Spherical Definition and 1000 Threads

Homework Statement The problem is to calculate the volume of the region contained within a sphere and outside a cone in spherical coordinates. Sphere: x2+y2+z2=16 Cone: z=4-√(x2+y2) Homework Equations I am having difficulty converting the equation of the cone into spherical coordinates...

There is a very heated debate in a forum for airsoft that I frequent. It is about what happens to ba bb pellet when it is fired from a bb gun. Two point of contention have formed. 1. A unbalanced bb, who's geometric center is disparate from it's center of mass will wobble, or oscillate on the...

Homework Statement Homework Equations All above. The Attempt at a Solution Tried the first few, couldn't get them to work. Any ideas, hopefully for each step?

Homework Statement Use spherical coordinates. Evaluate\int\int\int_{E}(x^{2}+y^{2}) dV where E lies between the spheres x2 + y2 + z2 = 9 and x2 + y2 + z2 = 25. The attempt at a solution I think my problem may be with my boundaries. From the given equations, I work them out to be...

Hello! I seem to have a problem with spherical coordinates (they don't like me sadly) and I will try to explain it here. I need to calculate a scalar product of two vectors \vec{x},\vec{y} from real 3d Euclidean space. If we make the standard coordinate change to spherical coordinates we can...

Correct me if I'm wrong about anything. I've browsed here many times, but this is my first post. I was thinking about Prince Rupert's Drop (http://en.wikipedia.org/wiki/Prince_Rupert's_Drop) and I wondered about spherical magnets. Prince Rupert's Drop is able to withstand high magnitudes of...

$$ Y_{\ell}^m = \sqrt{\frac{(2\ell + 1)(\ell - m)!}{4\pi(\ell + m)!}}P^m_{\ell}(\cos\theta)e^{im\varphi} $$ For ##\ell = m = 1##, we have $$ \sqrt{\frac{(2 + 1)(0)!}{4\pi(2)!}}P^1_{1}(\cos\theta)e^{i\varphi} = \frac{1}{2}\sqrt{\frac{3}{2\pi}}e^{i\varphi}\sin \theta $$ But Mathematica...

Homework Statement Determine the electrostatic energy, W, of a spherical shell of radius R with total charge q, uniformly distributed. Compute it with the following methods: a) Calculate the potential V in spherical shell and calculate the energy with the equation: W = (1/2) * ∫σVda...

$$ Y_{\ell}^m = \sqrt{\frac{(2\ell + 1)(\ell - m)!}{4\pi(\ell + m)!}}P^m_{\ell}(\cos\theta)e^{im\varphi} $$ For $\ell = m = 1$, we have $$ \sqrt{\frac{(2 + 1)(0)!}{4\pi(2)!}}P^1_{1}(\cos\theta)e^{i\varphi} = \frac{1}{2}\sqrt{\frac{3}{2\pi}}e^{i\varphi}\sin \theta $$ But Mathematica is telling...

Consider Laplace's equation on a sphere of unit radius with the boundary condition $$ u(1,\theta,\varphi) = f(\theta,\varphi)\begin{cases} 100 & -\pi/4 < \varphi < \pi/4\\ 0 & \text{otherwise} \end{cases} $$ Here we will consider a three-term approximation to the solution, i.e., involving the...

Laplace axisymmetric $u(a,\theta) = f(\theta)$ and $u(b,\theta) = 0$ where $a<\theta<b$. The general soln is $$ u(r,\theta) = \sum_{n=0}^{\infty}A_n r^n P_n(\cos\theta) + B_n\frac{1}{r^{n+1}}P_n(\cos\theta) $$ I am supposed to obtain $$ u(r,\theta) = \sum_{n =...

Homework Statement A ground spherical conductor of radius a lies at the center of a uniform spherical sheet of charge QB and radius b. a) How much charge is induce on the conductor's surface? Ans(-QBa/b) Evaluate V(r) at position between the conductor and the sheet and outside the sheet...

Homework Statement A total charge q is uniformly distributed throughout a sphere of radius a. Find the electric potential in the region where r1<a and r2>a. The potential is defined anywhere inside the sphere. Homework Equations letting ρ = volume charge density and ε = permittivity...

Is there somebody who can help me how to solve this integral \int_{0}^{+\infty} dr r^{^{n+1}} e^{-\alpha r} j_l(kr)

Homework Statement Determine the value of \int_{0}^{1} \int_{0}^{\sqrt{1-x^2}} \int_{0}^{\sqrt{1-x^2-y^2}} \sqrt{x^2+ y^2 + z^2} dz dy dx The Attempt at a Solution So in spherical polars, the integrand is simply ρ. \sqrt{1- x^2- y^2} = z = ρ\cos\phi = \cos\phi since we are on the unit...

