Spherical Definition and 1000 Threads

Hi. I'm trying to make a small simulation of several simple physical systems (C++). I have the differential equation of a spherical pendulum with only the gravity force and without friction. \theta'' = \sin(\theta) (\cos(\theta) \phi'^2 − \frac{g}{L}) \phi'' = −2 \cot(\theta) \theta' \phi'...

If a flash of light is emitted spherically and this is measured in terms of its duration by two distant observers with one twice as far away from the source as the other, and the source and observers are all at rest with respect to each other, will the flash appear to have the same duration for...

I have been studying gradience; divergence and curl. I think i understand them in cartesian coordinate system; But i don't understand how do they get such complex stuffs out of nowhere in calculating divergence in spherical and cylindrical coordinate system. Any helps; links or suggestion...

The term "negative energy" is used (a) for the energy below the vacuum energy between the two plates in the Casimir effect, (b) the energy carried by the sister particle to the radiated particle in Hawking radiation, that is, the particle from the matter-antimatter pair which goes into the...

So I'm asked to determine near which points of R^3 can we solve for ρ, δ, θ in terms of x,y,z: x = ρ sinδ cosθ y= ρ sinδ sinθ z= ρcosδ so the spherical co-ordinates using IFT. Attempt: Ok so in order to determine solutions, I need to first find where the determinant of the freceht...

Homework Statement The inner radius of a spherical insulating shell is c=14.6 cm, and the outer radius is d=15.7 cm. The shell carries a charge of q=1451 E−8 C, distributed uniformly through its volume. The goal of this problem is to determine the potential at the center of the shell (r=0)...

Hi all, In flat space-time the metric is ds^2=-dt^2+dr^2+r^2\Omega^2 The Schwarzschild metric is ds^2=-(1-\frac{2MG}{r})dt^2+\frac{dr^2}{(1-\frac{2MG}{r})}+r^2d\Omega^2 Very far from the planet, assuming it is symmetrical and non-spinning, the Schwarzschild metric reduces to the...

I was looking at the above equation here: http://mathworld.wolfram.com/SphericalBesselDifferentialEquation.html Which has the following equation: {(d ²/dx²)+(d/dx)+[x²-(n+1/2)²] }z =0. In my opinion, this equation is of the order n+1/2 but the website and books claim it's of the order of a...

Guys, I read that integrating the ds gives the arc length along the curved manifold. So in this case, I have a unit sphere and its metric is ds^2=dθ^2+sin(θ)^2*dψ^2. So how to integrate it? What is the solution for S? Note, it also is known as ds^2=dΩ^2 Thanks!

Hello all, Can someone explain why barrel distortion is present by lenses and if it is related to Spherical aberation yes or no? Descriptions tell us that this is caused by the magnification being less when the distance from the optical axis increases. What magnification how can i understand...

good evening! i am trying to calculate the electric field of a spherical charge distribution ρ=ρ_{0}e^{-kr}, where r is the radial distance. i am a little bit embarressed,but i have to say that i am not comfortable with spherical coordinates in practical calculations. i would appreciate if...

Are the orbitals circular or spherical or parabolic?? Are they 3D? Are the orbitals circular or spherical or parabolic?? Are they 3D?

Homework Statement A non-conducting spherical shell is uniformly charged. The electrostatic potential \phi at the centre of the sphere is \phi1 = 200V The potential at distance r = 50cm from the centre is \phi2 = 40V Find the radius of sphere: a Homework Equations I seem to have...

Look at the attached problem with solutions. I don't understand what the author means in c) when he says that succesive shells contribute less and less because the cross sectional area grows proportional to r2. The flux through a closed surface is always the same (Gauss' law). Rather the reason...

Homework Statement Find the volume of the solid that lies above the cone z = root(x2 + y2) and below the sphere x2 + y2 + x2 = z. Homework Equations x2 + y2 + x2 = ρ2 The Attempt at a Solution The main issue I have with this question is finding what the boundary of integration is for ρ. I...

(This is NOT homework) just my personal interpretation, because these are the formulas as you already know: r = √(x^2 + y^2 + z^2) φ = arctan(y/x) θ = arccos(z/r) using (x,y,z) = (∞,∞,∞) I come across a bit of a sinister problem: r = √(∞^+∞^+∞^) = √(3∞^2) which is right because if we just...

I googled it, and it says: \dot{x}=\dot{r}sinθcos∅ + (rcosθcos∅)\dot{θ} - (rsinθsin∅)\dot{∅} . . and so on for \dot{y} & \dot{z} And then they wrote "We will also need the inverse transformation obtained by solving the equations above w.r.t \dot{r}, \dot{θ}, and \dot{∅} for example...

