Charge density Definition and 419 Threads

Hello, I am confused about how charge density is only related to the material of a conductor and not on any external factors. I don't see how the molecular weight, density, and avogadro's number dictate the charge density. Any help is appreciated, thanks

Homework Statement a)Calculate the total charge a square capacitor plate would have with width x, height y, thickness z, and charge density f(x,y,z) = 1+x+y b)Calculate the total charge a sphere would have with radius r, and charge density f(x,y,z)=x+y+z Use the triple integration seen in...

We know that ∇.D = ρV My question is, if D is due to a linear or a surface charge distribution, can we apply this equation and get a surface or linear charge density? Thank you very much

Gauss' Law problem! Help please! infinite sheet with charge density? In the figure below, a small circular hole of radius R = 1.80 cm has been cut in the middle of an infinite, flat, nonconducting surface that has uniform charge density σ = 4.50 pC/m2. A z-axis, with its origin at the hole's...

help with practice test problem! curved rod with charge density?? Two plastic rods are curved. The left rod is a 120° circular arc of radius R, and has uniform charge density λ. The rod on the right is a 120° circular arc of radius 2R, and has uniform charge density -2λ. A point P is located...

Let's say you have a sphere which has a charge distribution where the charge behind a radius r can be expressed as Q(r). You also have the volume formula for a sphere, V(r). Why is ρ, the charge density, defined as: ρ=dQ(r)/dV(r) instead of simply ρ=Q(r)/V(r)?

Homework Statement A line charge starts at x = +x0 and extends to positive infinity. The linear charge density varies inversely with distance from the origin, λ(x)=(λ0*x0)/x derive the expression for the electric field at the origin, E0, due to this infinetly long line-charge (L→+∞)...

Homework Statement Given a sphere of radius R with a volumic charge distribution p find the function p. The electric field inside of the sphere is radial with a constant modulus E Homework Equations div E = p / ε ∫∫E.ds = 1/ε * ∫∫∫ p * dV The Attempt at a Solution I tried to solve it...

hey guys and gals, I'm normally pretty good at my physics homework, but this problem has my STUMPED, I think I am starting it right, but I have no idea how to proceed or if I am on a good path. Homework Statement A Very Long Cylinder with a radius of 7.2cm (.072m) has a uniform density of...

Homework Statement A proton orbits a long charged wire, making 1.30*10^6 revolutions per second. The radius of the orbit is 1.20cm. What is the wire's linear charge density? Homework Equations - q E = m w^2 r - 9*10^9 [2 λ /r] q = m w^2 r The Attempt at a Solution λ = linear...

1. A spherically symmetric charge distribution results in an electric potential of the form What is the charge distribution? 2. Hint: consider the difference in electric field between two values of r Show that the answer is of the form 3. I have attempted several solutions but haven't...

Homework Statement Consider a spherical shell with radius R and surface charge density σ = σ0 cosθ (a) What is the total charge carried by the shell? (b) Please evaluate the charge carried by the upper hemisphere, in terms of σ0. Homework Equations Q=∫σ0 cosθ da The...

I feel that I'm always struggling with these kinds of problems since I never know if the information is to be considered a density or not. Is there any trick/key words I should be on the look-out to determine whether they gave me a density charge or a point charge?

Homework Statement The sphere has radius R, and uniform volume charge density P. This sphere remains stationary (levitates) when placed above an infinite sheet of paper with a uniform surface charge density u. What is this sphere's mass? Homework Equations 4/3 pi R^3 is the volume of a sphere...

I have a conceptual problem. Homework Statement I was given a charge distribution for an electron cloud of a hydrogen atom in the ground state - ignoring the nucleus. Homework Equations charge density: ρ=charge of electron/(pi*Bohr radius^3)*exp(-2r/Bohr radius) The Attempt at a...

Homework Statement A solid ball of radius r1 has a uniform charge density ρ. a) What is the magnitude of the electric field E(r) at a distance r>r1 from the center of the ball? b) What is the magnitude of the electric field E(r) at a distance r<r1 from the center of the ball? Express your...