If I have a +5 nC charge on the inside of the shell, the inside surface would be -5nC, the outside would be +5 nC and between those surfaces there would a 0 charge, right? So just to make sure I have it all straight, the INSIDE of the shell would actually be 0 because the INNER SURFACE is -5...

1. Homework Statement A nonconducting spherical shell of inner radius R1 and outer radius R2 contains a uniform volume charge density ρ throughout the shell. Use Gauss's law to derive an equation for the magnitude of the electric field at the following radial distances r from the center of...

Homework Statement A nonconducting spherical shell of inner radius R1 and outer radius R2 contains a uniform volume charge density ρ throughout the shell. Use Gauss's law to derive an equation for the magnitude of the electric field at the following radial distances r from the center of the...

Homework Statement A person starts from rest at the top of a large, frictionless, spherical surface, and slides into the water below. At what angle θ does the person leave the surface? (Hint: When the person leaves the surface, the normal force is zero.) Homework Equations Don't Know...

Homework Statement An electron in a hydrogen atom is in a state described by the wave function: ψ(r,θ,φ)=R(r)[cos(θ)+eiφ(1+cos(θ))] What is the probability that measurement of L2 will give 6ℏ2 and measurement of Lz will give ℏ? Homework Equations The spherical harmonics The...

Homework Statement Calculate the area of a circle of radius r (distance from center to circumference) in the two-dimensional geometry that is the surface of a sphere of radius a. Show that this reduces to πr2 when r << a Homework Equations Surface area of a spherical cap = 2πah = π(r2 +...

Homework Statement A spherical charged ball of radius a has total charge Q; there is no charge outside the ball and no sheet-charge on its surface. The (radial) field inside the ball has the form Er(r) = constant x r2 for r between 0 and a. Use Gauss's Law in integral form to evaluate the...

Homework Statement A spherical capacitor contains a charge of 3.10nC when connected to a potential difference of 220V . If its plates are separated by vacuum and the inner radius of the outer shell is 5.00cm . Part A) Calculate the capacitance. Homework Equations C = Q/V C = Aε0/d...

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...

Hi, I am looking to use the definition from WGS84 to calculate Earth's gravitational potential using spherical harmonics, however I am having some difficulty finding the definition of one of the variables. Gravitational potential is given as the following: V = \frac{GM}{r}\left [ 1 +...

Homework Statement (1)A conducting sphere w/ charge +Q is surrounded by a spherical conducting shell. What is net charge on inner surface of the shell? (2) A charge is placed outside the shell. What is the net charge on the inner surface now? (3) What if the shell and sphere are not...

I have a problem; I am trying to show the spherical symmetry in a hydrogen atom, for a sum over the l=1 shell i.e the sum over the quadratics over three angular wave equations in l=1, |Y10|^2 + |Y11|^2 + |Y1-1.|^2 . This should equal up to a constant or a zero to yield no angular dependence...

Homework Statement The total energy may be given by the hamiltonian in terms of the coordinates and linear momenta in Cartesian coordinates (that is, the kinetic energy term is split into the familiar pi2/2m. When transformed to spherical coordinates, however, two terms are angular momentum...

A text I am reading displays the attached image. Can someone explain the general method for obtaining the velocity analogues of those terms (in parentheses) in 1.5? I know the second and third terms in parentheses in 1.6 and 1.7 are the squares of angular velocities, but can a general procedure...

Homework Statement A small charged ball lies within the hollow of a metallic spherical shell of radius R. Here, for three situations, are the net charges on the ball and shell, respectively: 1 +4q, 0 2 -6q, +10q 3 +16q, -12q (a) Rank the situations according to the charge on the...

Hey Guys, Does anyone know where I can find a derivation of the laplace operator in spherical and cylidrical coordinates?

Homework Statement Convert the following as indicated: 1. r = 3, θ = -π/6, φ = -1 to cylindrical 2. r = 3, θ = -π/6, φ = -1 to cartesian The Attempt at a Solution I just want to check if my answers are correct. 1. (2.52, -π/6, 1.62) 2. (-2.18, -1.26, 1.62)

Translate the rectangular equation to spherical and cylindrical equations. http://www.texify.com/img/%5CLARGE%5C%21x%5E2%2By%5E2%2B2y-3x%2Bz%5E2%3D25.gif

Homework Statement Show that the vector fields A = ar(sin2θ)/r2+2aθ(sinθ)/r2 and B = rcosθar+raθ are everywhere parallel to each other. Homework Equations \mathbf{A} \cdot \mathbf{B} = |\mathbf{A}||\mathbf{B}|\cos(0) The Attempt at a Solution So, if the dot product equals 1. They should be...

