Spherical Definition and 1000 Threads

Homework Statement "The shortest path between two point on a curved surface, such as the surface of a sphere is called a geodesic. To find a geodesic, one has to first set up an integral that gives the length of a path on the surface in question. This will always be similar to the integral...

Homework Statement Consider a uniformly charged sphere (an insulating sphere of radius R,) and a spherical Gaussian surface with radius R/2 concentric to the sphere. What is the total flux flowing through the Gaussian surface? Homework Equations Vsphere= (4∏R^3)/3 Asphere= 4∏R^2 Gauss' Law...

I am studying capacitors in an electromagnetism course and I am having trouble understanding/deriving the equation for voltage. We have a spherical capacitor with a positive charge on the surface on the center conductor (sphere radius R1), and negative charge on the outer conductor (sphere...

I'm not sure that I understand the vectors \hat{r}, \hat{\theta}, and \hat{\phi} in spherical coordinates correctly. I was looking through this link earlier. I understand that \hat{r} always points radially outward from the origin. That seems to imply to me that any position in space could be...

Find the volume of a cone with radius R and height H using spherical coordinates. so x^2 + y^2 = z^2 x = p cos theta sin phi y= p sin theta sin phi z= p cos phi I found theta to be between 0 and 2 pie and phi to be between 0 and pie / 4. i don't know how to find p though. how...

Hi all, Del = i ∂/∂x + j ∂/∂y + k ∂/∂z in x y z cordinate similarly I require to see the derivation of del in other coordinates too. Please give me a link for the derivation.

You have a spherical capacitor with inner conductor radius a and outer conductor with radius b. The capacitor is filled with a perfect homogeneous dielectric of permittivity ε and is connected to a low-frequency time-harmonic voltage v(t)=V_{0}cos(ωt). Find the displacement current density...

I'm trying to convert the below Cartesian coordinate system into cylindrical and spherical coordinate systems. For the cylindrical system, I had r,vector = er,hat + sint(e3,hat). While I do have a technically correct answer for the spherical coordinate system, I believe, I was wondering if there...

The question is as follows: A point source emits a spherical wave with λ = 500 nm. If an observer is far away from the source and is only interacting with the light across a small area, one can approximate the local wave as a plane wave. How far from the source must the observer be so that...

Let the position vector of an arbitrary point $P(x_1x_2x_3)$ be $\mathbf{x} =x_i\hat{\mathbf{e}}_i$, and let $\mathbf{b} = b_i\hat{\mathbf{e}}_i$ be a constant vector. Show that $(\mathbf{x} - \mathbf{b})\cdot\mathbf{x} = 0$ is the vector equation of a spherical surface having its center at...

Hello, this is my first post here, so hopefully I do this in the right way... Homework Statement A hollow spherical conductor carries a net charge of 21.5 μC. The radius of the inner hollow is 5.2 cm and thee full radius of the sphere is 7.8 cm. At the center of the sphere, in the...

Hi there, I'm having a little confusion regarding spherical aberration from some experiments I've been doing with a concave mirror. I've been directing the mirror so that it faces the distance (ie. objects at infinity) and then positioning a flat piece of paper so that an image forms on it. The...

Hi I am not familiar with spherical geometry. I am working with elliptical polarization that involves using poincare sphere that present the latitude and longitude angle in spherical geometry. I need to find the great circle angle if given two points that each specified by their longitude angle...

Homework Statement Despite the fact that this started as an extended AP Physics C problem, I turned it into a calc problem because I (sort of) can. If it needs to be moved please do so. There is a hollow solid sphere with inner radius b, outer radius a, and mass M. A particle of mass m...

Homework Statement A thin ,metallic spherical shell contains a charge Q on it. A point charge q is placed at the center of the shell and another charge q1 is placed outside it as shown in the figure .All the three charges are positive. Q.1 The force on the charge at the center is a) towards...

Homework Statement Consider 2 conductor spherical shells of radii a and b (where a>b). The inner shell is at zero potential and the outer shell is at a potential given by ##V(\theta, \phi )=V_0 \sin \theta \cos \phi ## where ##V_0## is constant and theta and phi are the usual spherical...

I am studying Riemannian Geometry and General Relativity and feel like I don't have enough practice with covariant vectors. I can convert vector components and basis vectors between contravariant and covariant but I can't do anything else with them in the covariant form. I thought converting the...

