Sphere Definition and 1000 Threads

Homework Statement Within the spherical shell, 3 < r < 4 m, the electric flux density is given as D = 5(r − 3)3 ar C/m2 a) What is the volume charge density at r = 4? b) How much electric flux leaves the sphere r = 4? Homework Equations ρv=Div D Electric flux = ∫sD.ds=∫vρvdvThe Attempt at a...

I was told it might be better to post this here. Homework Statement The trick to this problem is the E field is in cylindrical coordinates. ##E(\vec{r})=Cs^2\hat{s}## Homework Equations ##\int E \cdot dA## The Attempt at a Solution I tried converting the E field into spherical...

Homework Statement The trick to this problem is the E field is in cylindrical coordinates. ##E(\vec{r})=Cs^2\hat{s}##Homework Equations ##\int E \cdot dA##The Attempt at a Solution I tried converting the E field into spherical coords and I can find the flux that way but it is a complicated...

I need to know the Surface Area and Volume of a spherical ball at the origin radius a. What I want is to evaluate the integrals at each integral. ##\oint_S dS =\int\int d? d? = 4 *\pi*r^2## ##\oint_V dV = \int_0^{\pi}\int_0^{2\pi}\int_0^a dr d\theta d\phi## = ##\frac{4}{3}*\pi*a^2##

Refer to "2.jpg", it said that the shortest path on the surface of a sphere is Ay-Bx=z , which is a plane passing through the center of the sphere. I cannot really understand about this. Does it mean that the shortest path is a ring that connects two points with its center at the center of the...

I know that the E-field around a hollow non-conducting sphere charged with Q charge comes immediately from Gauss' Law but I'm wondering what the situation is if we somehow go inside the material, we make a very small hole through the material of the sphere and go inside it. What would there be...

Homework Statement A sphere of mass M and radius R is moving on a rough fixed surface, having co-efficient of friction μ, with a velocity v towards right and angular velocity ω clockwise. It will attain a minimum linear velocity at time (take v>ωR) The Attempt at a Solution Since v>ωR the...

Homework Statement http://i.minus.com/jbxIzu0P7sTqP0.png Homework Equations V(sphere) = 4/3(pi)(r^3) V = 36pi in^3 dr = -0.2 in dV = ? The Attempt at a Solution I basically solved for the radius, and took the derivative and plugged in the value of the radius and the...

So we have a cross sectoin of a sphere that is charged with Q (refer to attachment). electrostatics say the electric field within a charged conductor is 0, and the electric field is perpendicular to the surface. But for a hollow charged sphere (like in the attachment), does the hollow area...

Homework Statement A solid sphere of mass M and radius R is rolling,without slipping, down a curved rail. The sphere is initially at rest at a height of h1. Find the angular velocity ω2 and the center of mass velocity of the sphere vcm at the end of the rail of height h2. You may assume that...

Homework Statement Triple Integral: x^2+y^2+z^2dV over the ball x^2+y^2+z^2 ≤ 9 Homework Equations The Attempt at a Solution so With my integral I had Triple Integral: p^3sin∅dpd∅dθ 0≥p≥3 0≥∅≥∏ 0≥θ≤2∏ Does this look like the correct integral? I swear it is! Yet my answer...

Homework Statement Find the volume above the sphere x^2+y^2+z^2 = 6 and below the parabloid z = 4-x^2-y^2. Homework Equations The Attempt at a Solution I did a triple integral in cylindrical coordinates Triple Integral: dzdrdθ where z is between (6-r^2)^(1/2) to (4-r^2) and dr...

Homework Statement Computer the integral of f(x,y,z) = x^2+y^2 over the sphere S of radius 4 centered at the origin. The Attempt at a Solution so if the parameters for a sphere are in terms of (p,θ,∅) , triple integral (p^2((psin∅cosθ)^2+(psin∅sinθ)^2))dpdθd∅) where the boundaries...

We know,by symmetry,that the center of mass of a uniform sphere is at its center.So we expect the formula r_{com}=\frac{\int r \rho d\tau}{\int \rho d\tau} to give us zero for this case.So let's see: r_{com}=\frac{\int_0^{R} \int_0^{\pi}\int_0^{2\pi} r^3 \sin{\theta} d\phi d\theta...

