Sphere Definition and 1000 Threads

  1. Lone Wolf

    What Is the Effect of Friction on the Height of a Sphere Rolling Down a Ramp?

    Figure: a) The mechanical energy of the sphere is conserved because the weight is the only force which does work. My problem with this question is mostly because the original picture (which I tried to recreate here) is kind of ambiguous, as in I don't know if H already accounts for the radius...
  2. J

    Understanding the physics behind an elastic sphere

    First off, I'm not a scientist or engineer and I apologize if I don't give a clear description of my question. I'm beginning a personal project and was hoping for some knowledge and assistance. What I'm trying to achieve is to have a spherical object (it will be at least twice as wide as it is...
  3. JD_PM

    Why a charged sphere whose radius oscillates in and out won't radiate?

    In chapter 10 (Radiation; just after example 2 from 'Radiation from an arbitrary source') of Introduction to Electrodynamics by G. Griffiths he asserts that a charged sphere with oscillating radius doesn't radiate because, by Gauss law, ##E## stays the same no matter where the charges are...
  4. J

    I Finding a linear combination to enter a sphere

    Let's say we have n vectors in ℝ3. And say we have defined a subspace inside ℝ3 in the form of a sphere with radius r, and the center of the spheare is at P, where P is a vector in ℝ3. What methods exists to find any linear combination of the n vectors, so that the sum of all of them, lies...
  5. migueldbg

    Potential from point charge at distance ##l## from conducting sphere

    After looking around a bit, I found that, considering the polar axis to be along the direction of the point charge as suggested by the exercise, the following Legendre polynomial expansion is true: $$\begin{equation}\frac{1}{|\mathbf{r} - \mathbf{r'}|} = \sum_{n=0}^\infty...
  6. brotherbobby

    The Indeterminacy of Problems with Multiple Friction Interfaces

    For convenience, I have marked the C.G. of the sphere as ##G_S## and that of the bar only as ##G_B##. The C.G. of the combination is halfway between them, shown by the green ##G_C##. My answer is that the combination will rotate about ##G_C## (centre of the bar) as it falls. I wonder if I am...
  7. S

    Rotating Sphere: Conceptual Question

    As shown in figure there's a homogeneous solid sphere. It is rotating about axis which is passing through point P directed perpendicular to the plane of paper. (In short like a pendulum). I'm neglecting gravity and assuming a force F which is directed perpendicular to the string. (The string...
  8. Haorong Wu

    Can Bloch sphere be used to represent mixed states in quantum computation?

    Well, I have no clues for this problem. Since I can get nothing from the definition of ##\rho##, I tried from the right part. Also, I know that ##\left ( \vec r \cdot \vec \sigma \right ) ^2={r_1}^2 {\sigma _1}^2+{r_2}^2 {\sigma _2}^2+{r_3}^2 {\sigma _3}^2##. Plus, ##\rho## is positive; then...
  9. colemc20

    Hollow Sphere Inertia in Cartesian Coordinates

    Problem Statement: How do you calculate the rotational inertia of a hollow sphere in cartesian (x,y) coordinates? Relevant Equations: I=Mr^2 My physics teacher said its his goal to figure this out before he dies. He has personally solved all objects inertias in cartesian coordinates but can't...
  10. Haorong Wu

    I How to understand the Bloch sphere in the quantum computation?

    I've read that ##\left | \psi \right > =cos \frac \theta 2 \left | 0 \right > + e^{i \phi} sin \frac \theta 2 \left | 1 \right >##, and the corresponding point in the Bloch sphere is as the fig below shows. I think ##\left | 0 \right >## and ##\left | 1 \right >## are orthonormal vectors...
  11. J

    MHB Integral Over Unit Sphere of Inner Product

    Problem: Prove that for any $x \in R^n$ and any $0<p<\infty$ $\int_{S^{n-1}} \rvert \xi \cdot x \rvert^p d\sigma(\xi) = \rvert x \rvert^p \int_{S^{n-1}} \rvert \xi_1 \rvert^p d\sigma(\xi)$, where $\xi \cdot x = \xi_1 x_1 + ... + \xi_n x_n$ is the inner product in $R^n$. Some thinking... I...
  12. peguerosdc

    [Griffiths ex4.2] Electric field of a uniformly polarized sphere

    Hi! This is more a conceptual question rather than the calculation itself. So, Griffiths' section 4.2.1 "The field of a polarized object / Bound charges" says that if you want to calculate the field produced by a polarized material, you can find it from the potential of a surface charge and a...
  13. K

    What Potential Should Be Used for Energy Stored in a Charged Sphere?