I'm interested in working out an efficient and precise numerical method to find the charge density on a conductor with an axially symmetric shape that is essentially a deformed sphere. (I have in mind something like r(\theta)=\sum \beta_\ell P_\ell(\cos\theta), where P is a Legendre polynomial.)...

Homework Statement Find the electric charge centred in a sphere of radius a, centered at the origin where the electric potential is found to be (in spherical coordinates) V(r)=kr^-2 where k is some constant. The Attempt at a Solution We have E=-\nabla V = -2kr^{-3} \hat{r} So...

Homework Statement Solid ball of charge with radius R and volume charge density ρ(r) = ρ0r2, centred at the origin. I have already found the electric field for r<R and r>R and also the potential at the origin by using the formula: V = -∫E.dl Now i want to find the potential at the...

Solved.

Homework Statement A line charge in the x directio has a variable charge density given by the equation λ=4 λnot((1-x)/2L), where λnot is a constant. The rod has a length of L. i)What is the net charge of the rod? Hint-the net charge is calculated by integrating the charge density with respect...

Homework Statement Show that electrostatic field E = br where b is a constant is irrotational Find the charge density ρ(r) which can generate this electric field Homework Equations ∇ x E = 0 (following stoke theorem) ρ = ε0(div E) since: div E = \frac{ρ}{ε} The Attempt...

So the problem is: The electrostatic field is E =g|r|r where g is a constant. Find the charge density p(r) which can generate the field? My attempt was gauss law: divE=p/ε0 But I'm struggling to take divE. I guess r=x+y+z? Any advice much appreciated!

As shown in the figure, a rod of length 9.8 m lies along the x-axis, with its left end at the origin. The rod has a non-uniform linear charge density λ = αx, where α = 0.009 C/m2 and x is the position. Point A lies on the x-axis a distance 3.59 m to the left of the rod, as shown in the figure...

The divergence of electric field at a point is proportional to the charge density at the point. Divergence is the rate of change with distance, the rate of change of electric field due to a distant charge is not zero, so how can it be said that the divergence at a point depends only on the...

A NONCONDUCTING sphere with uniform volume charge density ? HELP! Homework Statement so this is the problem, a nonconducting sphere of radius \alpha has a uniform volume charge density with total charge Q. the sphere rotates about an axis through its center with constant angular velocity...

Homework Statement From the picture attached it can be seen that there are two plates with charge density σa and -σb. We will chose → as the n direction. What is that electric field everywhere for this system? Homework Equations ∫∫E.dS = ∫∫σ/ε0 dA The Attempt at a Solution Using Gauss' law...

I have no clue how to start this problem. The professor wrote: "Write the charge density of a ring." ...and that's it. I know it would probably be ρ as a function of the radius. But I don't know how to move forward. I was looking through the early section in Griffith's E&M Ch. 3...

As you probably can see from the above shot, I'm determining charge density via the Laplacian over the potential (phi). I understand the mathematical steps, just confused on the factor of 4pi that pops up in the denominator. I think I understand why you would do that and here's my reasoning...

Homework Statement Consider charge distribution \rho = \frac{A}{r} with spherical symmetry, for 0 \leq r \leq R, and \rho = 0 for r > R, and A is a constant. Find the Electric Field in all of space. Check your answer obtaining \rho from your answer. Homework Equations Gauss's law...

So I bugged the folks in General Physics about the latter form of the question a while back, and got some rather unconvincing "can't be done" replies. To state the problem specifically (and my motivation): Let's say that the probability density of finding a particle at any place/time is given...

Homework Statement A nonconducting wall carries charge with a uniform density of 8.55 µC/cm2. (a) What is the electric field 8.55 cm in front of the wall if 8.55 cm is small compared with the dimensions of the wall? Homework Equations σ= Q/A E=σ/2Eo The Attempt at a Solution...

In statistical mechanics, a probability current (http://en.wikipedia.org/wiki/Probability_current) can be derived from the probability amplitude via ψ*ψ,i - ψψ*,i (i=x,y,z) ...and it would be nice or any number of reasons to be able to do the same thing with a non-probability...

