Sphere Definition and 1000 Threads

Hello, Im creating a physics simulator and I am struggling to expand my collisions from 2D to 3D. In 2D the velocity only changes parallel to the line of center so I presume this is the same for 3D.I can get a Cartesian equation of line but I am not sure how to get the velocity component...

Homework Statement Three charged metal spheres are arrayed in the xy plane so that they form an eqilateral triangle. What is the net electrostatic force on the sphere at the origin? http://imgur.com/a/4XnoO (sorry I forgot to put this but the angles are 90 for each vertex, which should be...

I am discussing physics with a friend and we need someone to confirm a thing that we're not agreeing on. We are discussing incident light that is passing through different geometries, and I want to know how the light behaves when it reflects inside a half sphere (of glass for example). Maybe...

@fresh_42 @FactChecker After thinking, I understood that the answer for this question might make the complex numbers comprehensible for me. My question in detail is as follow Let the equation of a sphere with center at the origin be ##Z1²+Z2²+Z3² = r²## where Z1 = a+ib, Z2 = c+id, Z3 = s+it...

Hi, I am looking to simulate a very - seemingly - simple case. Any advice on a software package would be helpful - preferably gui which doesn't have a steep learning curve. I want to model the heat flux into a sphere from the outside. The dimensions of the sphere are not important to me. I...

Homework Statement Homework EquationsThe Attempt at a Solution Because of the external magnetic field ##\vec B_0 ## , a uniform magnetization will be in the direction of external magnetic field. Because off this uniform magnetization, there will be a uniform magnetic fied in the direction of...

Homework Statement A sphere of radius 6 has a cylindrical hole of radius 3 drilled into it. What is the volume of the remaining solid. The Attempt at a Solution [/B] I am able to solve this using cylindrical coordinates but I'm having trouble when I try to solve it in spherical coordinates...

Homework Statement A small sphere of radius R held against the inner surface of a smooth spherical shell of radius 6R as shown in figure. The masses of the shell and small sphere are 4m and m respectively. This arrangement is placed on a smooth horizontal table. The small sphere is now...

I'm trying to understand connections and their arbitrariness. Many diff. geom. books or webpages appear to be contradictory. A chapter or page on connections may start off stressing that a connection is an arbitrary method of mapping between tangent spaces, then shortly after, show that nice...

Hey I was just practicing Gauss's law outside a sphere of radius R with total charge q enclosed. So I know they easiest way to do this is: ∫E⋅da=Q/ε E*4π*r^2=q/ε E=q/(4*πε) in the r-hat direction But I am confusing about setting up the integral to get the same result I tried ∫ 0 to pi ∫0 to...

Homework Statement "*Question 44: Uniform Circular Motion Inside Sphere of Charge The tau particle is a negatively charged particle similar to the electron, but of much larger mass - its mass is 3.18 x 10-27 kg, about 3480 times the mass of the electron and about twice the mass of a proton or...

Homework Statement I uploaded the Ex. 3.2. Homework EquationsThe Attempt at a Solution On the spherical surface, the potential due to q'' at center is going to be constant. q''= V0 R\kLet's say that the potential of the neutral conducting sphere is V0. Now, to calculate the force of...

Homework Statement Two fully equal sphere's of lead are placed next to each other so that the gravitational force between sums up to 10N. Calculate mass and radius of the two sphere's. F=10N , ρlead=11300kg/m2 Homework Equations F=gm, F=GMm/r2 , V=4πr3/3 , ρ=m/VThe Attempt at a...

An interesting problem posed to me by a friend: A small sphere, initially neutral, of radius ##a## emits ##n## charges ##q## of mass ##m## per unit time isotropically from its surface at a radial velocity of constant norm ##v##. Determine the spatial distribution of charges and currents at...

Homework Statement A + q = 5 pC charge is uniformly distributed on a non-conducting sphere of radius a= 5 cm , which is placed in the center of a spherical conducting shell of inner radius b = 10 cm and outer radius c = 12 cm. The outer conducting shell is charged with a -q charge. Determine...

Homework Statement A sphere of radius R has total charge Q. The volume charge density (C/m^3) within the sphere is ρ = ρ_0 (1 - r/R). This charge density decreases linearly from ρ_0 at the center to zero at the edge of sphere. a. Show that ρ_0 = 3Q/πR^3. b. Show that the electric field inside...