    Hi. When I am asked to figure out the Energy stored in a charged sphere and I use this equation: ## U = \frac {1}{2} \cdot \int \phi (r) \cdot \rho(r) dV ## what is the potential ## \phi ( r) ## stands for? I tried to use the potential inside the sphere, because out side of the sphere ## \rho...
  14. L

    Pressures distribution: solid sphere on a flat surface

    In a real case (not ideally rigid bodies), a (e. g.) hard metal sphere is on a flat (e. g.) hard metal surface (a table) and the sphere is "charged" vertically on the table by a vertical force directed downward. In this situation, an engineer told me that the maximum pressure on the table is not...
  15. P

    The capacitance of an isolated sphere

    according to http://230nsc1.phy-astr.gsu.edu/hbase/electric/capsph.html#c2 isolated spheres have capacitance but how can it be measured with an instrument?
  16. fight_club_alum

    Volume charge density and potential difference in sphere

    Homework Statement The charge of uniform density 50 nC/m3 is distributed throughout the inside of a long nonconducting cylindrical rod (radius = 5.0 cm). Determine the magnitude of the potential difference of point A (2.0 cm from the axis of the rod) and point B (4.0 cm from the axis). a . 2.7...
  17. Kaguro

    Analyzing the Sphere Image Charge Problem

    Homework Statement A charge q is kept at distance d from center of grounded conducting sphere of radius R. Find V everywhere outside. Homework Equations V = k*q/r Cosine Law. The Attempt at a Solution [/B] What do I do with the theta? And how would I analytically find out what Q and b...
  18. ?

    Rotating sphere which separates into hemispheres

    Hi all, The scenario I'm considering is a solid sphere (of uniform density) rotating with constant angular velocity when it abruptly splits into two hemispheres along a cut which contains the rotation axis. The hemispheres will begin to separate; if, for example, we consider the rotation to be...
  19. J

    How do you calculate the inductance of a metal sphere with electrical contacts?

    Hey everyone this is my first thread i was wondering how you calculate the inductance of a solid sphere. Say a sphere for example of 5cm diameter with electrical contacts on opposing sides 0.5 cm in diameter. Any help would be much appreciated
  20. hagopbul

    I Absorption of Radiation: Calculating Sphere Area

    Hello: Do anyone remember a law to calculate an area of a sphere ,some thing like the specific surface area but relative to absorption of radiation ?
  21. L

    I Finding the coordinates of a point on a sphere

    I have three points: A, B and C, which are all on the surface of the same sphere. I need to find the xyz coordinates of C. What I know: - the radius of the sphere - the origin of the sphere - the xyz coordinates of A and B - the arc distance from A to C and from B to C - the angle between AB and...
  22. arturo

    Potential across a conducting sphere surrounded by an insulator

    Homework Statement A conducting sphere has a radius of 2.25 m and carries a positive surplus charge of 35.0 mC. A protective layer of barium titanate is applied to the surface of the sphere to make it safe for laboratory workers nearby. Safety considerations dictate that the potential...
  23. PhysicS FAN

    Will the 2 dimensional sphere rotate?

    Homework Statement A 200kg sphere is in touch with two walls. The horizontal wall has no coefficent of friction and the vertical has μ=0.25. If we apply a force F=400N will the sphere rotate? Homework EquationsThe Attempt at a Solution [/B] What I can't understand is, if there is balance in...
  24. CharlieCW

    Conductor sphere floating on a dielectric fluid

    Homework Statement A conductor sphere of radius R without charge is floating half-submerged in a liquid with dielectric constant ##\epsilon_{liquid}=\epsilon## and density ##\rho_l##. The upper air can be considered to have a dielectric constant ##\epsilon_{air}=1##. Now an infinitesimal...
  25. L

    I Humanity: Master fusion reactors or build a dyson sphere?

