color on the picture Homework Equations - black color on the picture The Attempt at a Solution - black color on the picture...

Homework Statement We know that free charges inside a conductor will eventually move to the conductor surface. Consider a free charge initially placed inside a conductor at t=0. Show that the free charge density \rho_f will dissolve exponentially with time. Express the characteristic time...

Homework Statement Center a rod of length L at (0,0) with the length going horizontally. Take a point P at (0,y). Find the electric field at P. Homework Equations \lambda=Q/L E= \int k*dQ/R^{2} The Attempt at a Solution I am integrating from -L/2 to L/2 Since Q=lambda*L, I...

This is actually a problem in my Vector Calc class, but is very fitting for this section. I have been trying to understand this problem, and cannot seem to figure out where to go. The z-axis carries a constant electric charge density of λ units of charge per unit length with λ > 0. The...

Homework Statement A sphere of radius R, centered at the origin, carries charge density ρ(r,θ) = (kR/r2)(R - 2r)sinθ, where k is a constant, and r, θ are the usual spherical coordinates. Find the approximate potential for points on the z axis, far from the sphere. Homework Equations...

Homework Statement i have: a nonconducting sphere of radius 25 cm. the electric field points radially away from the center of the sphere, and increase linearly from 0 to 3700V/m at the surface of the sphere. determine charge density? Homework Equations i think the E=E0+r*148 The Attempt at a...

Calculate the dipole moment of a spherical shell of radius 'a' whose surface charge density is σ=σ0(1+cos(θ)). The origin is at the center of the sphere. What I know: 1) p=∫r'*ρ*dV' I'm having trouble understanding how to transform this equation so that I can calculate the dipole moment...

Homework Statement What is the electric field inside a a solid of uniform chage density i.e. \mathbf{E}(\mathbf{r})=\frac{1}{4\pi\varepsilon_0}\int_V\rho(\mathbf{r}')\frac{\mathbf{r}-\mathbf{r}'}{|\mathbf{r}-\mathbf{r}'|}dV' What is the electric field at \mathbf{r}'=\mathbf{r} if...

Homework Statement the volume charge density Pe= Po (1- (r^2/r0^2)) the sphere has a radius of r0 and r is measured from the center for a point P inside the sphere (r<r0), determine the electric potential V if V=0 at infinity Homework Equations E= Qencl/ eps0*A= kQ/r^2 Qencl=...

Homework Statement The surface of a sphere of radius a is charged with a constant surface density \sigma. What is the total charge Q' on the sphere? Find the force produced by this charge distribution on a point charge q located on the z axis for z > a and for z < a.Homework Equations The...

Homework Statement Express the 3D charge density \rho for a thin wire with length Z and uniform linear charge density \lambda along the z-axis in terms of a two-dimensional dirac-delta function. Homework Equations The three dimensional charge density is the total charge over a...

Homework Statement Express the 3D charge density \rho for a thin wire with length Z and uniform linear charge density \lambda along the z-axis in terms of a two-dimensional dirac-delta function.Homework Equations The three dimensional charge density is the total charge over a volume.The...

Homework Statement A sphere of radius a has a charge density which varies with distance r from the center according to http://img14.imageshack.us/img14/9577/wangsnessproblem594.gif where A is a constant and http://img35.imageshack.us/img35/555/wangsnessproblem593.gif .[/URL] Find the...

Homework Statement Ok, here's the problem. It deals with the superposition of electric fields from uniformly charged shapes: A uniformly charged infinite plane is located at z = 0, with a surface density of charge σ. A uniformly charged spherical shell with the same surface density is located...

Homework Statement I was just wondering if I had done this problem correctly Take the rod axis to be the x-axis and the lefthand end of the rod to be x = 0. Assume lambda is not constant but that lambda = μx where μ is a constant. What are the units of μ? Find the force Vector F on the...

Homework Statement This is a three part problem. My first task is to calculate the divergence of \vec{r}/r^{a}. Next, I am to calculate its curl. Then I'm supposed to find the charge density that would produce the field \vec{E}=\frac{q\vec{r}}{4\pi\epsilon_{0}r^{a}} The Attempt at a...

Homework Statement A straight wire 7.0m long carries 30uC distributed uniformly over its length. What is the line charge density on the wire? _____ uC/m Homework Equations A) E = 2k/lamda / B) E = kq/r some other ones? The Attempt at a Solution I sub B into a...