I thought of this question the other day, and I was unable to solve it. A Google search has not helped, so I thought I might post it here. A point mass hangs from a rod of length "l" from the center of a pendulum. The only forces acting upon the point mass are the force of gravity and the...

Homework Statement find the limits on spherical coordinates. where ε is the region between z²=y²+x² and z = 2(x²+y²) no matter what i try i can't seem to find the limits, especially for "ρ", so far i got 0<θ<2Pi and 0<φ<Pi.

If we were to consider a nucleon-nucleon interaction: We know that the incident wave (plane wave) is ψ= Ae^{ikz}, propagating in z direction But for some mathematical facilities, we tend to use spherical coordinates, the wave becomes = \frac{A}{2ik}[e^{ikr}/r - e^{-ikr}/r] How come...

Spherical, Cylindrical or Polar Coordinates Homework Statement I have attached an image of the problem. I know that the solution is number 1 but I'm having some difficulty understanding why. In solution one is it using cylindrical coordinates> My first response to this question had been to...

Homework Statement given I=∫∫∫ρ^3 sin^2(∅) dρ d∅ dθ the bounds of the integrals: left most integral: from 0 to pi middle integral: from 0 to pi/2 right most integral: from 1 to 3 i have no idea how to graph this, i was hoping someone would be able to recommend some techniques.

Homework Statement Consider the interated integral I=∫∫∫ρ^3 sin^2(∅) dρ d∅ dθ -the bounds of the first integral (from left to right) are from 0 to pi -the bounds of the second integral are from 0 to pi/2 -the bounds of the third integral are from 1 to 3 a)express I as an interated...

Homework Statement I am trying to derive the line element for this geometry. But I am not sure how to show that ds can't contain any crossterms of d\theta and d\phi Homework Equations ds must be invariant under reflections \theta \rightarrow \theta'=\pi - \theta and \phi...

Homework Statement I don't have a specific problem in mind, it's more that I forgot how to solve the particular equation from first principles. \nabla^{2} \Phi = k^{2}\Phi Places I've looked so far have just quoted the results but I would like the complete method or the appropriate...

questioning what ρ does. What is the difference between the two equations? Let k be the angle from the positive z-axis and w be the angle from the pos x-axis parametric equation of a sphere with radius a paramet eq. 1: x = asin(k)cos(w) y = asin(k)sin(w) z= acos(k) 0≤w≤2pi 0≤k≤pi...

Homework Statement Please see the attached. It is a badly drawn sphere :-p By common sense,the area of the shaded region in the sphere = area of square = r^2 But can anyone show me the mathematical proof? Moreover,does it apply to the reality? Imagine when you bend a square sheet with...

Homework Statement Calculate the deformation of a sphere of radius R and density \rho under the influence of its own gravity. Assume Hooke's law holds for the material. Homework Equations Not applicable; my question is simply one of understanding. The Attempt at a Solution I want...

∫03∫0sqrt(9-x2)∫sqrt(x2+y2)sqrt(18-x2-y2) (x2+y2+z2)dzdxdy x=\rhosin\varphicosθ y=\rhosin\varphisinθ z=\rhocos\varphi Change the integrand to \rho and integrate wrt d\rhodθd\varphi I don't know how to find the limits of integration. Normally I would draw a picture and reason it out...

In spherical coordinates we have three axes namely r, θ, ∅ the ranges of these axes are 0≤r≤∞ 0≤θ≤∏ 0≤∅≤2∏ what will happen in a physical situation if we allow θ to change from zero to 2∏

Homework Statement A speck of dust is 3cm from the center of a glass sphere with radius of 5cm. If the glass sphere is placed in a tank of glycerin with a refractive index of 1.47, find the image distance, as viewed along the diameter through the speck of dust from the far side. Refractive...

Let's say we have a scalar function U in terms of r,theta and phi. why cannot this be the gradient at any point P(r,theta,phi)- partial of U wrt. r in the direction of r+partial of U wrt. theta in direction of (theta)+partial of U wrt. phi in the direction of (phi)?

Hey everyone, I'm reading a chapter on reflection of Light and I had some doubts:- 1 Is a real, erect image possible? What about a virtual, inverted image? 2 How can you see a real image without a screen? Can you see it in the air or something? 3 When you move away from a plane mirror...

Hello, I am struggling with what was supposed to be the simplest calc problem in spherical coordinates. I am trying to fid the center of mass of a solid hemisphere with a constant density, and I get a weird result. First, I compute the mass, then apply the center of mass formula. I divide...

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...

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...