    What are are your thought on the future of energy on Earth? Personally, in the long term I believe that Dyson spheres would be more useful and allow us to terraform other planets and became a multiplanetary species much quicker and efficiently, but what are your thoughts?
  26. Zack K

    Potential at center of sphere of radius R and charge -Q

    Homework Statement What is the potential at the center of the sphere relative to infinity? The sphere is dielectric with uniform - charge on the surface of the sphere. Homework Equations ##k=\frac {1}{4\pi\epsilon_0}## ##V=\frac {KQ}{r}## The Attempt at a Solution If the distance r=0 it would...
  27. D

    Electronics Need a small motor and fan to blow air into a 4 inch sphere

    I have a 4 inch sphere with a 22 mm opening. Inside this sphere I will have 3 styrofoam balls 20mm diameter each and 3 styrofoam balls about 5 mm each. I need a wind source to blow wind into the ball through a tube approximately the diameter of a drinking straw, the wind being strong enough to...
  28. C

    Flow of Water into a Bowl with Holes

    I'm facing a problem with that rhyming title up there. The design is thus: a downward-facing, vertical pipe with known constant flow and diameter has water flowing out of it, into a short (15cm-91cm) free fall. At the end of that fall is a bowl of indeterminate depth made of steel with holes...
  29. C

    Find the electric field of a point outside sphere

    Homework Statement Find the electric field of a point outside sphere without using Gauss's law. (Do not evaluate the integral) Homework Equations Coulomb's Law Spherical Co-ordinate System The Attempt at a Solution I have attached my attempt as a picture but now I am stuck, I don't know how I...
  30. K

    I Integrating discs to find the gravitational force of a sphere

    I am attempting to prove Newton's shell theorem. There are multiple solutions to this problem, but I am attempting a solution involving adding up the gravitational force of an infinite number of infinitely small disks that are placed together (the discs facing a point mass "m") to form a...
  31. T

    A ball (sphere) rotating along a moving incline

    Homework Statement We have a ball of mass ##m##and radius ##r##. it is placed on an incline (We don't know the angle of the incline, nor we do whether the angle is constant along the incline - maybe it is a curved incline) and then released. The COM of ball is ##h## meters above the incline at...
  32. A

    Variable induced surface charge density on a sphere

    Homework Statement Homework Equations While solving this problem at r >>a ,the corresponding potential due to the dipole is kpcosθ/r2(potential due a dipole) where k is the electrostatic constt. ...(1) If σ(θ) is the surface charge density induced due to external electric field. then the...
  33. AZFIREBALL

    B What would it be like on Earth if it were not a sphere?

    Since I was very young I have wondered what life would be like if the Earth was a different shape. For example, what if Earth were two spheres stuck together rather than just a single sphere?Say the Earth consisted of two, same size, spheres connected at what is now our north pole with a...
  34. M

    Surface area of a shifted sphere in spherical coordinates

    Homework Statement find the surface area of a sphere shifted R in the z direction using spherical coordinate system. Homework Equations $$S= \int\int \rho^2 sin(\theta) d\theta d\phi$$ $$x^2+y^2+(z-R)^2=R^2$$ The Attempt at a Solution I tried to use the sphere equation mentioned above and...
  35. jk22

    B Dimension of the metric of a projection of a sphere

    Let ##(x_1,x_2,x_3)=\vec{r}(\theta,\phi)## the parametrization of a usual sphere. If we consider a projection in two dimension ##(a,b)=\vec{f}(x_1,x_2,x_3)## Then I don't understand how to use the metric, since it is ##g_{ij}=\langle \frac{\partial\vec{f}}{\partial...
  36. Abdullah Wahid

    Positively Charged Metal Sphere: Reactivity & Capacitors

    When we make a metal sphere positively charged by electricity, why doesn't it react with oxygen or any other element in air as metal has positive charges and one of the element in air must react with sphere as I think an ion can never stand in air without reacting? If it reacts, why doesn't...
  37. A

    Question regarding Ray Optics and Probability

    Let there be a sphere whose inner surface consists of a perfectly reflecting surface. It has a hole on it which allows a ray of light to enter. Give the angle made with the normal of the hole when the ray of light enters such that the probability that the ray comes out is the least?Assuming the...
  38. Clara Chung

