Sphere Definition and 1000 Threads

We have the (I think FRW) metric in the coordinates y^{0}=t,~~y^{1}=\psi,~~y^{2}=\theta,~~y^{3}=\varphi g_{00}=1,~~g_{00}= - \frac{f^{2}(t)}{\alpha} ,~~ g_{00}= - \frac{f^{2}(t)}{\alpha} \sin^{2}\psi ,~~g_{00}= - \frac{f^{2}(t)}{\alpha} \sin^{2}\psi sin^{2}\theta Suppose we have define a...

Hi, Attached is the equation relating the vibration of a sphere radius R, to the pressure field it generates. ρ is the density of the medium in which the sphere sits. The article I got this from just states the equation - I haven't been able to find anywhere that derives this equation...

Homework Statement We take a sphere (1mm) which has a parabolically changing refractive index, which is given in a function. Homework Equations Depending on the gradient of the refractive in the sphere, how does it correlates with the focal length. The Attempt at a Solution I...

Hi guys. Consider the problem of calculating the multiplicity (phase space volume) of N hard sphere gases each of whose center of mass is confined to a volume V. The spheres themselves have volume ##\omega## and do not interact with one another in equilibrium time scales. Then ##\Omega \propto...

Homework Statement A solid conducting sphere having a charge Q is surrounded by an uncharged concentric conducting hollow spherical shell. Let the potential difference between the surface of the solid sphere and that of the outer surface of the hollow shell be V. If the shell is now given a...

Homework Statement A small solid sphere of mass M0, of radius R0, and of uniform density ρ0 is placed in a large bowl containing water. It floats and the level of the water in the dish is L. Given the information below, determine the possible effects on the water level L, (R-Rises, F-Falls...

So this is some what of a silly question, I was bored and watching YouTube and there was a guy trying to say that the Earth is hollow ( crazy people are funny to watch) but it got me thinking could a planet form so that it was hollow? Or could a something like a small moon be hollowed out? I...

Homework Statement In general, a sphere with conductivity ##\kappa##, heat capacity per unit volume ##C## and radius ##R## obeys the differential equation at time t: C\frac{\partial T}{\partial t} = \kappa \frac{\partial^2 T}{\partial r^2} + \frac{2\kappa}{r}\frac{\partial T}{\partial r}...

Homework Statement "A boy is initially seated on the top of a hemispherical ice mound of radius R = 13.8 m. He begins to slide down the ice, with a negligible initial speed. Approximate the ice as being frictionless. At what height does the boy lose contact with the ice?" 2. The attempt at...

Homework Statement A Gaussian Sphere with a radius of 1m surrounds an unknown charge at the center. At this surface a uniform outward directed electric field is 1 N/C. Use Gauss' Law to calculate the amount of charge enclosed by the sphere. Homework Equations E = q/4∏εor^2 The Attempt at a...

Rolling sphere, problems with the fundementals. Homework Statement A sphere with the mass of 2.5 kg rolls without slipping. The speed of the center of gravity is 10 m/s. a) Calculate the translational kinetic energy of the sphere b) Calculate the rotational energy of the sphere c)...

Homework Statement So in this video: https://www.youtube.com/watch?v=rm3x2X0X_Sc&t=210 Why does g.out and g.in have values as shown on the video? I can not for life of my understand it. Homework Equations The Attempt at a Solution

So the problem statement is: A conducting solid sphere (R = 0.167 m, q = 6.63·10–6 C) is shown in the figure. Using Gauss’s Law and two different Gaussian surfaces, determine the electric field (magnitude and direction) at point A, which is 0.00000100 m outside the conducting sphere. (Hint: One...

Homework Statement A dipole is placed next to a sphere (see image), at a large distance what is E proportional to? 3. The Attempt at a Solution or lack thereof I'm having trouble figuring out what's happening in any variations of these. How does the dipole affect the sphere's charge...

Homework Statement Part (a): Find potential inside the sphere and outside of the sphere. Part (b): Find the electric fields in these two cases. Show for the first case it is identical to a conducting sphere in an electric field. Homework Equations The Attempt at a Solution I have found...

I was wondering how could I hold a lot of charge inside, for example, a ball. I thought by wrapping it in an isolant and using a hole with a semiconductor to charge it without letting anything out. But them it also could blow apart by the repulsive force of itself. Therefore, I got curious of...

