Charged sphere Definition and 123 Threads

~Electrodynamics~ Potential from charged sphere. I am lost :/ Homework Statement A sphere of radius R, centered at the origin, carries a charge density ρ(r,θ)=κ/r^2(R-2r)sin^2(θ). κ is constant. Find exact potential. Homework Equations 1/4∏ε∫ρ∂t/r The Attempt at a Solution Question and...

Homework Statement An insulating sphere of radius a, centered at the origin, has a uniform volume charge density ρ. A spherical cavity is excised from the inside of the sphere. The cavity has radius a/4 and is centered at position h(vector) , where |h(vector) |<(3/4)a, so that the entire...

When we Earth a positively charged sphere, the positive charge of the sphere vanishes. Why does this happen? When we connect two charged bodies doesn't charge redistribute till we get equipotential surface? Now when there is no charge on the sphere means the sphere has 0 potential. So that means...

I am wondering about why the electric field in a hollow sphere with charges on its surface would be zero. I have thought about the gaussian law argument for it. It only guarantees that the net number of electric field lines that pass the encloved surface are zero. But it says nothing about...

Homework Statement The question asks to find the potential due to a uniformly charged sphere at r<R where R is the radius. Homework Equations Va-Vb= ∫ E dr from a → b The Attempt at a Solution My attempt was like this Va is to be a the point of interest r.. Vb to be R... We...

My book gives the electric potential of a uniformly charged sphere as \frac{1}{4\pi \epsilon_0}\frac{Qr^2}{r_0^3}. I can't derive this forumula. What I get is \frac{1}{8\pi \epsilon_0}\frac{Qr^2}{r_0^3}. I can guess how the book did it which is by taking the equation for voltage of a single...

Homework Statement In the section on the discontinuity of the electric field (Griffiths introduction to electrodynamics) there is the following. "Where there is no surface charge, the perpendicular component of the electric field (to the surface) is continuous, as for instance at the...

Gauss' Law has been fairly tough for me and I seem to be struggling to analyze situations properly and, specifically, decided on the net charge included in arbitrary symmetrical-shapes used for this law. Specifically, this one includes two spherical shells. Homework Statement A point charge q1...

Charged Sphere with a Hole -- Check my work? Homework Statement You have a spherical shell of radius a and charge Q. Your sphere is uniformly charged except for the region where θ<= 1° (which has σ = 0). Imagine that your field point is somewhere on the positive z-axis (so z could be...

Imagine an electron of mass m_e inside a hollow dielectric sphere. Assume that the electron is traveling with constant velocity v relative to the sphere. The momentum of the system p comprises just the momentum of the electron p = m_e v There is also a circulating magnetic field B...

What would be the pattern of electric field lines 'inside' a solid charged sphere..?

Hi guys, this is more of a conceptual question, so I hope you guys can give me a detailed explanation if possible. Homework Statement Find the Electric Field inside a Charged Sphere (charge only on the surface) and between two Parallel Plates (oppositely charged) separated by some distance d...

[b]1. A solid sphere of radius a = 12.8 cm is concentric with a spherical conducting shell of inner radius b = 37.1 cm and outer radius c = 39.1 cm. The sphere has a net uniform charge q1 = 9.00×10-6 C. The shell has a net charge q2 = -q1. Find expressions for the electric field, as a function...

I wanted to know how to find the electric potential inside a uniformly charged sphere of radius R. What i understand is that my textbook uses a reference point as infinity and then expresses the potential as the difference of 2 integrals. Sooo, V(r)= -∫E dr and the electric field is...

Homework Statement A point charge q1 = -9.7 μC is located at the center of a thick conducting shell of inner radius a = 2.3 cm and outer radius b = 4.5 cm, The conducting shell has a net charge of q2 = 1.4 μC. 1) What is Ex(P), the value of the x-component of the electric field at...

Homework Statement What are the strength and direction of an electric field that will balance the weight of a 1.0g plastic sphere that has been charged t0 -3nC ? Homework Equations E= F/q The Attempt at a Solution Newton's laws on the charged sphere ƩFnet(y) = F -mg=0...