Homework Statement Consider a cylinder, radius R and length L. Suppose the cylinder is charged with a volume charge given by P+P[SIZE="1"]0 + Bz, where p[SIZE="1"]0 and B are constants. Find the force on a charge Q at the center of the cylinder. Homework Equations E=q/4*pi*e*r^2...

Homework Statement We learned in E&M about the Dirac Delta function and its applications to representing the densities of point charges in space. For example, the charge density of space with a point charge q at the origin is given by q*delta(r). How does this density representation work with...

Can anyone tell me if the potential distribution equations V= x2-Y2+Z2 holds in free space, if not, please help me to find the charge density from the given potential .

Homework Statement A charge of -310e is uniformly distributed along a circular arc of radius 4.15 cm, which subtends an angle of 43°. What is the linear charge density along the arc in C/m? Homework Equations Density = Charge/length The Attempt at a Solution Charge =...

In this problem we assume that the photon mass is m > 0. We take a conducting sphere of radius R and put a charge of Q on it. Some fraction of the charge will then reside at the surface and a fraction will move into the bulk. Evaluate the volume charge density in the bulk. I was shocked to...

Hello I have a conceptual question about the following. Suppose I have a spherical shell with charge density \sigma that is uniformly distributed throughout its surface. My shell has radius a. Then I cut a little circular piece of radius b with b << a. Then I know that my electric field at...

Statement: If a volume charge distribution existed inside a conductor at t = 0, the charges would quickly migrate to the outside surfaces due to repulsion. The rate at which the charge density would decrease is given by: \rho_{v}(t) = \rho_{v}(t = 0)e^{-\frac{t}{t_{r}}} where the relaxation...

How would one determine the charge density of a fluid? I'm using the equation of I = qnvA . Amperes = charge of electron * charge density * velocity * Area. The only thing I'm not sure of is how to determine charge density. I've read several websites and I have a few textbooks here...

Homework Statement A surface is defined by a hemisphere of radius b, centered on the x-y plane. The surface charged density is given by \rho_s(z) = z (\frac{Coul}{m^3}). Homework Equations \rho_s(z) = z = Rcos(\theta) = bcos(\theta) (\frac{Coul}{m^3}). 3. Question My question is...

Let's say we have an electric field, (ax, 0, 0). (a is a constant) The divergence of the field is a, so the charge density is a*epsilon. This implies a uniform charge density, but the field only points in one direction! Furthermore, it switches directions at the x-axis. But that's...

Homework Statement A uniform line charge of density λ lies on the x-axis between x=0 and x=L. Its total charge is 11 nC. The electric field at x=2L is (500 N/C)ˆı. Find the electric field at x=3L. Answer in units of N/C. Homework Equations The Attempt at a Solution I have no clue...

What is the difference between charge density and charge carrier density? If each electron has an elementary charge of -1 (natural units), and the electric field and voltage are manifestations of the effects of charge, then why is charge referred to as seemingly separate of electrons in text...

Let me know if the following reasoning is correct : If the surface charge density on the internal surface of one of the plates in a parallel plate capacitor is Sigma, which becomes Sigma/K, when a dielectric material is inserted between the plates with dielectric constant...

Hi there. Long time no see. I hope you're all well. Homework Statement An infinite 1D system has electron plane waves occupying states 0 <= E <= E_F. At time t=0, a potential step is introduced such that V=0 for x<0 and V=V' for x>0. What is the electron density when the system reaches...

I need the answer to this question A charge belt, 50cm wide, travels at 40m/s between a source of charge and a charging object at a rate corresponding to 100microA . Compute the surface charge density on the belt Some one told me the answer may be 5 microC/m2 but how ??

Does current density being constant in time and the charge density NOT being constant in time imply that the charge density has to be a linear function of time? i.e of the form p(r,t) = p(r,0) + \dot{p}(r,0)t } Can this be derived using the continuity equation alone?

Homework Statement A 1.0-mm-diameter wire has 1000 excess electrons per centimeter of length. What is the surface charge density? Homework Equations \eta = Q/A The Attempt at a Solution \eta = (100000 * 1.6*10^-19)/(\pi * (5*10^-4)2) But that gets me 2.037 * 10^-8 C/m^2 The...

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 In the air over a particular region at an altitude of 500 m above the ground, the electric field is 120 N/C directed downward. At 600 m above the ground, the electric field is 100 N/C downward. What is the average volume charge density in the layer of air between these two...