Charge density Definition and 419 Threads

Hi. Is the Maxwell equation $$\nabla\cdot\vec{E}=\frac{\rho}{\varepsilon_0}$$ even true in the stronger form $$\frac{\partial E_i}{\partial x_i}=\frac{\rho}{3\cdot\varepsilon_0}\enspace ?$$ I guess not, since I haven't found a source suggesting this. But shouldn't the isotropic electric field...

Homework Statement The electric dipole moment for the water molecule equals $$ p = 6.13 × 10−30 C · m $$ Suppose that in the glass of water all molecular dipoles could be made to point down. Calculate the resulting surface charge density at the upper water surfaceHomework Equations [/B] ## P...

Why must steady currents be non-divergent in magnetostatics? Based on an article by Kirk T. McDonald (http://www.physics.princeton.edu/~mcdonald/examples/current.pdf), it appears that the answer is that by extrapolating the linear time dependence of the charge density from a constant divergence...

1. Homework Statement Calculate the resultant electric field acting on some point ##x##. The electric field is generated by a long thin rod and the line charge density is given. ##p_l=\frac{dQ}{dL}## Homework Equations 3. The Attempt at a Solution [/B] I have uploaded two images, one of the...

Homework Statement Hi everybody! I'm preparing for an exam of electromagnetism, and I am struggling with the last question of this problem (hopefully the two first ones are correctly solved): Given potential: ##\phi(\vec{r}) = k \frac{q}{r} e^{-r/R}## with ##r=\sqrt{x^2 + y^2 + z^2}## and ##R...

I thought that insulators cannot be charged in the inside or the outside, so how can they have any charge density inside? I know that electric fields pass through a insulator, so is that why they can have charge density? I am currently reading about electric flux.

At this point I was given rho, sigma and landa to hold value of these three different kinds of density ρ = Charge/Volume -------------- Volume Density σ = Charge/Area ----------------- Area Density λ = Charge/Length ---------------- Length Density How do I know which type of density to use over...

Homework Statement It is known that the potencial is given as V = 80 ρ0.6 volts. Assuming free space conditions, find a) E, b) the volume charge density at ρ=0.5 m and c) the total charge lying withing the closed surface ρ=0.6, 0<z<1 Homework Equations E[/B]=-∇VThe Attempt at a Solution (this...

In the situation consisting of a steady current of 1A in an arbitrary closed path, what would the consequences be for the electric field if the drift velocity was non-uniform along the path due to non-uniform carrier density? This would be a case of a "uniform" 1 amp, but where the charge...

Homework Statement A thin rod of length 2L has a linear charge density that isλ0 at the left end but decreases linearly with distance going from left to right in such a way that the charge on the entire rod is zero. Given E = −kλ0/L(d/(L−d)−ln(d−L)+d/(L+d)+ln(L+d)) for a point P that is...

As the name of the thread says, I am wondering what would the amount and the direction of the electric field at some point in the uniformly charged ball of radius R(it has a constant charge volume density) be at the distance r from the centre of the ball. Does anyone know what would they be? I...

Homework Statement This is problem 3.4 from Prucell and Morin if you have the book. Homework Equations None The Attempt at a Solution Electric field inside a conducting sphere is zero. Let P be a point on one of its equatorial plane. The field along the plane is zero. So I know the charge...

I am currently interested in a system, where I have a big box of charges for which the density goes to zero at the boundary. What I wanted to do is try to derive what charge density will minimize the total electrostatic energy in the box. Now a cubic box gave me some complicated so I switched...

Homework Statement I am trying to calculate the charge density in the first subband (n=1) of the quantum well of length L as shown in the below figure. here is the electron wave function for the first sub-band and its value (from relevant equation 1) is given as Ψ12(x) = 2/L*sin2(πx/L) from...

Homework Statement Electric current of I amperes flows along the z-axis from (0, 0,-∞) to (0, 0, -a) and from there it spreads over a conducting sphere r = a in the -aθ direction, comes to the point (0; 0; a) and goes to (0, 0, ∞) again along the z-axis. What is the surface current density at...

Homework Statement A thin rod of length 2ℓ has a linear charge density that is λ0 at the left end but decreases linearly with distance going from left to right in such a way that the charge on the entire rod is zero. What is the magnitude of the electric field along the rod's axis at a...