Just wondering if we have a non-conducting spherical shell which is uniformly charged and we know the potential at the centre and the potential at some radius how can we find the radius of the shell?

Homework Statement Find the pressure on a uniformly charged spherical conducting shell of Radius R and total charge Q. The answer is (Q^2) / (32*π*ε*R^4) I´m fine doing this using the derivative of the energy as the sphere grows to get the force. My question is: Why do I get twice the answer...

This problem is driving me mad suppose that we have a positive charge inside a non conducting spherical shell uniformly charged the charge is at a random place inside the shell but not in the center the textbook says the charge will feel no force from the charges of the shell and the...

The volume charge density of spherical shell varies as ρ=-kr.If we have to calculate electric filed using gauss's law, can we treat as E. dA as E(dA) as there is azimuthal symmitry Homework Equations The Attempt at a Solution

Homework Statement I struggle to write equations of motion for spherical magnetic pendulum. The forces acting on the pendulum are: gravity, tension in the rope, and 4 repelling forces Here is the picture for the problem: first attachment (I didn’t add forces to not mess it up) There are...

Hi everybody, I am trying to solve the following problem and I get stuck on the last question. I would appreciate a lot that someone helps me . Here is the problem: Let D be the region bounded from below by the cone z= the root of (x^2 + z^2), and from above by the paraboloid z = 2 – x^2 –...

Converting to Spherical Coordinates...then integrating? Am I doing this right? Homework Statement Consider the integral ∫∫∫(x2z + y2z + z3) dz dy dx, where the left-most integral is from -2 to 2, the second -√(4-x2) to √(4-x2) and the right-most integral is from 2-√(4-x2-y2) to...

Homework Statement Suppose a planet whose surface is spherical and the gravitational potential exterior to it is exactly -GM/r, like that of a point mass. Is it possible to know if the inner mass distribution is actually shperically symmetric? Can a non-spherical mass distribution produce...

Homework Statement Two conducting spheres of radii R1 and R2 are kept widely separated from each other. What are their individual capacitance? If the spheres are connected by a metal wire, what will be the capacitance of the combination? Think in terms of series-parallel connections...

Q: Consider your own eyesight. Can you detect any indication of spherical aberration? If so, describe what you see. A: I understand spherical aberration is generated by spherical lenses or mirrors and causes light to spread, which results in a blurry image. My initial thought was yes, a...

Homework Statement where λ= thermal conductivity \dot{q}= dissipation rate per volume Homework Equations qx=-kA\frac{dT}{dx} The Attempt at a Solution I don't know where to start from to be honest, so any help would be greatly appreciated

Homework Statement http://img109.imageshack.us/img109/1065/87070684.png Homework Equations 1) L_{\pm}=\pm\hbar e^{\pm i \phi}(\frac{\partial}{\partial\theta}\pm i cot\theta \frac{\partial}{\partial\phi}) 2) L_{\pm}Y^m_l = \hbar\sqrt{(l \mp m)(l \pm m+1)}Y^{m \pm 1}_{l} 3)Answer...

Homework Statement Firstly sorry for my bad english,i have a one question for you(İ try it but i didn't solve it ) Homework Equations The Attempt at a Solution i know problem will be solved spherical coordinates but i don't know how i get angles (interval) theta and fi ...

Hi all, Suppose I have measured an antenna's nearfield pattern and have a set of data f(theta, phi), where theta and phi are spherical coordinates, at a distance r from the antenna (we'll assume that the antenna is a point source to make it easier). How would I go about transforming this data...

The normalization condition is: ∫|ψ|^{2}d^{3}r=1 In spherical coordinates: d^{3}r=r^{2}sinθdrdθd\phi Separating variables: ∫|ψ|^{2}r^{2}sinθdrdθd\phi=∫|R|^{2}r^{2}dr∫|Y|^{2}sinθdθd\phi=1 The next step is the part I don't understand. It says: ∫^{∞}_{0}|R|^{2}r^{2}dr=1 and...

Homework Statement Consider a particle in a 2nm sphere with infinite potential energy outside and zero potential energy inside the sphere. Calculate the energy of the following wavefunctions: 1s, 2p, 3d Homework Equations H(hat) = p(hat)^2/2m(sub zero) + V(r) V(r) = ∞ when r ≥ 2 nm...

