Charge distribution Definition and 236 Threads

Homework Statement Examine the diagram provided, Sphere 1: q=3.0x10-4C Sphere 2: q=-3.0x10-4C Sphere 3: q= 3x10-4C a) Find the total electric potential energy of the charge distribution b) Find the total electric potential at point Z Homework Equations EE=kq1q2/r...

A line of positive charge is formed into a semicircle of radius R = 57.8 cm, as shown in the figure below. (The figure is a semicircle above the x-axis with angle θ measured from positive y axis centred at the origin) The charge per unit length along the semicircle is described by the...

Say you have two spherical conductors, of radius r, centers a distance d apart. Both have charges of +Q. What are the charge distributions on them? My physics book more or less handwaves and says it'll be more or less unaffected, but is there a way to solve this exactly?

What is the electric field for the following charge distribution: ρ = ρ0 x/a for -a < x < a 0 elsewhere Use the differential form of Gauss' Law. I know that the differential form is \nabla . D = ρv and that E = D/ε, but how do I find D from what is given...

Hi. I have this problem, which I must solve. It says: two concentric conducting spherical shells, of radius a and b (a<b), are charged at Q and -Q respectively. The space between the spheres is filled at its half by an hemisphere of dielectric with dielectric constante ε. a)Find the field for...

Homework Statement three point charges q,q and -2q are located at (0,-a,a), (0,a,a) and (0,0,-a) respectively. what is the net dipole moment of these charge distribution.? Homework Equations moment p =qd. The Attempt at a Solution Here we have to consider only the yz plane as x...

We are presenting you a very perplexing but interesting problem which you may have probably encountered in electrostatics. We were trying to calculate the potential of an infinite line charge distribution at a general point by first principle method i.e. the usual integration of the...

Homework Statement At time t = 0 a charge distribution \rho(r) exists within an idealized homogeneous conductor whose permitivity \epsilon and conductivity \sigma are constant. Obtain \rho(r,t) for subsequent times. Homework Equations Maxwell's equations = Gauss' Equation + Ohm's...

Homework Statement Compute the electric field generated by a spherically symmetric charged sphere of radius R with charge density of \rho = kr^{2} Homework Equations \oint _S \vec{E} \cdot \vec{dA} = \frac{Q_{enclosed}}{\epsilon_0} The Attempt at a Solution I know that this question...

V=\frac 1 {4\pi\epsilon_0}\int \frac {\rho(\vec r\;')}{\eta} \;d\;\tau'\;\hbox{ where }\; \vec{\eta} = \vec r - \vec r\;' \vec r\; is the position vector of the field point and \;\vec r\;'\; is the position vector of the source point. Using multiple expansion, the quadrapole term of...

1. The problem statement Consider an infinite spherical charge distribution with constant charge density. According to symmetry of the problem, I expect the electric field at any point to be zero. But if you construct a Gaussian sphere and apply Gauss theorem, it will give you some finite field...

The example is about finding the retarded scalar potential V at the origin from a plastic circular ring on xy plane center at origin spining at constant angular velocity \omega with line charge density: \lambda = \lambda_0\left | sin \left (\frac {\theta}{2}\right ) \right |[/itex] For...

This is part of the problem in the exercise to find charge distribution of a point charge at origin. I know \nabla \cdot \vec E = \frac {\rho}{\epsilon_0} \rho = \epislon \nabla \cdot \hat r \frac q {4\pi\epsilon_0 r^2} \;\hbox { where } \vec r = \hat x x + \hat y y + \hat z z \nabla...

Homework Statement Calculate the surface charge distribution on a metal disc of radius R having total charge +q. Homework Equations The Attempt at a Solution

I will refer to Griffiths' textbook Introduction to Electrodynamics, Third Edition. On page 70 he calculates divergence of E and implicitely assumes that divergence of rho is 0, where rho is charge density distribution. On page 223 he calculates rotB and says that rotJ = 0, where J is current...

Hello guys, I tried to figure this out and I got my answer. I just want to check it. So would you guys please help me with it? Thank you! Here is the question: A nonconducting rod of length 2a has a charge Q uniformly distributed along it. Find the expression for x-component of the electric...

