Sphere Definition and 1000 Threads

A sphere (from Greek σφαῖρα—sphaira, "globe, ball") is a geometrical object in three-dimensional space that is the surface of a ball (viz., analogous to the circular objects in two dimensions, where a "circle" circumscribes its "disk").
Like a circle in a two-dimensional space, a sphere is defined mathematically as the set of points that are all at the same distance r from a given point in a three-dimensional space. This distance r is the radius of the ball, which is made up from all points with a distance less than (or, for a closed ball, less than or equal to) r from the given point, which is the center of the mathematical ball. These are also referred to as the radius and center of the sphere, respectively. The longest straight line segment through the ball, connecting two points of the sphere, passes through the center and its length is thus twice the radius; it is a diameter of both the sphere and its ball.
While outside mathematics the terms "sphere" and "ball" are sometimes used interchangeably, in mathematics the above distinction is made between a sphere, which is a two-dimensional closed surface embedded in a three-dimensional Euclidean space, and a ball, which is a three-dimensional shape that includes the sphere and everything inside the sphere (a closed ball), or, more often, just the points inside, but not on the sphere (an open ball). The distinction between ball and sphere has not always been maintained and especially older mathematical references talk about a sphere as a solid. This is analogous to the situation in the plane, where the terms "circle" and "disk" can also be confounded.

View More On Wikipedia.org
Recent contents Top users
  1. D

    Electric field inside and around a hollow sphere

    Hi everyone, I am wondering if anybody could help me out. For my study I got the following question but I got stuck in part C (see image below). I Found at A that due to symmetry all components which are not in Ar direction will get canceled out I found at B that there is only charge density at...
  2. S

    What Is the Electric Field Inside a Sphere with Varying Charge Density?

    Homework Statement A sphere with radius R has a spherically symmetric charge density that varies as 1/r. What is the electric field outside and inside the sphere? Homework Equations E=kQ/r^2, ε=permitivity of free space, Q=total charge, ρ=charge density, dτ=infinitesimal volume The Attempt at...
  3. J

    Potential Outside charged metal sphere in uniform E field

    Homework Statement Find the potential outside a charged metal sphere (charge Q, radius R) placed in an otherwise uniform electric field E0. Explain clearly where you are setting the zero of potential. 2. The attempt at a solution So for this problem I figured I could exploit superposition and...
  4. moenste

    Distance traveled and the kinetic energy of a sphere

    Homework Statement A 'hammer' thrown in athletics consists of a metal sphere, mass 7.26 kg, with a wire handle attached, the mass of which can be neglected. In a certain attempt it is thrown with an initial velocity which makes an angle of 45 degrees with the horizontal and its flight takes 4...
  5. S

    Wall effect on falling sphere of small Reynolds number

    If I were to drop a sphere down a tube of fluid. What are the effects of the wall of the tube on the sphere? Assuming the sphere has an extremely low Reynolds number of less than 1. Is it right to say that the ratio of the radius of the tube and the radius of the sphere has an effect on the...
  6. G

    Geometry on a Sphere: Euclidean or Something Else?

    Hope I am on the right forum (and that my question makes some sense-so here goes. Imagine we are a race of people living on a sphere (not hard because we are) However , rather than buying into the idea that lines are ideally straight we are and have always been well aware of how "parallel...
  7. not_waving

    Electric field of a sphere in a point A

    My first homework for electrostatics course I'm taking is to find the vector of electric field of a completely hollow sphere (radius r, surface charge density σ in a point A, by integrating the electric field through the whole sphere. I already figured out the electric field of a ring in a point...
  8. KastorPhys

    Moment of Inertia of a sphere with different methods

    Hi everyone, I am trying to find out the Moment of Inertia of a sphere which is all known to be 2/5(m)(r^2) I calculate this in 2 ways. One by triple integration and one by disk method. From the textbooks, moment of inertia should be in the form, dI = (r^2) dm, However, the textbook, University...
  9. P

    Capacitance of Connected Spheres: Finding dq1/dt

    Homework Statement 1) Two solid conducting spheres have radius r1 = 3 cm and r2 = 42 cm. The two spheres are connected by a thin conducting wire. Assume: - the wire is very long and thin, with negligible surface area, so it does not affect the capacitance of the system. - the switch is...
  10. T

    Area of triangle on sphere problem.