Q1: What is the percent uncertainty in the volume of a spherical beach ball whose radius is r = 3.85 plus or minus 0.06 m? I found the volume of the original sphere, as well as one with a radius of 3.91. I then subtracted the volumes to find the difference between the two, divided that by the...

Homework Statement Evaluate \iiint\limits_B e^{x^2 + y^2 + z ^2}dV where B is the unit ball. Homework Equations See above. The Attempt at a Solution Does this evaluate the volume of f(x, y, z) within the unit ball (i.e. anything falling outside the unit ball is discarded)...

Homework Statement I'm trying to express spherical coordinates in terms of cylindrical and vice versa. I would appreciate it if someone could give me some feedback on my attempt at a solution. Thanks for the help! The Attempt at a Solution Spherical(cylindrical) r=(ρ^2+z^2)^(1/2)...

Homework Statement For a charged solid metal sphere with total charge Q and radius R centered on the origin: Select "True" or "False" for each statement: 1.If the solid sphere is an insulator (instead of metal) with net charge Q, the net charge on the inside of the solid sphere is...

Homework Statement By making two successive simple changes of variables, evaluate: I =\int\int\int x^{2} dxdydz inside the volume of the ellipsoid: \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}+\frac{z^{2}}{c^{2}}=R^{2} Homework Equations dxdydz=r^2 Sin(phi) dphi dtheta dr The...

Homework Statement An insulated spherical conductor of radius R1 carries a charge Q. A second conducting sphere of radius R2 and initially uncharged is then connected to the first by a long conducting wire. (a) After the connection, what can you say about the electric potential of each...

This isn't exactly homework, but I'm still in high-school and I feel guilty posting in the big guys' forums. I've recently learned about the shapes of spdf orbitals and the way they interact to form different bonds. This is completely different to the nice spherical atoms we were shown back...

A sphere of radius a in free space is nonuniformly charged over its surface such that the charge density is given by ρs(θ) = ρs0 sin 2θ, where ρs0 is a constant and 0≤θ≤∏. Compute the total charge of the sphere. So I know ρs = dQ/dS Integrating the surface charge density function will...

When i think of electromagnetic waves i think of a fast moving sphere of expanding or contracting fields,either magnetic or electrical depending on where its at in its cycle. So i guess I am picturing a single photon as a sphere. Is this a correct visualization?(i doubt it). If so, how does a...

I read this Scientific American link and I found it very interesting. I have a problem understanding it, though, because I had read that one of the explanations for the existence of Solar Systems is based on Angular Momentum. The argument goes that if all the mass were concentrated in the host...

Fluid flows with velocity 2i - 3j m/s at point P having coordinates (1,2,4). Consider a plane through P which is normal to the vector b=-i+2k. What is the speed at which the fluid passes through the plane? Should I do the dot product of the position vector P=[1,2,4] and b vector, then...

In deriving the Schwarzschild metric, the first assumption is that the transformation of r^2 (dθ^2 + sin^2 θ dψ) remains unchanged due to the spherical symmetry. What does that mean exactly? What is the logic behind it? Please apply any math involved in algebraic form. Thanks.

Hello Folks, I have this equation to solve (expressed in LaTeX): \frac{\partial{h}}{\partial t} = \frac{1}{n} \left[ \frac{1}{r^2 \sin^2{\phi}} \frac{\partial}{\partial \theta} \left( K \frac{\partial h}{\partial \theta} \right) + \frac{1}{r^2 \sin \phi} \frac{\partial}{\partial \phi}...

Homework Statement three concnetric conducting spherical shells are there with charges +4Q on innermost shell,-2Q on middle shell and -5Q on outermost shell. what is the charge distribution and charge on inner side of outermost shell? Homework Equations The Attempt at a Solution...

Homework Statement Find the volume enclosed by the spherical coordinate surface ρ = 2sin∅ Homework Equations dV = ∫∫∫(ρ^2)sin∅dρd∅dθ The Attempt at a Solution (Sorry about my notation!) Alright, here's what I've done so far... Since the region is a torus, centered...

Hi, There are, for example, lists of spherical tensor operators for l=\text{integer} steps, e.g. l=0,1,2,.... T_{k}^{q}(J)\rightarrow T_{0}^{0}=1, \quad T_{1}^{\pm 1}=\mp \sqrt{\frac{1}{2}}J_{\pm},\quad T_{1}^0=J_z and this continues forever. I was wondering if there are operators...