Homework Statement Two point charges, -q and q/3, are situated at the origin and at the point (a,0,0) respectively. At what point on the x-axis does the Electric Field Vanish? Find the potential function and show that the V = 0 equipotential surface is a sphere Homework Equations...

I have problem understanding why the surface integral disappear when taking the volume to very large in this equation: W_e = \frac 1 2 \int_{v'} \rho_v V dv' = \frac 1 2 \int_{v'} (\nabla \cdot \vec D)V dv' = \frac 1 2 \int_{s'} V \vec D \cdot \hat n ds' \;+\; \frac 1 2 \int_{v'} \vec E...

I'm very sorry for the initial post - I was having trouble working with LaTex (I've never used it before and the preview post wasn't showing me what I had expected it to look like - it kept giving me a square root symbol for every code). Find the electric field a distance z above the centre of...

Homework Statement 2 capacitors C1 = 4 and C2 = 6 are connected to a battery of emf V=12V in parallel. The battery is disconnected and the capacitors are rearranged in series. Find out the final charges on the capacitors. The Attempt at a Solution Why doesn't the charge conservation...

Homework Statement Two infinitely long wires running parallel to the x-axis carry uniform charge densities \lambda and - \lambda. a.) Find the potential at any point (x, y, z) using the origin as your reference. b.) Show the equipotential surfaces are circular cylinders, and locate the...

Homework Statement I need to find the electric field along the Z-axis for a hemispherical open shell of radius R (open face down). the shell is oriented so its symmetrical about the Z axis. The Attempt at a Solution What I've done is set it up, taken the vector from the origin (at the...

Homework Statement A charge distribution with spherical symmetry has the density \rho = \rho _0 r/R for 0≤ r ≤ R. Determine the total charge content of the sphere. Homework Equations \rho = Q / V The Attempt at a Solution I started by thinking of the charge dQ of a small...

Why are the integration bounds from -pi/2 to pi/2 and not 0 to pi?

Homework Statement Say we have an infinitely long wire with radius r1 with a linear charge density +u and we have a coaxial conducting cylinder with radius r2->r3 and a linear charge density of +2u. http://img573.imageshack.us/img573/3419/coaxialcable.png" Now the overall aim of the...

Hey guys, I'm kind of stuck on how to do this one. Positive charge Q is distributed uniformly along the x-axis from x=0 to x=a. A positive point charge q is located on the positive x-axis at x=a+r, a distance r to the right of the end of Q. (a) Calculate the x- and y- components of the...

Homework Statement We have a rectangular box with diagonal corners at (0,0,0) and (-1,2,3)cm. We place charge inside this box with distribution, ρ(r)=2x-3(z-1) with units of nC/m3. What is the total charge inside this box? Homework Equations The Attempt at a Solution I have an...

Homework Statement Using the method of images: discuss the problem of a point-charge “q” inside a hollow, grounded, conducting-sphere-shell of inner radius “a”. That charge "q" is located at {\left| {{{{\bf{\vec r}}}_0}} \right|}. We don't care about its angular position. Oh yes: the problem...

Homework Statement Four identical metallic plates, each of area A, are seprated by a distance d as showen in the Figure. Plate 2 is given a charge Q. Plates 1 and 4 Both are earthed. Homework Equations Charge Distribution i.e. Charge on each Plate and On each Side of the Plate. Will the Outer...

Hey everyone! I need some help. Can a non uniform charge distribution exist on a conductor's surface due to some external influence? Please explain bearing in mind that a conductor's surface is equipotential.

I started reading through "Electricity and Magnetism" by Purcell and came across the derivations for infinite line and infinite plane charge distributions and noticed the former has a 1/r dependency (on perpendicular distance from the wire) and a constant value for the plane. Would an...

The problem was to give the charge distribution of a uniformly charged disk of radius R centered at the origin and perpendicular to the z-axis. The professor explained us how to do so (though many parts were unclear to me and I couldn't copy everything that was on the blackboard because we were...

