Sphere Definition and 1000 Threads

Homework Statement A sphere with radius R = 0.200 m has density ρ that decreases with distance r from the center of the sphere according to \rho = 3.00 \times 10^3 \frac{kg}{m^3} - (9.00 \times 10^3 \frac{kg}{m^4})r a) Calculate the total mass of the sphere. b) Calculate the moment of inertia...

The problem statement Based on an analytical solution for the concentration profile of a dissolving sphere, I am supposed to use a numerical method to find the time at which the sphere has fully dissolved. This is not so much a question about specific values - but about the technique by which I...

I'm stuck on this problem: A small sphere is attached to a fixed point by a string of length =30cm , and whirls round in a vertical circle under the action of gravity at such speed that the tension in the string when the sphere is at its lowest point is three times the tension when the sphere is...

Homework Statement Suppose a grounded spherical conducting shell of radius R surrounds a pointlike dipole at the center with \vec{p}=p\vec{k} Find the potential V(r,\theta) for r <= R. Hint: Use spherical harmonics regular at r=0 to satisfy the boundary condition. Homework Equations General...

I've tried this problem at least 10 times using the equations in my book and I keep getting the same answer. What am I doing wrong? Homework Statement A solid steel sphere of density 7.6 g/cm3 and mass 0.2 kg spin on an axis through its center with a period of 1.5 s. Given Vsphere =4/3π^3, what...

Homework Statement A spherical conductor of radius ##a## carries a charge q and also there is a jelly of constant charge ##rho## per unit volume extending from radius ##a## out to radius ##b##. I'm looking to see if I got the correct set up for the electric field of this spherical conductor for...

I have a question regarding LQC that I can't find anywhere, and since most of the relevant answers to similar questions are here I may as well ask, here... For a simple background, when I was introduced to the big rip and combined that with the big bang, I immediately thought the two co-existed...

Homework Statement I need to create an equation that can tell me the electric flux through the surface of a sphere (centered at the origin) due to a point charge placed at various locations in/around the sphere. For example, find the electric flux through the sphere (of radius = 1) with a point...

I'm trying to follow Schwabl Thermodynamics, and I found the following equation for the surface area of a unit d-sphere: $$ \int d\Omega_d = \frac{2 \pi^{d/2}}{\Gamma(d/2)} $$ But this formula clearly fails for d=1: should be $$\pi$$ and d=2: should be $$ 4 \pi $$. What gives?

I caught a video online released by UIUC entitled "The Optiverse." Very cool video! Anyways, the idea is that a sphere can be turned inside-out under the premises that 1.) you cannot tear, puncture, or crease the edges, and 2.) that the sphere can pass through itself. While I understand that...

Homework Statement What is reduced density matrix ##\rho_A## and the Bloch vector representation for a state that is 50% ##|0 \rangle## and 50% ##\frac{1}{\sqrt{2}}(|0 \rangle + |1 \rangle)##Homework Equations The Attempt at a Solution [/B] I haven't seen many (any?) examples of this so I'm...

Am I right when I say that you can orbit the photon sphere and still be not pulled towards the Event Horizon but you need to orbit (In your spaceship) at the speed of light?

Homework Statement A charged insulating spherical shell has winner radius of a/3 an an outer radius of a. The cross section is as shown on the picture. The outer shell has a non-constant volume charge density of ρ = 6*α*r^3. Find the electric field magnitude in each region (outside the...

The extended plane (E2 U ∞) is a non-orientable surface, and yet topologically is a sphere which is orientable, can someone comment on how this is reconciled?

I have a question for E&M and I feel like I am over complicating it. As the title says, the is a positive charge on the x-axis and I must prove that flux = q/εo. Since the charge is on the z-axis, could I just add in a term (z-z') to account for the charge not being at the origin into...

Homework Statement The electric field at a distance of 0.143m from the surface of a solid insulating sphere with radius 0.381m is 1630N/C . a) Assuming the sphere's charge is uniformly distributed, what is the charge density inside it? b) Calculate the electric field inside the sphere...

Homework Statement What is the electric field at a point .12m outside the surface of an isolated plastic sphere .23m in diameter that produces an electric field of 1350 N/C just outside the surface of the sphere? Homework Equations E = kQ/(r^2) The Attempt at a Solution First I...