Given a sphere x^2 + y^2 + z^2 = a^2 how would I derive the surface area by using surface integrals? The method I've tried is as follows: dA = sec\ \gamma \ dxdy where gamma is the angle between the tangent plane at dA and the xy plane. sec \gamma = \frac{|\nabla \varphi|}{\partial \varphi...

Homework Statement A solid sphere of aluminum (density 2.7 g/cm^3) is gently dropped into a deep ocean. (The density of ocean water is approximately 1.03 g/cm^3.) Calculate the sphere's acceleration at the point where it is completely submerged into the ocean. As the sphere drops deeper...

Homework Statement (a)Consider a charged sphere of radius R centred at the origin with the spherically symmetric charge density ρ(r) = ρ0(r4/R4) where ρ0 is a constant and r is the radial coordinate. Find the charge dQ0 contained in a spherical shell of radius r0 < R and infinitesimal...

Homework Statement Three identical metal spheres are uncharged at the vertices of an equilateral triangle. One at a time, a small sphere is connected by a conducting wire with a large metal sphere that is charged. The center of the large sphere is in the straight line perpendicular to the...

how to go step by step from the classical lagrangian to the schrodinger equation? i would like to work with the two angles. whether the quantization is right or not is a matter of experiment, is not it? I mean, you might have many schemes of quantization, but which one is the right one...

Homework Statement Use double polar coordinates x=rcosθ y=rsinθ z=scosφ w=ssinφ in R^4 to compute the 4-dimensional volume of the ball x^2 +y^2 +z^2+w^2 = R^22. The attempt at a solution I first substituted the polar coordinates into the given equation getting...

hi pf! basically, i am wondering how to find the velocity profile of slow flow around a sphere in terms of a stream function ##\psi = f(r,\theta)## where we are in spherical coordinates and ##\theta## is the angle with the ##z##-axis. (i think this is a classical problem). i understand the...

I'm considering a system where an electron is subjected to magnetic field which is produced by dirac monopole. Here I'm interested in looking for a translation operator. Now how can I get a translation operator in presence of field and in absence of field.?? I need both the operators. Can...

Homework Statement Refer to the attached photo for the problem statement. Homework Equations Electric Field Strength = 1/(4*pi*EpsilonNaught)*q/r^2 The Attempt at a Solution So, I need to find the charge magnitude of q. Because the electric field strength is given at a point...

From my textbook: "An electric charge that is uniformly distributed on the surface of a sphere, affects a different charge outside the sphere as though the whole charge was collected in the center of the sphere. This we exploit when we use Coulumbs law." Ive tried to prove this mathematically...

Homework Statement Let S be the piece of ρ=3 that is below Φ=∏/6 and is oriented up. Write one dS (vector) for all of S.Homework Equations The Attempt at a Solution It's a sphere of radius 3. S=<x,y,\sqrt{9-x^{2}-y^{2}}> Therefore dS = < \frac{-x}{\sqrt{9-x^{2}-y^{2}}}...

The tension in the rope is actually being provided by a solid sphere with radius 23.5 cm that rolls down an incline as shown in the figure. The incline makes an angle of 32° with the vertical. The end of the rope is attached to a yoke that runs through the center of the sphere, parallel to the...

Homework Statement Find the flux of F=<y,-x,z> through the piece of ρ=2 that lies above z=1 and is oriented up. Homework Equations The Attempt at a Solution S = < x, y, \sqrt{4-x^{2}-y^{2}} > Take Find Sx and Sy, cross them and end up with: dS = <...

So I have the equation for Barometric law in terms of density as: \frac{\phi(z)}{\phi_{0}}=exp(-g.M.z/R.T) where R=Universal gas constant, z=height of sedimentation, T=Standard temperature, g=Gravitational acceleration, M=Molar mass. When this equation is used to calculate the height of the...

Homework Statement Find the area of the part of the sphere x^2 + y^2 + z^2 = 4z that lies inside the paraboloid x^2 + y^2 = z Homework Equations The Attempt at a Solution I solved for the intercepts and found that they are z=0 and z=3. The sphere is centered two units in the z-direction above...