    Question about a conducting sphere in a varying magnetic field

    Homework Statement 3. A spherical conducting shell is placed in a time-varying magnetic field. Is there an induced current along the equator? Homework EquationsThe Attempt at a Solution I don't know what is the right answer. I mean...why not? Is the magnetic field is changing, there should be...
  39. T

    Electric field of a non-conducting sphere

    Homework Statement A solid non-conducting sphere of radius R carries a uniform charge density. At a radial distance r1= R/4 the electric field has a magnitude Eo. What is the magnitude of the electric field at a radial distance r2=2R? Homework Equations Gauss's Law: ∫EdA=Qencl / ε0 Charge...
  40. C

    Path of a conducting sphere through a uniform magnetic field

    Hello, could someone help answer this question for me: How would the path of a conducting sphere (i.e. AL) be affected as it passes through a strong uniform magnetic field orthogonal to the direction of motion. I believe the Lenz effect/Eddy currents will create a magnetic field opposing the...
  41. Clara Chung

    Metal sphere in an electric field

    Homework Statement The question is exactly the same as this question https://physics.stackexchange.com/questions/250297/metal-sphere-in-a-uniform-electric-field However, it says "Then by symmetry the entire xy plane is at potential zero" in the book. I don't understand this. Homework...
  42. J

    Solid sphere rolling along a track

    Homework Statement Please see the attached file. Homework Equations Ei = Ef The Attempt at a Solution I don't have an answer key provided, but I'd really like to verify that I'm right (or if I'm wrong, why). I think ti'd be (c) because assuming that due to inertia, B will continue going...
  43. X

    I How Do You Transform Qubit States Between Different Bases on the Bloch Sphere?

    Anyone know how to change a basis of a qubit state of bloch sphere given a general qubit state? There are 3 different basis corresponding to each direction x,y,z where |1> ,|0> is the z basis, |+>, |-> is the x basis and another 2 ket notation for y basis. Given a single state in the x basis...
  44. Robin04

    Particle falling inside a sphere due to gravity

    Homework Statement We drill a hole from the surface of the Earth to the other side through the center, drop a test particle and measure the time it takes to come back. How does this time depend on the radius and density of the Earth? Homework EquationsThe Attempt at a Solution The gravitation...
  45. C

    Is there any tensor that gives the radius of a sphere?

    Can I calculate a tensor of a system( lots of particles) shaped like a sphere, then get exactly the radius of the system? (I want to get lengths of three axes of ellipsoid, and I'm trying to examine the way with a sphere. )
  46. H

    A Reference frame conversion for a moving sphere

    Hi here is the situation; There's a spherical particle contained with a MEMS sensor (3D accelerometer and gyroscope) moving down a bed. What we want is to estimate the total kinetic energy of the particle. The total kinetic energy has two parts, translational part and rotational part. for the...
  47. Krushnaraj Pandya

    Ring and solid sphere rolling down an incline - rotation problem

    Homework Statement A solid sphere, hollow sphere, disk and ring are released simultaneously from top of a incline. Friction is sufficient to prevent slipping of hollow sphere- what will reach the bottom first? Homework Equations a in pure rolling down an incline=gsinθ/(1 + I/mR^2) The Attempt...
  48. B

    Optics Experiment involving transmission through a gel and a sphere

    Assume you have the following scenario: Light begins traveling through a gel of index of refraction n=1.34 in a straight line along the x axis. It is then incident on a solid sphere(n=1.36) of radius R in 3-space. Upon transmittance, the light again travels through the gel(n=1.36) and finally...
  49. C

    Finding the energy density outside of an isolated charged sphere

    Homework Statement A charged isolated metal sphere of diameter d has a potential V relative to V = 0 at infinity. Calculate the energy density in the electric field near the surface of the sphere. State your answer in terms of the given variables, using ε0 if necessary.Homework Equations Since...
  50. E

    Formula to calculate the charge in a sphere

    1. The problem is: Which charge will a sphere have if it has a diameter of 0.26 meters and produces an electric field of 1030 N/C in the surface? 2. Gauss Law3. I need the charge of the sphere but i couldn´t find any formula to calculate the charge given the distance (r) and electric field (E)
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