Homework Statement Calculate volume of the solid region bounded by z = √(x^2 + Y^2) and the planes z = 1 and z =2 Homework Equations The Attempt at a Solution

Homework Statement i am trying to solve for the magnetic torque a circular loop of radius R exerts on a square loop of side length b a distance r away. The circular loop has a normal vector towards the positive z axis, the square loop has a normal towards the +y axis. The current is I in both...

Homework Statement Find the capacitance of an isolated ball-shaped conductor of radius R1 sorrounded by an adjacent concentric layer of dielectric with permitivity ε and outside radius R2. Homework Equations The Attempt at a Solution The official solution says something like...

A spherical capacitor contains: Region1: solid spherical conductor (radius=0.5mm, Q=7.4 micro coulombs) Region2: surrounded by a dielectric material (er=1.8, radius extends to 1.2mm, Region3: outer spherical non-conducting shell (variable charge per unit volume p = 5r, outer radius=2.0 mm)...

Homework Statement Hi I have an expression on the form df(v, \theta, \phi) = v e^{-v^2/C}\cos(\theta)v^2\sin(\theta)\,dv\,d\theta\,d\phi and I am trying to write it in cylindrical coordinates. Note that θ runs from 0..π, v is a velocity and C a real constant. So I wish to write it in terms...

∅θ,θI've come across two distinct 'versions' of the spherical coordinates. Could someone tell me which is correct or if both are fine. Version 1: A spherical coordinate is (rho,θ,∅) x=rhocos(θ)sin(∅) ; y=rhosin(θ)sin(∅) ; z=rhocos(θ) Version 2: A...

Hello, I am trying to solve the following integral (limits from 0 to inf). ∫j_1(kr) dr where j_1 is the first order SPHERICAL Bessel function of the first kind, of argument (k*r). Unfortunately, I cannot find it in the tables, nor manage to solve it... Can anybody help? Thanks a lot! Any...

Homework Statement Calculate the flux of vector field F = -3r through sphere radius 5 at the origin. Homework Equations The Attempt at a Solution Since the orientation is always exactly opposite of the orientation of the surface, I expect a negative answer. Also, since they...

Reading through my electrodynamics textbook, I frequently get confused with the use of the del (nabla) operator. There is a whole list of vector identities with the del operator, but in some specific cases I cannot figure out what how the operation is exactly defined. Most of the problems...

The Green's functions for a 3d wave are like δ(r - ct)/r -- so if you have static source at the origin that is turned on at t=0, you get an expanding ball around it of radius ct, with strength 1/r. If you look just at the XY plane, you see an expanding disc of value 1/r. Similarly, if you...

Homework Statement http://img13.imageshack.us/img13/5793/84188411.jpg Homework Equations Find a condition on b such that x = 0 is a local minimum of the potential function. The Attempt at a Solution To find local minimum, potential function (V) of the system should be written. V...

Homework Statement Prove the complex amplitude reflectance of a spherical mirror is given as exp[-jk(x2+y2)/R] Homework Equations Transmittance of a spherical mirror is also exp[jk(x2+y2)/2f] The Attempt at a Solution I have totally no idea how to go about doing this. Can I just...

Homework Statement Given two concentric spherical metal shells, with radii a and b (a < b), and surface charge densities Sa and Sb. Find the capacitance if Sa = - Sb. Homework Equations C = Q/V The Attempt at a Solution I would know how to solve this if the absolute values of the...

So I've done some problems where a sphere intersects with a cylinder and I needed to find the volume of the intersected region using triple integrals. For example, if I needed to find the domain of integration for the intersection of the sphere $$x^2+y^2+z^2=a^2$$ and the cylinder...

Homework Statement The point is (0, -8, 0) r≥0 0≤θ≤2∏ 0≤\varphi≤∏ Homework Equations The Attempt at a Solution So here is what I've done so far: I know that r=8 because x and z are 0 I know that θ=∏/4 or 3∏/4, but which one? both of these satisfy the following equation...

Homework Statement Consider a solid sphere of radius r to be placed at the bottom of a spherical bowl radius R, after the ball is given a push it oscillates about the bottom. By using the Lagrangian approach find the period of oscillation.Homework Equations The Attempt at a Solution Ok so this...

This is one of my homework problems. If h(x) is continuous in x, show that the spherical mean: M_{h}(x,r) = \frac{1}{w_{n}}\int_{|\xi|=1} h(x+r\xi) dS_{\xi} is continuous for all x and r \geq 0. A lot of PDE textbooks state this fact (in regards to the wave equation in 3 dimensions)...