Hello Everybody! Concept of Solid Angle was pretty much straight forward until they were on surface patches were taken into account which were visualized as base of cone. I am having difficult when 3d Objects like Sphere/Cylinder . We can very easily calculate the respective area and plugin the...

Homework Statement http://imgur.com/a/wEUgn question #70 in the attached image. Three charged spheres are at rest in a plane as shown in the figure. Spheres A and B are fixed, but sphere C is attached to the ceiling by a thread. The tension in the string is .240 N. Spheres A and B have charge...

If I construct a set of qubit gates, say {G1, G2 ... Gk ... Gn}, that can act on a state |ψ>, what does it mean for the set of states Gk |ψ> to span the Bloch sphere? As an example, take the set {G1, G2, G3, G4} = { I, X π/2 , Y π/2, Xπ } Here, X π/2 denotes a π/2 rotation about the x-axis, Y...

Homework Statement [/B] Find the radius and center of sphere ρ = 28 cos ϕ. Homework Equations Relevant equations would be the spherical and rectangular coordinate equations. The Attempt at a Solution I started off by multiplying both sides of the equation by ρ to get ρ^2 = 28 ρ cosϕ Then...

Homework Statement Two conducting spheres having same charge density and with radius “R” & “2R” are brought in contact and separated by large distance. What are their final surface charge densities ? Homework Equations No equation in question. The Attempt at a Solution Tried using the fact...

Homework Statement A solid sphere of radius 16cm and mass 10kg starts from rest and rolls without slipping a distance of 9m down a house roof that is inclined at 43 degrees. What is the angular speed about its center as it leaves the house roof? The height of the outside wall of the house is...

Hello Guys! This is my first post so bear with me. I am currently studying the basics of electrostatics using the textbook "Introduction to electrodynamics 3 edt. - David J. Griffiths". My problem comes when i try to solve problem 2.21. Find the potential V inside and outside a uniformly...

Hi! I'm thinking how would the velocity of a sphere change if it falls from rest in a tall beaker full of oil. I know that the direction of acceleration is upwards, and the acceleration should be decreasing at a decreasing rate. But how would the velocity change if the velocity is initially zero...

Reading the post below on event horizon of a black hole (BH) got me thinking about the photon sphere of the BH. We all know light will travel around this photon sphere and how light from a source would completely travel back to it's source if one could see it real time, we all know this from...

Is it possible to create a hollow magnetic sphere?

Homework Statement A sphere of radius R is rolling without slipping with a velocity v and collides inelastically with a step of height h < R. ¿What is the minimum velocity for which the sphere will be over the step? Homework Equations Total kinetic energy (maybe)...

Homework Statement Consider the map ##\phi: \mathbb{R}^4 \rightarrow \mathbb{R}^2## defined by ##\phi(x,y,s,t) = (x^2 + y, x^2 + y^2 + s^2 + t^2 + y)##. Show that ##(0,1)## is a regular value of ##\phi##, and that the level set ##\phi^{-1}(0,1)## is diffeomorphic to ##\mathbb{S}^2##. Homework...

Can you please direct me to ref that shows the derivation of the escape velocity from a spherical object that moves in velocity v~c with respect to rest frame? I suspect the escape velocity is increasing (intuitively since the mass increases). Please comment and suggest alternatives.

I know that mie theory is used to analyze the absorption/scattering/extinction of a homogeneous sphere within a homogeneous dielectric medium. However, if I wanted to perform the same analysis on a sphere enclosed by two different media, is there an analytic solution to this?

I have done it by the parametric form of σ, but if I change σ to implicit form that is G(x,y,z)=x^2+y*2+z^2-R^2=0 I don't know how continue. The theory is: where Rxy is the projection of σ in plane xy so it's the circumference x^2+y^2=R^2

Specifically, how deep can an enclosed space of a polycarbonate (I'm thinking about strong plastics) material withstand underwater before cracking and breaking. Say a 2 liter bottle

Hello, I want to prove that a graph represent a manifold, for this i take the opposites edges of a vertex (edge connected between vertex connected to the current vertex) and this subgraph need to be homeomorphic for example to the 1-sphere if i want a 2 manifold. This criterion ensure that my...

Homework Statement Find electrostatic potential of a solid sphere with reference point of 0 statvolt at infinite. Homework EquationsThe Attempt at a Solution Potential energy of a solid sphere is ##\dfrac35 \dfrac{Q^2}{r}##. And I know ##\displaystyle U = {1\over 2} \int \rho \phi dv##. So...