I have this question on the calculation of the geometric phase (Berry phase) of a parallel transporting vector over the surface of a sphere, illustrated by Prof. Berry for example in the attached file starting on page 2. The vector performing parallel transport is defined as ψ=(e+ie')/√2...

Done editing I hope. Homework Statement If Jf = 0 everywhere, then (as we showed in class), one can express H as the gradient of a scalar potential, W. W satisfies Poisson’s equation with ∇⋅M as the source. Use this fact to find the field inside a uniformly magnetized sphere. (Griffiths has...

If I had a sphere with a radius of 100 meters, a diameter of 200 meters, a volume of 4,188,790.20 square meters, and I wanted to place within this sphere a single dot (one dimensional so it doesn't take up any extra space and there is no displacement --if you're thinking in terms of water--)...

Homework Statement Use the theorem of pappus to find the volume of the given solid A sphere of radius r Homework Equations V = 2∏xA The Attempt at a Solution V = 2∏(4r/3∏)(4∏r^2) = (16/3)∏r^3 So something is wrong I should end up with (4/3)∏r^3 no?

Homework Statement Find the energy stored in a uniformly charged sphere of charge q, radius R Homework Equations The Attempt at a Solution Ein=\frac{qr}{4\pi\epsilon o R^3}, Eout=\frac{q}{4\pi\epsilon o r^2}... W=\int_{0}^ {R}\int_{0}^{2\pi}\int_{0}^{\pi}[\frac{qr}{4\pi\epsilon...

Homework Statement An insulating sphere of radius R , centered at point A, has uniform chagre density ρ. A spherical cavity of radius R / 2 , centered at point C, is then cut out and left empty, see Fig. (a) Find magnitude and direction of the electric field at points A and B. (b) Find...

Homework Statement Consider a charge density of ρ=k/r , k>0 , located between a sphere surface of r=a and another sphere surface of r=b, b>a. I'm supposed to find the electric field on all space, which I did. Now I have to find the electric potential in all space, which I also did for r>b...

Homework Statement A hole of radius r is bored through the center of a sphere of radius R. Find the volume V of the remaining portion of the sphere. Homework Equations The Attempt at a Solution Wouldn't is be (4/3)∏(R^3-r^3)?

Homework Statement A beam of parallel light rays from a laser is incident on a solid transparent sphere of index of refraction n1 (see figure). (a) If a point image is produced at the back of the sphere, what is the index of refraction of the sphere? (b)What index of refraction, if any, will...

Sorry to go on about this scenario again but I think something is going on here. Imagine a stationary charge ##q##, with mass ##m##, at the center of a stationary hollow spherical dielectric shell with radius ##R##, mass ##M## and total charge ##-Q##. I apply a force ##\mathbf{F}## to charge...

Homework Statement (From Physics for Scientists and Engineers, 7E, Serway-Jewett Chapter 25 Q11) (i) A metallic sphere A of radius 1 cm is several centimeters away from a metallic spherical shell B of radius 2 cm. Charge 450 nC is placed on A, with no charge on B or anywhere nearby. Next...

Homework Statement To assemble a uniformly charged sphere, assemble it like a snowball, layer by layer, each time bringing in an infinitesimal charge dq from far away and smearing it uniformly over the surface, thereby increasing the radius. How much work dW does it take to build up the radius...

Homework Statement A small magnetic sphere of initial mass Mo and initial radius Ro is moving through a space filled with iron dust. During its motion, 5% of displaced dust is deposited uniformly onto the surface of sphere. Given the density of dust to be ρ, find: 1. relation rate of increase...

Homework Statement Find the potential inside and outside a uniformly charged solid sphere of radius R and total charge q. Homework Equations V(r) = -∫E dl The Attempt at a Solution I just have a question about finding the potential inside the sphere. Why integrate from infinity...

Homework Statement A solid non-conducting sphere of radius R = 1.12m. The sphere posses a total charge Qtot spread uniformally throughout its volume. a) derive equations for electric field for 1) 0<r<R 2) r>R result in terms of r R and Q b) Derive an equation that gives...