Homework Statement I am trying to solve Problem 2.45 in Electrodynamics by Griffiths, however, my answers were different from those in the book, I am suspect I got a missing step but I could not find it, so here is the Given Problem Find the charge density \rho given by a potential...

All, I am wanting to see why charge density divided by e nought is equal to F/q and V/d. Unit cancellation makes it easy to equate F/q = V/d, but why is charge density alone enough to be equal to the electric field? I feel like something is missing here but I can't reconcile it nicely in my...

Homework Statement 1.0 mA proton beam accelerated through potential difference of 1 keV. Determine the volume charge density of the beam after acceleration assuming uniform current distribution within diameter of 5mm, with zero current outside of this. Particle starting from rest. Final answer...

Homework Statement There is an electrostatic potential, given by ## \phi(r)=\phi_0 e^{-\alpha r}## where ##\phi_0## and ##\alpha## are some constants. A: Find the electric charge denisty ##\rho(r)## which produces this aforementioned potential. A: What is the electric field...

Homework Statement This is a wire whose shape is given by y = acos(x/L). This wire has a linear charge density of +λ, and is it desired to determine the electric field at the point (0,y) where y > a. a) If a=0, determine the amount of charge the wire has. b)If a > 0, is the total charge on...

Suppose I want to collect 1 esu (2.081 billion charges) on a plate or on a ball, what is the smallest radius that will carry such a charge? From data I gathered around a ball of 1 mm of radius would be large enough, can you confirm that? What material is best, steel, silver or non-conductive...

Homework Statement a) and b) are no problem. I need help to solve c) and d) Homework Equations c) Delta dirac function Gauss' law d) Gauss' law ## \int_V {\rho \, d\tau} = Q_{enclosed} ## The Attempt at a Solution By taking laplace on the potential I get: ## \rho(\mathbf{r}) =...

Homework Statement A rather large non conducting slab of area A and thickness d has a charge density given by ρ = αx2. The origin is through the center of the slab. That is, it bisects the slab into two equal volumes of d/2 thickness and with an area A, with -L/2 to the left of x=0 and L/2 to...

Homework Statement Given a spherical shell of radius R and the surface charge density ( being the angle from the top of the sphere and being a constant) find the electric potential and the electric field inside and outside the sphere. Check that both the potential is continuous inside and...

Homework Statement Find the total charge Q given the charge density ρ(r)=ε0A(4πδ3(r)-π2e-λr/r The Attempt at a Solution I know the solution's steps start with: Q=∫ρdr=ε0A(4π∫δ3(r)dr-λ2∫e-λr(4πr2)/rdr) What I don't understand is where that 4πr at the end comes from. That last step is only...

A disk with a uniform positive surface charge density lies in the x-y plane, centered on the origin. The disk contains 2.5 x 10-6 C/m2 of charge, and is 7.5 cm in radius. What is the electric field at z = 15 cm? I have used the formula...

Hi... I want to know why charge density is higher at sharp points in a conductor? I have gone through the analogy of two spheres connected by a wire... But is there any other explanation which is not specific to spheres...?

Homework Statement Find potential and charge per unit length of every cylindrical hollow shell if the outer shell is grounded. The length is considered to be infinite. Homework Equations V=∫Edl The Attempt at a Solution I am not sure how to derive potentials for first two conductors...

Homework Statement Three very long (theoretically infinite long) hollow cylindrical conductors, with radius a,b,c (c>b>a) are in vacuum. Inner and central conductor are charged, and outer conductor is grounded. Potentials of inner and central conductors with reference point relative to outer...

I have one question. Charge density waves are usually defined as phase transitions on metal in which electrons started to behave like collective. Is this happen always in quasi one dimensional metals? Also why this transition actually happens?

Homework Statement A cylinder of radius a and length l has charge distribution ρ=Cr2 where C is a constant and r is radial distance in cylindrical coordinates. Derive an expression for the average charge density within the cylinder. Homework Equations Well, charge density given is within the...

Homework Statement Note - I have used an image here. For the simple reason I don't want to confuse anyone by missing out subscripts. But if that is not acceptable let me know and I will attempt to write it out. Homework Equations I have considered using Poissons equation - but couldn't...