Given a charged sphere, the electric field within it is zero at every point. Why is this? Why is not merely zero only at the center? If a sphere is conducting, then its charge is all across the surface. If electric field is inversely proportional to distance from charge squared, won't the field...

Homework Statement A point charge +q is placed outside a grounded conducting sphere of radius a. which of the following is ##not## true. a) There is an attractive force between the sphere and the charge b) The induced surface charge density on the sphere is not same everywhere c) The electric...

Homework Statement We place a cylinder with radius R, a sphere with radius R and a sphere with radius (2R). Which of the solids will roll out of the plane first? Assume no rolling resistance and no air resistance. Homework Equations 1) The net torque is the torque of the force of static...

So i was going through derivations of moments of inertia of objects. For objects like the disk and rod, i was able to assume a relationship between mass and volume and integrate From there like $$ \frac{d_m}{m} = \frac{dl}{l} \\ d_m = \frac{dl*m}{l} \\ \int_{0}^{L}r^2\frac{dl*m}{l} \\...

Homework Statement To calculate moment of inertia of a solid sphere of uniform density[/B]Homework Equations $$ I = \int r^2 dm$$ The attempt at a solution I consider an elemental disk of small thickness ##d\theta## ##dm = \frac{M}{4/3 \pi R^3}*\pi R^2\cos^2\theta* Rd\theta##...

Would a hollow sphere measure the same gravitationally as a solid sphere if it was the same mass? Just sharing an interesting question

If a smooth sphere with radius a is fixed on a plane, and a particle is projected horizontally at the highest point outside/on of the sphere with speed (4ag/5)^0.5, I know that the particle will lose contact with the sphere when it makes an angle of theta with the upward vertical, where theta is...

Homework Statement For the vector field F(r) = Ar3e-ar2rˆ+Br-3θ^ calculate the volume integral of the divergence over a sphere of radius R, centered at the origin. Homework Equations Volume of sphere V= ∫∫∫dV = ∫∫∫r2sinθdrdθdφ Force F(r) = Ar3e-ar2rˆ+Br-3θ^ where ^ denote basis (unit vectors)...

Homework Statement I'm having a bit of trouble with this problem: "A spherical ball of charge has radius R and total charge Q. The electric field strength inside the ball (r≤R) is E(r)=r^4Emax/R^4. a. What is Emax in terms of Q and R? b. Find an expression for the volume charge density ρ(r)...

Homework Statement Homework Equations None The Attempt at a Solution My thinking was that the positively charged sphere would repel the electrons to the far side of the neutral sphere, creating a repulsive force between the two spheres until they touch and the charge is shared. Since the...

To find the surface area of a hemisphere of radius ##R##, we can do so by summing up rings of height ##Rd\theta## (arc length) and radius ##r=Rcos(\theta)##. So the surface area is then ##S=\int_0^{\frac{\pi}{2}}2\pi (Rcos(\theta))Rd\theta=2\pi R^2\int_0^{\frac{\pi}{2}}cos(\theta)d\theta=2\pi...

Homework Statement Find the magnetic field of a uniformly magnetized sphere. (This is an example in my book, I have underlined what I am having trouble understanding down below.) Homework Equations $$\vec{J}_b = \nabla \times \vec{M}$$ $$\vec{K}_b = \vec{M}\times \hat{n}$$ $$\vec{A}(\vec{r}) =...

Hey, is it possible to have a cylindrical ring (made of permanent magnet) and a magnetic sphere sitting inside it and staying in one place without touching the inner sides of the ring and not falling through? The object doesn't necessarily have to be a sphere. If it would work with any other...

Homework Statement A conducting sphere, radius R, charged with Q is inside a conducting shell (2R<r<3R) with charge 2Q. Find the electric potential and the energy. Homework Equations \Phi =-\int_{r_1}^{r_2} \vec{E}\cdot\vec{dl} U=\int_{V}E^2dV The Attempt at a Solution I think i got it...

Homework Statement Originally the statement: Find a length of two points on sphere. It was easy. ##\int \sqrt{g_{\phi\phi}}d\phi## I hope you agree :-) But I have idea, how to find a length of path which is NOT a part of arc (circle). For example sinusoid. Is possible to find length of sinusoid...

1. Homework Statement a point mass is projected at an angle of 60° from the horizontal. it collides with the sphere at a maximum height of trajectory with a sphere of radius of 72.5cm such that it is projected off the sphere once again at an angle of 60° from the horizontal.The sphere, due to...