Homework Statement I have a simple question. There is positive point charge in the center of a sphere 2.5 micro c. The spherical shell has inner radius of 60 cm and outer radius of 90 cm. The net charge of the spherical shell is equal to zero. Homework Equations The...

This is a general question, I was reading my textbook and this statement confuses me: "The symmetry of the electric field must match the symmetry of the charge distribution" this is said regarding symmetry in relation to GAuss' law. I do not understand what they mean by symmetry of charge...

Homework Statement Three concentric spherical shells ,r=1m ,r=2m and r=3m, respectively, have charge distributions 2, −4, and 5 μC/m2. Calculate the flux through r=1.5m and r=2.5m Homework Equations Since we are talking about Gaussian surfaces I assume that the flux at 1.5m is...

The most general way of calculating the value of the vector electric field at a certain point P is given by the formula E = k times Integral of (dq/r² times unit vector). That means you break the charge distribution into infinitesimal elements dq and vectorially add the contributions of each at...

I am having two metal sheets which are curved and fitted on the outer sides of a pipe. A 9V pottential is applied to both the plates. Dimensions of the plate = 130mm X 65mm (L X B) How can i find the charge distribution on the plates to find the total charge. I need this to calculate the...

Homework Statement The charge distribution on the figure below is referred to as a linear quadrupole. Show that the potential at a point on the x-axis where x>a is given by: PLEASE go to the attached MS Word document to view the rest of the problem / diagrams. It is easier to post...

If charge distribution inside sphere is non-uniform, how is distribution on outside of sphere uniform? (Think spherical shell with point charge anywhere inside) And how can a non-uniform surface charge be still equipotential. If there was a strong enough induced charge, wouldn't the behavior...

Homework Statement http://uberlycool.com/2.jpg" Homework Equations Working on the conceptual first...The Attempt at a Solution 2a. My understand is that the electric potential inside the shell is only affected by the enclosed q? Is that correct? Because if I was to place an image charge to...

Homework Statement Design a charge distribution so that the resulting E is proportional to r^2. The Attempt at a Solution This is not really a homework problem just something our professor told us to think about at the end of our lecture. It made me really curious as to how you would do...

Here is the problem. I've been messing around with it for a while but I'm not sure if what I'm trying to do is the right way to approach this. The form factor F(q) = \int\rho(\vec{r})e^{i\vec{q}.\vec{r}/\hbar}d^{3}\vec{r} is the 3D Fourier Transform of the normalised charge distribution...

Hello everybody, I have to calculate the electric field and the potential for a charge q placed at distance d from an infinite plane charge distribution \sigma. For the electric field there's no problem, but how I can get the electric potential for an infinite charge distribution?

Claim: A charged sphere will have it's charges disperse (uniformly for symmetrical objects) on the outer surface. Proof: Consider a sphere charged to some amount q. If we take small gaussian surfaces within the sphere, it will have \vec{E} = 0 on the closed gaussian sphere [since it is an...

Homework Statement "A thin conducting spherical shell of radius a carries a charge q. Concentric with this is another spherical shell of radius b>a carrying a net charge Q. Describe how the charge is distributed between the inner and outer surfaces of the shells. What is te capacitance of the...

Homework Statement Two insulated metal spheres of equal sizes are given equal positive charges. The two spheres are brought very close to each other without touching. Draw the new charge distribution on the spheres if one sphere is much larger than the other. Homework Equations...

http://www.vias.org/physics/bk4_06_07.html This is a quote from the mentioned website, " For example, a charged metal ball will have charge spread nearly uniformly all over its surface, and in for most purposes it will make sense to ignore the fact that this uniformity is broken at the atomic...

In the Electric field of a Continuous Charge Distribution, what is "conti.." exactly? -I know its the "distribution"! but I`m asking about, like, how would the "distribution" be continuous? -I think the word "symmetry" should be used? -why is the word "continuous" used?

Homework Statement Show that any charge distribution in a conductor of conductivity σ and relative permittivity κ vanishes in time as ρ = ρ0exp(−t/ζ) where ζ = κǫ0 σ Homework Equations Maxwell's equation ∇ · D = ρfree equation of continuity for a free charge density ∇ · Jfree =...

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...