Homework Statement Suppose a strength that acts between two charges depends on the distance, 1/r^a, where 1) a>2 2)a<2 What will happen with a punctual charge, if it is put within a uniformly charged sphere. At the initial moment the punctual charge is in rest. Homework Equations F...

A metallic sphere of radius R is cut in two parts along a plane whose minimum distance from the sphere's centre is h and the sphere is uniformly charged by a total electric charge Q. What minimum force is necessary to hold the two parts of the sphere together? The Real trivia The solution...

Let's say I have a sheet of charge that is composed of a certain amount of charged atoms summing up to Q and a certain area A. The charge density would be Q/A = σ. I wish to find the elctrostatic potential from the sheet at point X. I believe that the electric potential should follow the...

Homework Statement An electron starts from rest 2.80 cm from the center of a uniformly charged sphere of radius 1.83 cm. If the sphere carries a total charge of 1.01×10-9 C, how fast will the electron be moving when it reaches the surface of the sphere? Homework Equations UI + KI =...

Hey, I have a series of questions on a basic charged sphere and deriving quantities such as the infinitesimal charge, the total charge and the electric field. The question is part (b) in the image below: So I found dQ' by equating it to the surface area of a shell at a distance r'...

Homework Statement The outer conductor (radius b, length l) of a long cylindrical capacitor is earthed. The inner conductor (radius a, length l) is hollow, insulated and uncharged. A sphere of radius R is charged to a potential V far from any other bodies and is inserted inside the inner...

Homework Statement The sphere has a radius a and is filled with a charge of uniform. They way I am asked to do this is by building the sphere up layer by layer. And I know that the field outside the sphere is the same as if it were a point charge. Homework Equations U = ε/2∫E^2 dv The...

Homework Statement Consider a sphere uniformly charged over volume, apart from a spherical off-center cavity. The charge density is ρ, radius of the sphere is a, radius of the cavity is b, and the distance between the centers is d, d < a-b. (a) Find the total charge and the dipole moment...

Homework Statement Consider a sphere uniformly charged over volume, apart from a spherical off-center cavity. The charge density is ρ, radius of the sphere is a, radius of the cavity is b, and the distance between the centers is d, d < a-b. (a) Find the total charge and the dipole moment...

hi i know that the energy of a conducting charged sphere is E=Q²/(8epsilon_0*pi*r) and i know how to calculate this. now i found that a homogenously charged sphere has E=3/5*Q^2/(epsilon_0*pi*r). does anybody have an idea how to calculate this? i don't know where this 3/5 come from?

Homework Statement If you have a uniformly-charged negative hollow sphere of charge, with a positive circular piece of charged shell superimposed on the outside, what is the electric field in the center of the circular piece? Also what part of the field going through the piece's center is...

An insulating solid sphere of radius a = 1.2 m is uniformly charged with charge Q = 4.5 x 10^-6 C. Point P inside the sphere is at a distance r = 0.60 m from the sphere center C. What is the magnitude of the electric field at point P? So I'm using Gauss' Law: q,enc = Q[(pi * r^2)/ (pi *...

Not much more to add to the title. I was just wondering, under what conditions can a charged sphere be treated as a point charge?

If a conducting sphere has a negative net charge and there is a positive point charge at the center of the sphere, what charge would you use to find the Electric Field at a point outside the sphere? The equation is E=kq/r^2. Would I use the net charge of the sphere, or do I need to...

Homework Statement A point charge q1 = -7 μC is located at the center of a thick conducting shell of inner radius a = 2.6 cm and outer radius b = 4.9 cm, The conducting shell has a net charge of q2 = 1.1 μC. What is Ex(P), the value of the x-component of the electric field at point P...

Hi I'm sorry if this is posted in the wrong section or it's laid out wrong but I have a question that I need a bit of help with. Homework Statement I'm given: A spherically symmetrical charge distribution is contained within a sphere of radius a with no charge outside. At a distance r (r...

Homework Statement Two identical metal spheres, each with a positive charge q, are separated by a centre-to-centre distance r. What effect will the following change have on the magnitude of the electric force exerted on each sphere by the other: -one sphere is touched by an identical...