Hello I'm struggling with well-known problem of finding shortest path between two points on a sphere using calculus of variations. I managed to find correct differential equations of great circles, but I'm not confident about validity of methods I used. Below I describe my approach. In...

Homework Statement An insulating hollow sphere has inner radius a and outer radius b. Within the insulating material the volume charge density is given by ρ(r)=\alpha/r,where \alpha is a positive constant. What is the magnitude of the electric field at a distance r from the center of the...

Homework Statement Find the electrical potential inside a spherical shell carrying a total charge Q by integrating over the surface.Homework Equations E=k q/r^2The Attempt at a Solution I know the answer is zero from Gauss's law, but I don't know how to do the integration to get it.

Case 1. You have a sphere with Radius R and middle point X with the charge Q. The charge is equally distributed over the sphere. for E(X,r) = 0 for r_1 < R, E inside the sphere is 0. If r_2 > R then E ≠ 0 ; but let's say E(X,r_2) := w If you put all the charge of the sphere into X then...

Homework Statement What is the flux of r through a spherical surface of radius a? Homework Equations I'm guessing I should use a surface integral? ∫v.da ? The Attempt at a Solution Plugging in: I would get ∫r.da ? but what is a small patch of a sphere? I'm kind of confused...

Given sphereRadius and piVal, compute the volume of a sphere and assign to sphereVolume. Look up the equation online. Use (4.0 / 3.0) to perform floating-point division, instead of (4 / 3) which performs integer division. Sample program: #include <iostream> using namespace std; int main() {...

I am sure this should have already be discussed somewhere in the past... I have an intuitive problem with the area of a sphere. Following the mathematics of the metric and surfaces, I can easily derive the area of a sphere which is 4 \pi R^{2} . Now I'm have this problem: Suppose I get a ring...

Homework Statement A house is 62 ft long and 29 ft wide, and has 7.3 ft high ceilings. What is the volume of the interior of the house? Answer in units of cm3 Homework Equations LxWxH ?? The Attempt at a Solution 62x29x7.3= 13125.4 Then I converted it to cm and got 400062

Hello , firs of all I know that every magnet has two poles ad the field lines exit one pole and enter into the other , now if we take a bunch of magnets , for simplicity assume an infinitely long line of magnets each separated by a distance , all of the magnets facing N-S N-S N-S , now do the...

I am not sure if this is the right forum for this question, but I arrived at the question while studying the principle of stationary action so here it is: Consider the problem of finding the shortest path between two non-antipodal points on a sphere. Usually one solves this by using calculus of...

Hello, I am trying to design an experiment where I can calculate the distance at which polarization will not have a measurable effect on a neutral object, from a sphere charged by a Van Der Graaf generator. I am measuring the weight change caused by the polarization of the neutral object with...

Homework Statement "A small plastic sphere (with a mass of 2.60 X 10-15 kg) is suspended between two plates, with a potential difference of 265.4 V across the plates. The separation of the plates is 0.500 cm. The upper plate is negative and the lower one is positive. a)What type of...

10 000 cubic km of water can cover all the continents with a layer 7 cm deep. Find the depth of the water layer if 10 000 cubic km of water is spread over a sphere with radius R = 6370 km. ________________________________________________ My calculations: Volume of the sphere...

Homework Statement A metal sphere, of radius R and cut in two along a plane whose minimum distance from sphere's centre is h, is uniformly charged by a total electric charge Q. What force is necessary to hold the two parts of the sphere together? Homework Equations Elestrostatic equations...

Homework Statement Hi all, need a little help on an electrostatic induction problem. A positively charged metal rod is brought near to a neutral metal sphere. What is the charge of the metal sphere and the rod when the positively charged rod touches the neutral sphere. Homework Equations...

Homework Statement the electric field at the surface of a charged, solid, copper sphere with radius 0.160m is 3600N/C , directed toward the center of the sphere. what is the potential at the center of the sphere, if we take the potential to be zero infinitely far from the sphere...

The Riemann curvature of a unit sphere is sine-squared theta, where theta is the usual azimuthal angle in spherical co-ordinates, and this is shown in many textbooks. But since a sphere is completely specified by its radius, then as far as I can see its curvature should be a function of its...