    Homework Statement What is the area of a triangle on Earth that goes from the North Pole down to the equator, through the prime meridian, across the equator to 30 degrees east longitude, then back up to the equator? The radius of the Earth is about 6378 km. Homework Equations alpha + beta +...
  11. H

    Electric Potential in an Insulating Sphere

    Homework Statement A solid insulating sphere of radius a = 4.3 cm is fixed at the origin of a co-ordinate system as shown. The sphere is uniformly charged with a charge density ρ = -421 μC/m3. Concentric with the sphere is an uncharged spherical conducting shell of inner radius b = 14.6 cm, and...
  12. goonking

    Intersecting Line & Unit Sphere: Find Point of Intersection

    Homework Statement Does the line through the points (−1, −1, −2) and (1, 2, 1) intersect the unit sphere? If so, find the point(s) of intersection. Homework EquationsThe Attempt at a Solution do i also use r = r0 + vt but instead , use equation of sphere this time? so it would be: v=<2,3,3>...
  13. xSpartanCx

    Flux through a sphere due to a charge outside of it

    Homework Statement A point charge of +5.00 μC is located on the x-axis at x= 5.00 m , next to a spherical surface of radius x= 4.00 m centered at the origin. [/B] According to Gauss's law, the net flux through the sphere is zero because it contains no charge. Yet the field due to the external...
  14. S

    3D object represent with primitive shapes

    Hi, Given a 3D object in R3 space can we represent it using three basic primitive shapes like Sphere, Cone and Cylinder? Would this claim be valid?
  15. S

    Problem integrating over a sphere.

    Homework Statement Compute \int_S \vec{F} \cdot d\vec{S} \vec{F} = (xz, yz, z^3/a) S: Sphere of radius a centered at the origin.Homework Equations x = a \sin(\theta) \cos(\varphi) y = a \sin(\theta) \sin(\varphi) z = a \cos(\theta) Phi : 0->2 pi, Theta : 0->pi/2 . The Attempt at a...
  16. B

    2 sphere system, Conservation of Energy and Momentum

    Homework Statement [/B] A sphere of radius $1m$ and mass $25 Kg$ is put on another sphere of radius $5 m$ and $7 Kg$ which is placed on a smooth ground. Now the upper sphere is pushed very slightly from it's equilibrium position and it begins to fall. Now when the line joining the centre of...
  17. S

    Potential energy of a non-uniform density sphere

    Homework Statement Perform potential energy W of a non-uniform density sphere by density d=d(r) and o(r)=dW/dm. Homework Equations The answer is W=1/2.integral(from 0 to R)(4x3.14xd(r)xo(r)xr^2xdr). The Attempt at a Solution I have solved this by this way: o(r)=-GM(r)/r...
  18. SquidgyGuff

    Potential of a spherical shell (non-uniform charge density)

    Homework Statement Given a spherical shell of radius R and the surface charge density ( being the angle from the top of the sphere and being a constant) find the electric potential and the electric field inside and outside the sphere. Check that both the potential is continuous inside and...
  19. MidgetDwarf

    Cal 3, writing an equation of a sphere with r=7...

    Write the equation of the sphere with radius 7 and center on the positive z-axis, if the sphere is tangent to the plane z=0. I know this is an easy problem if i understood the terminology better. The equation of a sphere (x-h)^2 +(y-k)^2 +(z-l)^2 = 49. I know that the plane z is the set...
  20. M

    Rotations in Bloch Sphere, and Free Parameters of a Qubit

    This question is mostly about group theory but I would like to understand it in the context of qubits rotating in a Bloch Sphere. What my understanding of things are right now: In the rotation Lie Group ##SO(3)##, we have three free parameters (##\frac{n(n-1)}{2}##), and this is also why we end...
  21. P

    Matrix Representation of a Uniform Sphere Centered at the Origin

    What is the basic matrix form for a uniform (unit) sphere centered at the origin? Given a vector that specifies the radii (1,1,1) == (r1,r2,r3), I would like the matrix that implies no rotation (is it [[1,0,0],[0,1,0],[0,0,1]]?) and covers the rest of the necessary parameters. I am testing...
  22. R