Homework Statement In the case of charged conducting sphere, we find that the charge entirely resides on the surface because it always tries to cancel the field inside by moving to the surface. But in the case of a uniformly charged conducting sphere, we find that the charge is uniformly...

Homework Statement A sphere of radius a with a total charge q uniformly distributed on the surface and the sphere spins with an angular velocity w Find the electric dipole moment of the sphere/electric field outside the sphere/magnetic dipole moment of the sphere/magnetic induction outside the...

Homework Statement A non-uniformly charged sphere of radius R has a charge density p = p_o(r/R) where p_o is constant and r is the distrance from the center of the spere. a) find the total charge inside the sphere b) find the electric field everywhere (inside & outside sphere) c) find...

Imagine a sphere such that positive charge is evenly distributed throughout one hemisphere (not just on the surface) and equal negative charge is evenly distributed throughout the other hemisphere. Is there a simple or elegant way to map out the magnetic field inside/outside the sphere and...

A uniformly charged sphere (center 0,0) with radius 2a and volume charge density \sigma has a cavity within it (center 0,a) with radius a. Show that the electric field within the cavity is uniform and Ex=0 Ey=\frac{a\sigma}{3\epsilon} where \epsilon is the permittivity of free space. Hi, I...

Homework Statement I'm supposed to find the net force that the southern hemisphere of a uniformly charged sphere exerts on the northern hemisphere. I must express my answer in terms of the radius R and the total charge Q. Homework Equations F = QE \int E da = \frac{1}{\epsilon_{0}}Q The...

I can understand why the electric field inside a charged sphere is zero when there's electrostatic equilibrium. I can understand why the electric field outside a charged sphere equals kq/r². But I remember reading somewhere that the electric field AT the surface of a charged sphere equals...

QUESTION: Calculate the electrostatic energy of a homogeneously charged sphere of Volume V and compare the result with 2 times the electrostatic energy of a homogeneously charged sphere of V/2. SOLUTION: OK, so we have a charge Q which is uniformly distributed within a sphere of...

Homework Statement A sphere of radius 'a' contains a charge Q, uniformly distributed throughout it's volume. Calculate the total potential energy of this configuration. Homework Equations U=\frac{1}{2}\int \rho V d\tau with \rho=charge density and V=potential The Attempt at a...

Homework Statement Well, there are two problems, both of which would allow me to receive extra credit in my college physics class! Both are rather descriptive, so I have linked an image to it. http://img87.imageshack.us/img87/9570/1000497y.jpg" Homework Equations For the first, I was...

Homework Statement A nonconducting sphere has radius R = 2.70 cm and uniformly distributed charge q = +7.00 fC. Take the electric potential at the sphere's center to be V0 = 0. (a) What is V at radial distance r = 1.45 cm? (b) What is V at radial distance r = R? Homework Equations E...

Hi everybody... this is my first topic here. I'm solving problems for the phd test here in my university. Here's my question: I have to calculate the energy of charging a sphere (radius = R) with a uniform charge density "rho". I can use 2 formulas: the first is the integral over...

The electric field inside a hollow, uniformly charged sphere is zero. Does this imply that the potential is zero inside the sphere? Explain.

Homework Statement Show that the mean-square charge radius of a uniformly charged sphere (with radius R) is < r^2 > = 3*R^2 / 5 Homework Equations < r^2 > = \int \varphif* r^2 \varphii dV \varphif* = exp(-i q dot r) \varphii = exp(i q dot r) where q = kf - ki...

A general problem you run into during an E&M class is the one involving a point charge a distance from a charged sphere. In cases where the point is far enough away from the sphere, the system can be treated like two points. In my case I have a point charge "q" a distance "z" away from the...

Say you have a -vely charged sphere, you bring it close to a neutral sphere. Now the neutral sphere becomes +vely charged. What happens if you touch the 2 spheres (sphere 1 touches sphere 2)? Do the charges get recombined, with net charge=0?

1. The problem statement, all variables and given known data & Homework Equations & The Attempt at a Solution the charge density on a sphere readius a is \rho = \rho_{0} ( 1 - \frac{r^{2}}{a^{2}} ) intergrating this in spherical polar co-ords gives me: Q = \frac{8 \pi \rho_{0} a^{3}}{15}...