[>A heavy sphere of radius r = 1.00 meter is fixed with respect to the ground. A small uniform solid sphere is placed at the top of the larger sphere. After a slight disturbance, the smaller sphere begins to roll downward without slipping. How high h is the small sphere above the ground at the...

Homework Statement A girl pushes on a large stone sphere. The sphere has a mass of 8200 kg and a radius of 90 cm and floats with nearly zero friction on a thin layer of pressurized water. Suppose that she pushes on the sphere tangent to its surface with a steady force of F = 45N and that the...

I just wanted something to play with so I thought of this problem and solved it but now I have questions about it. Consider a charged particle with charge q and mass \mu which is constrained to move on the surface of a sphere of radius R. There is a magnetic dipole with moment \vec m=m \hat z...

Homework Statement A small sphere, with initial temperature ##T##, is immersed in an ideal Boltzmannian gas at temperature ##T_0##. Assuming that the molecules incident on the sphere are first absorbed and then re-emitted with the temperature of the sphere, determine the variation of the...

Are plane and surface of sphere different metric spaces? Can distance function of plane be applied as distance function of surface of sphere? Please correct my question if needed?

I have a question that has been puzzling me. If a beam of light was released within a sphere or cube with a completely opaque inner surface would the inner area remain bright for a prolonged period of time or perhaps indefinitely assuming a vacuum exists within the sphere? Perhaps a perfectly...

Definition/Summary A photon sphere is a spherical surface round a non-rotating black hole (or other extremely compact spherically symmetric body) containing all the possible closed orbits of a photon. All such orbits are circular and unstable. The radius of the photon sphere is 3M...

Definition/Summary A Lune is a diangle on the surface of a sphere whose two vertices are opposite points. So the two angles of a Lune are equal, and each of the two sides is half a circumference. The whole surface is a Lune of angle 2\pi. Equations Area of a Lune: 2 r^2 \theta...

Homework Statement "A solid sphere rolls down an incline plane without slipping. If the center of mass of the sphere has a linear acceleration of 1.21 m/s2, what is the angle of the incline to the horizontal?" Homework Equations a = g * sin(θ) The Attempt at a Solution I got home...

Homework Statement The problem is #1 given here: http://ocw.mit.edu/courses/physics/8-311-electromagnetic-theory-spring-2004/assignments/ps1.pdf And there is a solution publicly available here...

I recently noticed that I have blindly used optimization in some problems that involve symmetrical insulating/conducting spheres and cylindrical shells. For example, when calculating outer electric field caused by a spherical insulator/conductor, I just treated these as a simple point charge...

Dear All, I am trying to calculate the Riemann tensor for a 4D sphere. In D'inverno's book, I have this equation R^{a}_{bcd}=\partial_{c}\Gamma^{a}_{bd}-\partial_{d}\Gamma^{a}_{bc}+\Gamma^{e}_{bd}\Gamma^{a}_{ec}-\Gamma^{e}_{bc}\Gamma^{a}_{ed} But the exercise asks me to calculate R_{abcd}. Do...

I'm wondering why my method for finding the surface area of a sphere is invalid. Essentially I'm integrating the perimeter of the circle perpendicular to the radius along the entire radius, and then multiplying by 2 (because the radius only covers half the sphere) (I hope that made sense...

Homework Statement Hello everyone. Each minute, I have 3d coordinates of points at the surface of a unit sphere (with center at (0;0;0)) rotating with an axis which can (slightely?) change over time. I want to know the linear speed (s) of this sphere. I don't know how to find r at each time...

Suppose there were a supermassive, superdense hollow sphere. Inside of the sphere, would time move more slowly relative to outside? Would objects inside the sphere be contracted relative to outside? I did this calculation once about the center of a neutron star. (Of course, it isn't...

Homework Statement Find the area of the cylinder x^2 + y^2 -y = 0 inside the sphere x^2 + y^2 +z^2 =1 Homework Equations dA = sec \gamma dydz where sec \gamma = \frac{|\nabla \phi|}{|\partial \phi/ \partial x|} The Attempt at a Solution The method shown in this section is to...