Homework Statement We have a sphere of radius a with permanent magnetization \mathbf{M}=M\hat{e}_{\mathbf{r}}. Find the magnetic scalar potential. Homework Equations $$\Phi_M(\mathbf{x})=-\frac{1}{4\pi}\int_V \frac{\mathbf{\nabla}'\cdot\mathbf{M}(\mathbf{x}')}{|\mathbf{x}-\mathbf{x}'|}d^3...

Hello again I seen in this forum about this problem but not in the special case when the point charge is at the center of the sphere how do I solve the series legendre polynomials?

Homework Statement a) What charge would need to be placed on a metal sphere such that the electric field produced stored a total of 50 J if the radius of the sphere was 18 cm? b) How much work would need to be done to reduce the radius to 9 cm, assuming the sphere is (mechanically) easily...

If we are asked to place 3 points on the surface of a sphere so that they are equidistant, it's easy to visualize that the result will be such that the three points form an equilateral triangle. If asked to place 4 points it's easy to visualize that the result is such that the points arrange...

Are there any good sources to understand the physics behind a rolling sphere down an incline plane?

Hello, I'm currently working on simulations in Solidworks of the flow of air (v = 450 m/s) around a sphere (radius = 1.5 cm). The results have been used in a cut plot representing the velocity in the x direction. The image is similar to this one...

Homework Statement A sphere with radius r has uniform charge density ρ within its volume, except for a small hollow sphere located at the center with radius R. Find the electrical field. Homework Equations ρ=Q/V ∫∫EdS=Q/ε The Attempt at a Solution With the spherical Gaussian surface...

Homework Statement a 20 kg sphere is at the origin and a 10 kg sphere is at (x,y) = (20,0). at what point or points could you place a small mass such that the net gravitational force on it due to the spheres is zero? Homework Equations g=GM/r^2 The Attempt at a Solution Can not...

Here is the question: I have posted a link there to this thread so the OP can view my work.

I am looking for the e.o.m. of a particle moving inside a sphere of homogeneous dust with density ρ. I start with the Lagrangian (in cartesian coordinates with i=1,2,3) L = \frac{m}{2}\dot{x}_i^2 - \frac{4\pi}{3}Gm\rho x_i^2 The e.o.m. and their solution are given by the harmonic...

Homework Statement Copy-paste from my textbook: Let S_1 be the sphere of radius 1, centered at the origin. Let a be a number > 0. If X is a point of the sphere S_1, then aX is a point of the sphere of radius a, because ||aX|| = a||X|| = a. In this manner, we get all points of the sphere of...

Homework Statement Q a) A charge is placed at a distance x from the center of a conducting sphere of radius R.Find the charge flown through the switch(from ground) when it is closed . b) In the above question replace the switch with an ammeter .What is the reading of ammeter if charge is...

hi guys, i have been following griffith's book on electrodynamics and i m stuck with probably one of the basic concepts on electric field. i did not understand what would be the electric field, 1) inside and 2)outside of a sphere with radius R ? also there are two problems which deals with...

Homework Statement The region between two concentric spheres of radii a and b(>a) contains volume charge density ρ(r) = C / r where C is a constant and r is the radial distance, as shown in figure. A point charge q is placed at the origin, r= 0. Find the value of C for which the electric...

How do I calculate the acceleration of the falling weight? It is hanging from a string which goes through a wheel, and is attached to a sphere with thin walls. The string doesn't stretch and the wheel and the sphere spin without friction. The fact that the weight is connected to multiple...

Homework Statement A bullet of mass m and charge q is fired towards a solid uniformly charged sphere of radius R and total charge + q. If it strikes the surface of sphere with speed u, find the minimum speed u so that it can penetrate through the sphere. (Neglect all resistance forces or...

Homework Statement A positive charge q is placed at the center of a hollow electrically neutral conducting sphere (inner radius R1 9cm, outer radius R2 10 cm. Using Gauss' law determine the electric field of every point in space, as a function of r (the distance from the center of the...

Homework Statement This is not homework but it's kind of similar so may be I will post it here. I want to find the force between two charge sphere given radius, permittivity,distance, and voltage by diverge other equation to coulomb's law. Homework Equations Coulomb law F=k Q1 Q2 /r2 F...

Homework Statement The problem is as follows. I have two spins, m_S and m_I. The first spin can either be \uparrow or \downarrow , and the second spin can be -1, 0 or 1. Now, I envision the situation as the first spin being on the bloch sphere, with up up to and down at the bottom. What I...