    [mechanics] radius of a sphere with critical mass

    Homework Statement Here is the question: "In the fall of 2002, a group of scientists at Los Alamos National Laboratory determined that the critical mass of neptunium-237 is about 60 kg. The critical mass of a fissionable material is the minimum amount that must be brought together to start a...
  23. D

    Volume of a sphere with a cylindrical hole

    Hello all, I am doing homework and have come upon this question: A cylindrical hole is drilled all the way through the center of a sphere (as shown in the figure below). Show that the volume of the remaining solid depends only on the length L of the hole, not on the size of the sphere. Figure...
  24. Rene Manzano

    Solid conductor sphere with cavity inside

    Hi, this is my modified post since I've been told that I have to use certain format. I hope this is good now. Homework Statement Copper (conductor) sphere of radious R with an spheric bubble inside placed at distance c from the center, with radius b. The metalic sphere has charge Q.Homework...
  25. Grimble

    Does a cone cut from a sphere have a name?

    A very basic question: does such a cone, where the broad end is not cut flat but follows the surface of the sphere whose radius is the length of the cone's side, and is centred at the cone's point, have a name?
  26. B

    Conducting sphere within a conducting shell

    Homework Statement A hollow spherical shell (B) with inner radius R2 and esternal radius R3 is negatively charged with Q. A spherical conducter (A) with radius R1 is placed within the the shell. A is charged with Q. The centers of both shells coincide. Then a negative point charge q is placed...
  27. Ebenshap

    How inverse square law is derived from area of sphere

    I almost understand how the inverse square law is derived from the area of sphere equation, 4πr2, but I'm not quite clear on what happens to the 4π. I found one equation that seemed to say that the intensity is equal to the area of the sphere of the source point times the amount of whatever...
  28. Adoniram

    Particle sliding down a sphere - When does it leave the sphere?

    Homework Statement A particle is placed on top of a smooth (frictionless) sphere of radius R. If the particle is slightly disturbed, at what point will it leave the sphere? Homework Equations Same as first question, just F = ma = ΣF_i The Attempt at a Solution Similarly, we want to know when...
  29. Tony Stark

    Curvature of spacetime inside hollow sphere

    If mass curves spacetime in its vicinity, then consider the following case- Take a heavy hollow lead sphere which has 2 smaller lead balls placed in it. The Outer Sphere will curve spacetime around itself and thus will have its own gravity, but what about the 2 balls placed in it? The spacetime...
  30. T

    Power from Sound: Fans Create 12.56 Watts 1km Away

    Homework Statement Fans at a stadium produce sound that is heard 1km away, the intensity level is 60 dB. How much acoustic power is generated by the fans? Homework Equations B = 10 log (I÷I_0) P=I*A The Attempt at a Solution I= 10^-12*6^10= 10^-6W/m^2 P= 10^-6*4pi*1000^2 =12.56W However...
  31. fluidistic

    Uniformly magnetized sphere, calculate force between the hemispheres

    Homework Statement A uniformly magnetized sphere of radius R has a magnetization ##\vec M=M_0\hat z##. Calculate the force between the hemispheres whose contact surface is the zx plane. Indicate the direction of the force. Homework Equations Hints: ##\vec B_{\text{int}}=\frac{2}{3}\mu _0 M_0...
  32. Noctisdark

    Electric field due to a charged sphere

    Another problem that yet I haven't managed to solve, finding the electric field due to a charged sphere of radius R using integration Homework Equations Continuous charged distribution $$|\vec E| = \frac{1}{4\pi\epsilon_0}\displaystyle \int\frac{\rho (r') dV}{r'^2}$$ The Attempt at a Solution...
  33. fricke

    Calculating Line Integrals on the Surface of a Sphere

    What's the line integral of sphere? Is it possible to get the line integral in three dimensions? What kind of line are we integrating?
  34. fluidistic

    Moving sphere in magnetic field

    Homework Statement I got no credit in an exam for the following exercise and I've been told what's wrong but even then I am unable to solve it correctly. A conducting sphere with radius R moves with constant velocity ##\vec v =v \hat x## (v <<c) inside a constant magnetic field ##\vec B =B \hat...
  35. Dvorak

    Are Di-Atomic Molecules spherical?

