Charge distribution Definition and 236 Threads

Homework Statement [/B] Volume charge density in some space is given by a function ##ρ_v(x)=-ρ_0\frac{x}{a}e^{\frac{-x^2}{a^2}}## where ##ρ_0, a## are positive constants. Determine the electric field vector in arbitrarily chosen point in space. Homework Equations 3. The Attempt at a Solution...

Homework Statement Hi everybody! I'm very stuck trying to solve this problem, hopefully some of you can give me a clue about in which direction I should go: Determine the multipole expansion in two dimensions of the potential of a localized charge distribution ##\lambda(\vec{x})## until the...

This is my first time using this site so please excuse me if I missed any guidelines. 1. Homework Statement A plastic rod having a uniformly distributed charge Q=-25.6pC has been bent into a circular arc of radius R=3.71cm and central angle ∅=120°. With V=0 at infinity, what is the electric...

Homework Statement Consider the charge distribution of a uniformly charged ring of radius ##R## and charge ##Q## at a distance ##d## above the origin and a uniformly charged ring of radius ##R## and charge ##-Q## at a distance ##d## below the origin. (a) Calculate the dipole moment of this...

Homework Statement Homework Equations There are no equations here, only theoretical knowledge The Attempt at a Solution Hi, My approach was this: I know that with the positive charge on the sphere being lowered into the cup I will have the inner area of the cup have a negative charge and...

Homework Statement This is more of a general question, but a simple example would be find the force on a test charge q at the center of a ring of charge with a total charge Q and a charge distribution given as λ(θ) =ksin(θ) where θ is measured clockwise with respect to the positive x-axis. The...

This is a question that is vaguely related to coursework but is more for curiosity. Lets say there are two spheres joined by a thin wire in the presence of an electric field: Assume the conductors initially have no charge. Now I am pretty sure without the wire, the charge distribution would...

Homework Statement Consider a long, cylindrical charge distribution of radius R with uniform charge density ρ. a) Using Gauss’s law, find the electric field at distance r from the axis, where r < R b) Using Gauss’s law, find the electric field at distance r from the axis, where r > R...

Hi everyone, I am self-studying Electricity and Magnetism. I have a good grasp in Calculus, but still I am confused on how to figure out volumes of arbitrary figures(rest is easy). I know it's a bit silly. I mean how do we know how to choose a figure (like in case of hemisphere, you imagine...

Hi everyone, I am self-studying Electricity and Magnetism. I have a good grasp in Calculus, but still I am confused on how to figure out volumes of arbitrary figures(rest is easy). I know it's a bit silly. I mean how do we know how to choose a figure (like in case of hemisphere, you imagine...

Homework Statement Using direct integration, compute the electric field at the point (0,0,Z) of a semi-espherical (z > 0) charge distribution of radius R < Z and density ##\rho=constant## having a spherical hole of radius ##r_h<R## centered at (0,0,##r_h##). Homework Equations Coulomb's law...

Homework Statement A charge distribution has uniform density in the x-y directions and varies with z according to: ρ(z) = ρ0e−|z|/t where ρ0 and t are constants. (a) Find the potential V (z) and the electric field E(z) (b) Sketch them clearly showing their behaviors in the regions |z| ≪ t...

Hello. I have a problem calculating the electric field from spherical charge distribution. The exercise is: 1. Homework Statement Homework Equations To solve the problem for $$ 0\le R < a$$ i tried 2 ways: $$ \vec{E} = \frac{\vec{a_R}}{4\pi\epsilon_0}\int_v\frac{1} {R^2}\rho dv $$ and the...

I have two metal half-spheres, each with a hole in the center. If I put these two together, perhaps with electrical tape, and apply a charge, how will the voltage due to the nonuniform charge distribution be different from that of a perfect sphere? I am assuming that the charge distribution...

I don't understand charge distribution properly. Here is what I found somewhere Figure (1)shows three concentric thin spherical shells A,B and C of radii a,b and c respectively.The shells A and C are given charges q and -q respectively and the shell B is earthed.Find the charge appearing on the...

Problem: Consider two parallel and large sheets with a surface area . One has a charge and the other is uncharged. q | | | | | | | | | | What would be the electric fields on the three regions as divided by the sheets ? General solution to problems like as told...