Problem Statement: I'm having some trouble understanding how to write charge densities using delta functions, particularly when they involve geometries other than Cartesian. So I have a disk moving with velocity v (along the z-axis) that has total charge Q, and I'm trying to write ρ(x,t) so that...

In the diagram attached, the 3 resonance structures of arenium ion bonded to H electrophile are shown.I labelled the carbon atoms in one of the structures for convenience. From the diagram, the A and B carbons, and D and E carbons, have a double bond between them for two of the resonance...

I answered my own question but thank you for the help.

Homework Statement This is not really a homework just studying but I'm kinda stuck. So I am trying to find out how to formally write down the Charge Density for any distribution. Although I will not get into Green's Function or how to find V, I got that fine. My example will be a Rod of...

Homework Statement Two large parallel metal plate sheets carrying opposite electric charges of equal magnitude are separated by a distance of 38.0mm. The electric field between them is uniform and has magnitude 480 N/C. a) What is the potential difference between the sheets? b) Which sheet is...

Homework Statement There is a region of space containing a uniform electric field of strength E. A neutral conducting cube with side length s is placed into this field. The cube is aligned with the field. You may assume that the electric field outside the cube is unaffected by any changes that...

Homework Statement A long, non conducting, solid cylinder of radius 4.2 cm has a nonuniform volume charge density ρ = Ar^2, a function of the radial distance r from the cylinder axis. A = 2.5 µC/m5. (a) What is the magnitude of the electric field at a radial distance of 3.2 cm from the axis...

Homework Statement Two charged conducting spheres of radii a and b are connected to each other by a wire. What is the ratio of electric fields at the surfaces of the two spheres? Use the result obtained to explain why charge density on the sharp and pointed ends of a conductor is higher than on...

Suppose we have two metal plates, one with a charge density of 3 C/m^2, the other -3C/m^2 We are told that the charge density on surfaces 1 and 4 are zero and the charge density on surface 2 is 3C/m^2, on surface 3 is -3C/m^2 Any reason for that? Is it possible that the charge density on...

Homework Statement I have attached the question in a picture. I also attached a picture a drew as my attempt at understanding the question. Homework Equations flux = EA = Qencl/εo The Attempt at a Solution So I am not sure how to interpret this question. Is the charge distributed...

We are doing electricity now in school and it made me wonder.. When there is too much mass in a certain amount of volume, it supposedly forms a black hole, right? Well, does anything happen when there is too much charge density? I know this excess charge would want to neutralize itself and...

A 20-cm radius ball is uniformly charged to 80 nC. (a) What is the ball’s charge density (C/m3)? (b) How much charge is enclosed by spheres at points 5, 10 and 20 cm from the center? (c) What is the electric field strength at points 5, 10 and 20 cm from the center? ATTEMPT: part a: i...

Homework Statement A disk of radius 2.30 cm has a surface charge density of 5.22 μC/m2 on its upper face. What is the magnitude of the electric field produced by the disk at a point on its central axis at distance z = 11.2 cm from the disk? Homework Equations Formula for an electric...

Homework Statement Calculate the total charge embodied in a solid with charge density that decreases linearly with height from a value of λ at the bottom to 0 at the top. Solve for a rectangular prism and a sphere. Homework Equations ∫∫∫ρdxdydz ∫∫∫pr^2sinθdrdθd∅ The Attempt at a Solution...

Homework Statement A straight, nonconducting plastic wire 8.00 cm long carries a charge density of 125 nC/m distributed uniformly along its length. It is lying on a horizontal tabletop. A) Find the magnitude and direction of the electric field this wire produces at a point 5.50 cm directly...

Hello, I am solving schrodinger and poisson's equation in a self consistent way. I solved schrodinger equation and obtained eigen values which are allowed energy states. now I am calculating electron density with n=sum(psi*psi*f(E)) where f(E)=1/(1+exp((E-Ef)/kT)) fermi function. Now...

VOLUME charge density from SURFACE/LINE charge density?? So I'm doing a problem from Jackson, but this is a more general question anyway. He says that there is a charge Q uniformly spread over a spherical shell of radius R, and asks for the three dimensional charge density ρ(x). Obviously...