Homework Statement Homework Equations E= kq/(r^2), E*dA = Q/e0 The Attempt at a Solution Typically I understand how to interpret basic graphs such as going for V (potential) vs x graph to Electric field vs x graph by finding the slope of V since E= -grad V...and from their it's basic...

Homework Statement In a particular region of the Earth's atmosphere, the electric field above the Earth's surface has been measured to be 148 N/C downward at an altitude of 260 m and 165 N/C downward at an altitude of 410 m. Calculate the volume charge density of the atmosphere, assuming it to...

Homework Statement Two plane parallel electrodes are separated by a plate of thickness s whose conductivity \sigma varies linearly from \sigma_0 near the positive plate to \sigma_0 + a near the negative plate. Calculate the space charge density \rho_f when the current density is J_f ...

Homework Statement The electric field is described by E = \frac{C e^{-br}}{r^2} , find the charge density and then integrate over all-space and show it's zero. [/B]Homework Equations E = \frac{C e^{-br}}{r^2} \\ \\ \nabla \cdot E = \frac{\rho}{\epsilon_0} \\ \\ \rho(r) = Q \delta^3...

1. A charge density ρ (charge per unit volume) is distributed uniformly throughout a non-conducting cylinder of radius R. What is the magnitude of the electric field a distance r = R/2 from the cylinder's axis? Homework Equations E ∫dA = q(interior)/ε0[/B]3. So I tried doing EA =...

1. Portion of z-axis for which |z| < 2 carries a non uniform charge density of 10|z| (nC/m). Using cylindrical coordinates, determine E in free space at P(0,0,4). Explicitly show your integration.Homework Equations E = (1/4πε0) ∫ dQ*aR/(R2)The Attempt at a Solution...

Homework Statement Find the potential V(r) inside and outside of a uniformly charged sphere with radius R and total charge q. A) Fix first the charge density ρ(r) in the two regions 1: r>R and 2: 0<r<R the results should only be in terms of q and R[/B] Homework Equations ρ= qtot/Vtot dq=...

I am working on a problem of electrostatics, and I am having troubles in trying to figure out one part of it. 1. Homework Statement It consists of an inner solid cylinder of radius ##a## with a voltage ##V_A##, and an outer coaxial cylindrical shell of inner radius ##b## and outer radius ##c##...

Homework Statement [/B] We need to use the equation for the E field of a ring to set up the integral for calculating the E field of a cylindrical shell with a charge density of σ and a radius of R and a height of H, at a point P that is D distance away from the cylinder.Homework Equations [/B]...

Homework Statement Find electrostatic field and potential created by a two-dimensional charge density: \rho \sin (kx) \cos (ky) \delta (z) at the distance d from the the plane z=0 where the charge is placed (taking into account that it is embedded in a three dimensional space). In your...

Homework Statement An infinite line of charge with linear density λ1 = 6.7 μC/m is positioned along the axis of a thick insulating shell of inner radius a = 2.4 cm and outer radius b = 4.7 cm. The insulating shell is uniformly charged with a volume density of ρ = -722 μC/m3. What is λ2, the...

Hi,there are many literatures concered with band decomposed charge density(As an example,see FIG.3 in PHYSICAL REVIEW B 78, 235430 2008). For condution band,there should not be charges or electrons when the system is in the ground state,but,those literares still show a band decomposed charge...

I am confused about the coupling of the Dirac equation to electromagnetism. The 4-current that is the source for Maxwell's equation that arises from the Lagrangian \begin{equation} \mathcal{L}=i\overline{\psi}\gamma^\mu(\partial_\mu+ieA_\mu)\psi-m\overline{\psi}\psi \end{equation} is...

Homework Statement Consider a nonconducting sphere of radius r2. It has a concentric spherical cavity of r1. The material between r1 and r2 has a charge density p (C/m3). Take V=0 and r=infinity. Determine the electrical potential V as a function of the distance r from the center for (a) r>r2...

How would one go about estimating the relative position of the center of charge density (with respect to oxygen) in ruthenium oxide vs. silicon oxide? (Hypothetically) My real quandary is with the relative screening experienced by oxygen core electrons in silicon dixoide vs. ruthenium dioxide...

Homework Statement I actually have three problems that have one thing in common that I don't understand. I will try to shortly describe all of them: 1. We have two perpendicular planes. (See Attachment: sketch1.png) The idea is to describe the electric potential in space. Now you can believe...

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...