So here we are talking about solving this problem by method of images. The approach taken by most of electrodynamics textbooks is as follows: "If we wish to consider the problem of an insulated conducting sphere with total charge Q in the presence of a point charge q, we can build up the...

~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...

Hi, Assume that one has a pair of metal spheres, A and B, some distance apart. A is connected to, say, a small van der Graaf generator and B is connected to a voltmeter which is then connected to ground. I expect charge to be induced on sphere B. How would one calculate the voltage one...

Most lattices I've come across in condensed matter, like the Kitaev model, are regular lattices and don't fit on a sphere. Are lattice simulations ever put on a sphere in condensed matter, and if so what sort of lattice is used?

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...

Homework Statement Homework Equations The Attempt at a Solution Just checking if this is correct, and if the equation in part c implies that the flow rate out changes with time, or is just based off the initial height..I think it changes and therefore requires this integration. Also, I looked...

Homework Statement I. A non-conducting sphere of radius a has a spherically symmetric, but non-uniform charge distribution is placed on it, given by the volume density function: p(r) = C·r, where C is a positive constant, and 0 < r < a. a. Find an algebraic expression for the total charge...

The mass of a sphere with density as a function of radius is M=4\pi \int_0^r\rho(r) r^2dr Lets say the radius increases and decreases as a function of time t. So: M(t)=4\pi \int_{0}^{r(t)}\rho (r) r(t)^2dr I want to know the basic equation describing the mass added or removed...

An insulating sphere with a radius of (3.3E-2) m has a uniform charge density of (6.74E-6) C/m^3 throughout its volume. (1)Find the magnitude of the electric field at a point (5.7E-2) m from the center of the sphere. (2) Find the magnitude of the electric field at the surface of the...

Homework Statement Standard E field problem where I'm to find the field at 3 positions of a hollow sphere that has a charge density k/r^2 r ≤ a a ≤ r < b b ≤ r Homework Equations ∫Eda=Q/ε The Attempt at a Solution I guess the thing that is tripping me up are the limits. I know...

So I am probably understanding something wrong but would gauss's law \frac{Qinside}{\epsilon0} for a sphere surrounding an electric dipole, with a point charge just outside of the sphere. If you imagine this scenario without the outside charge, the field lines through the surface all come...

Hello, In my electrodynamics course, there's a "maths" introduction and there's something i don't get ! Homework Statement It says that : the integral on the surface of a sphere is ∫1/r da = 4πr'/3 with r=|r'-R|, R the vector from the element da to the center. r'=r'*z^ The Attempt...

Homework Statement Consider a small frictionless puck perched at the top of a fixed sphere of radius R. If the puck is given a tiny nudge so that it begins to slide down, through what vertical height will it descend before it leaves the surface of the sphere? [Hint: Use conservation of...

Homework Statement At a distance of 0.206cm from the center of a charged conducting sphere with radius 0.100cm, the electric field is 485N/C . What is the electric field 0.612cm from the center of the sphere? Homework Equations E(r)=1/4∏ε_0 * qr/R^3 where r is radius of the Gaussian...

Homework Statement Derive the formula for surface area of a sphere using integration of circlesHomework Equations Need to get : S = 4πr2The Attempt at a Solution Consider a sphere of radius r centred on the origin of a 3D space. Let y be an axis thru the origin. The sphere can be sliced into...

A spherical shell and a conducting sphere each of radius R are charged to maximum potential. Which of the two has more charge? My attempt: Since in a conductor, no charge can reside inside the conductor so all charge is on the surface of the conductor just like the spherical shell. Now ...

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...

Homework Statement There is a grounded sphere of radius R in the origin of the coordinate system. In the distance L (L>R) from the sphere’s center there is a point charge Q. The electric field (both intensity and potential) should be computed in the area of radius rg = 5L (in the plane...

Homework Statement First, the problem, quoted verbatim: "Neutrons are created (by a nuclear reaction) inside a hollow sphere of radius R. The newly created neutrons are uniformly distributed over the spherical volume. Assuming that all directions are equally probable (isotropy), what is...

Hi does anybody here know whether there already exists a theory that describe Mie scattering for spheres that have a constant dipole moment?

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...