Homework Statement A triangle is given with the points: Q1 = +2.0 x 10-5 C 2.0 m from Q3 = -3.0 x 10-5 C AND Q1 = +2.0 x 10-5 C 2.0 m from Q2 = -3.0 x 10-5 CThe triangle is a right triangle, with Q1 at the 90 degree angle.FIND THE NET FORCE OF CHARGE 1Homework Equations [/B] FE21 = FE31...

Homework Statement A nonconducting sphere 1.3 m in diameter with its center on the x axis at x = 4 m carries a uniform volume charge of density ρ = 4.8 µC/m3. Surrounding the sphere is a spherical shell with a diameter of 2.6 m and a uniform surface charge density σ = -1.2 µC/m2. Calculate the...

Homework Statement Essentially it gives the potential above the xy-plane as and I am tasked with verifying it satisfies laplace's equation, determining the electric field, and describing the charge distribution on the plane. Homework Equations then The Attempt at a Solution As far as I...

Homework Statement The Earth is constantly being bombarded by cosmic rays, which consist mostly of protons. Assume that these protons are incident on the Earth’s atmosphere from all directions at a rate of 1366. protons per square meter per second. Assuming that the depth of Earth’s atmosphere...

Homework Statement Hi, I am stuck with this homework. I have been asked to make an equation out of a diagram for V(z) using V=kQ/r equation, where z is a positive axis centred with four negative charges. Here is the diagram. 2. Relevant equation E=F/q F of point charge: F=kQq/r^2 E=kQ/r^2...

Homework Statement Can we consider the universe to have a uniformly charged distribution? If so, shouldn't the field at any point in space be zero? Since the universe is infinite, will it be symmetrical about any point, field should be zero right? Why is this not true?[/B]2. The attempt at a...

Homework Statement An infinitely long cylinder of radius R is placed above an infinite grounded plane. The centre of the cylinder is a distance (d) above the plane, and the cylinder has a surface charge density of σ. (a) Initially ignoring the grounded plane, what is the electric field due to...

Homework Statement A ring of radius R has a current density ##\vec J=J(r, \theta) \sin \phi \hat \phi## where phi is the azimuthal angle in spherical coordinates. Calculate the charge distribution considering that it was initially null. Homework Equations Not sure. Maybe ##\nabla \cdot \vec J...

Homework Statement A sphere of radius R has a volume charge distribution ##\rho(r)## given by: ##\rho(r)= \rho_0 \left( \frac{r}{R_0} \right) \ \ for \ 0 <r<R## ##\rho(r)=0 \ \ elsewhere## Where ##\rho_0## is a constant. Use Gauss's law to find E field outside the sphere. Homework Equations...

http://www.colorado.edu/physics/phys3320/phys3320_sp12/AJPPapers/AJP_E&MPapers_030612/Griffiths_ConductingNeedle.pdf I was reading this paper, and was confused by a result in section 2-A. (Heck they even mention they weren't expecting it themselves). The purpose of the paper is to find the...

I recently read that the charge density is less on surfaces with greater radius of curvature on the surface of a charged irregular conducting body . if anyone can provide a proof or explanation , please help!

Homework Statement If charged is place on a spherical conductor, it distributes uniformly. If charged is placed on a conical conductor, it does not spread uniformly. Homework Equations Remember that, in a conductor, the motion of electrons is fluid. The Attempt at a Solution Taking the given...

Imagine an uncharged solid spherical conductor. Inside this spherical conductor, there is a cavity of a weird shape carved out of it. And somewhere inside this cavity, there is a charge +q (or rather, a charge distribution of total charge +q). The charge +q induces an opposite charge -q on the...

Homework Statement http://imgur.com/EiCFIDe Homework Equations E = kq/r2 λ = dq/dx Q = λa The Attempt at a Solution Here is the book solution: http://imgur.com/aKSeKo0 I need help with part (a). I understand everything in the solution except for the distance they used for between (r2 in...

Homework Statement If you have a ring of charge, is it valid to say lambda = Q/L, or is it lambda = dQ/dL? Homework EquationsThe Attempt at a Solution

dE = ke(dq/r2) How to change to complicated equation in the following picture?

I'm trying to understand how a diode works and for this I've used(among other resources) the book written by Albert Malvino, Electronic Principles. Everywhere I read about this topic, it says that when the N-type and P-type semiconductors are joined together, the free electrons from the N-type...

A negative charge cloud distribute as a ellipsoid and a positive point charge situated at the centre of the ellipsoid.What should be the dipole moment of charge distribution.I mean, if the negative charge distribution is spherical and positive point charge at the centre then surely dipole moment...

Homework Statement A cylindrical distribution of charge ρ = α/sqrt(r) where α = 2 µC/m^(5/2) extends from 0 cm to 9.3 cm (has radius 9.3 cm). Concentric with this is a dielectric shell with k = 5.44 of inner radius 16.6 cm and outer radius 24.9 cm. What is the electric field at 3.53 cm, 12.6...

I have a question regarding electric potential and infinity. So, "A square of side length a with uniformly distributed positive charge lies on the yz plane with its center at the origin. What does the graph of the potential along the x-axis look like? The answer given in the textbook is a...

Homework Statement All charges in space are distributed on the xy-plane. The potential above the plane is known as \phi = \phi_0 exp(-kz) cos(kx) What's the charge distribution on xy-plane? Homework Equations \vec E =- grad(\phi) The Attempt at a Solution Applying the relationship between...

Homework Statement A thin line of charge is on the x-axis from x = -L/2 to L/2. The charge density is non uniform and given by λ = ax where x are the points on the charge distribution. Calculate the electric field for all points along the y axis. Homework Equations E = kQ/r^2 The Attempt at...

In the figure given the capacitance for the two pair would be same. Can anybody please explain me how the charge would be distributed across each plate? I think that the middle plate being isolated should have +Q on one side and -Q on other, but how would be the charge distribution about the...

Homework Statement A Non-Uniform but spherically symmetric charge distribution has a charge density: \rho(r)=\rho_0(1-\frac{r}{R}) for r\le R \rho(r)=0 for r > R where \rho = \frac{3Q}{\pi R^3} is a positive constant Show that the total charge contained in this charge distribution is...

If the electric field and boundary conditions are known exactly for a region of space, is it true that there exists only one charge distribution in that region of space that could have produced it? My understanding of the uniqueness theorem in electrostatics is that for a given charge...

Homework Statement Question Homework Equations Equation The Attempt at a Solution Attempt I am not sure how to write the |r-r'| in a way that allows me to actually solve the integral. I have tried writing |r-r'| in spherical co ords, but all I seem to be able to get is this as the separation...

Homework Statement A spherical charge distribution is given by p = p_0 (1- \frac{r^2}{a^2}), r\leq a and p = 0, r \gt a , where a is the radius of the sphere. Find the electric field intensity inside the charge distribution. Well I thought I found the answer until I looked at the back of...

Homework Statement Hi all - I have been trying to evaluate part II of this problem for a long time now... For a simplified model of a proton's charge distribution, Find the constant of proportionality required to normalise ρ correctly. Show that Homework Equations N/A The Attempt at a...

Homework Statement Two test charges are located in the x–y plane. If q1 = -3.50 nC and is located at x = 0.00 m, y = 0.680 m and the second test charge has magnitude of q2 = 3.60 nC and is located at x = 1.00 m, y = 0.650 m, calculate the x and y components, Ex and Ey, of the electric field, ...

I'm going over the Physics GRE and this question has me a little confused. The configuration of the potassium atom in its ground state is 1s2 2s2 2p6 3s2 3p6 4s1. The answer to which of the following is true is this statement: "Its electron charge distribution is spherically symmetrical." Is...

Homework Statement Here is the question, which itself is rather confusing. A nonuniform surface charge lies in the yz plane. At the origin, the surface charge den- sity is 3.5 μC/m^2. Other charged objects are present as well. Just to the right of the origin, the electric field has only an x...

How does the texture of a surface affect the concentration of charge on that surface? Say we compare a balloon (smooth) and a football (textured) (ignoring material differences) and give them the same total charge. Then we introduce dust particles. How do the two surfaces attract dust...

Homework Statement A solid conducting sphere of radius 2.00 cm has a charge 16.00 µC. A conducting spherical shell of inner radius 4.00 cm and outer radius 5.00 cm is concentric with the solid sphere and has a total charge of -3.00 µC. (Take radially outward as the positive direction.) Find...

Homework Statement Basically, I'm told that two insulated metal spheres, one positively charge (+20uc, sphere A) and one negatively charged (-10 uc, sphere B) come into direct contact (so obviously conduction is the method of charge), and that sphere A's radius is twice the size of sphere...