    It is usually said that molecules are spherical in shape, that is what we learn from our textbooks. May be what they are saying is true but only in the case of a monatomic molecule. If one considers a diatomic molecule there are two atoms that means two spheres and if it is polyatomic there is...
  36. I

    Pressure exerted by water on Sphere partially exposed at end

    Homework Statement There is a cylindrical container that has a small hole of radius ##a ( < R)## at the bottom. A sphere of radius ##R## and density ##\rho_{s} > \rho_{w}## is placed in the cylinder such that it completely covers the hole (a part of it sticks out as in attached figure). The...
  37. G

    Sphere enclosed in shell is expanded, find work done

    Homework Statement Consider a non-conducting sphere of radius 'R' and charge 'Q' is enclosed by spherical shell of radius '5R' and charge '4Q'. If inner sphere is expanded to radius '3R'.Then amount of work done by the field in this process is Homework Equations W=ε0/2∫E2dτ The Attempt at a...
  38. P

    Why is black hole photon sphere outside the event horizon?

    Homework Statement I am preparing a report on black holes and I recently learned about a phenomenon I was previously unaware of: the photon sphere of a black hole. While reading an article on said occurrence (I have now confirmed this on multiple sources) the photon sphere which is the minimum...
  39. J-dizzal

    Statics, equilibrium sphere in a groove on an incline plane

    Homework Statement The smooth homogeneous sphere rests in the 132° groove and bears against the end plate, which is normal to the direction of the groove. Determine the angle θ, measured from the horizontal, for which the reaction on each side of the groove equals the force supported by the end...
  40. ckirmser

    How Do 3D Coordinates and Radii Affect Vector Paths Between Points?

    I'm not sure if this is the right forum - please move the thread, if not - but, here goes... I have a collection of 3d coordinates, each with a radius of varying amounts. Each of the coordinates is to be linked to each of the others, unless a third coordinate - with its radius - blocks the...
  41. Tony Stark

    Calculating Area and Volume of a sphere through line element

    Homework Statement Flat space-time in polar coordinate is considered. The line element is ds2= -dt2+dr2+r2(dθ2+sin2θdΦ2) The actual answers are given below, but I can't come up to them. Need urgent help. Homework Equations dA = √g11g22 dx1 dx2 dV = √g11g22g33 dx1 dx2dx3 The Attempt at a...
  42. L

    Coulomb triple integral for a sphere

    Homework Statement Find the electric field of a sphere of radius R and charge Q outside sphere. Use only a Coulomb integral to do this. Homework Equations I know that I have to use a triple integral to find the E-field. I am just unsure of my whole setup really. The Attempt at a Solution...
  43. J

    Rolling down a sphere: slipping vs. separating

    There is a nice problem in Taylor: Classical Mechanics of a puck sliding without friction down a sphere in a uniform gravitational field (problem 4.8). The question there was at which height the puck takes off from the sphere, which is not hard to solve using conservation of energy. This...
  44. S

    1g (gravitational acceleration) Sphere of U238

    How big would a sphere of U238 have to be to reach 1g at its surface?
  45. X

    Understanding the RCS of a Sphere: Deciphering Confusing Results

    Hello, I am having an issue understanding something about the RCS of a sphere. The radar cross section of a sphere in the back-scattered, mono-static direction is simply equal to the spheres cross sectional area, for wavelengths much less than the circumference. In the following link...
  46. T

    What slows down a rolling sphere?

    Homework Statement My teacher said that static friction can't slow down a sphere, when I during his office hours, and he gave he said that they don't do work on a rolling sphere... instead rolling friction is what slows down a sphere. Can someone explain to me how rolling friction works and...
  47. V

    Calculating Area on Sphere: Unit Sphere & Rings

    How to calculate some general area on a sphere for simplicity the unit sphere. Let's say I have a ball and I draw a ring on it. What is its area? I guess I need some initial point (some coordinate). Let's take a spherical coordinates with r=1. Element of area is \sin(\theta) d \theta d \phi ...
  48. gimak

    Gauss' law for point charge inside sphere off center

    Homework Statement If a point charge is inside a Gaussian sphere but is off center, why is its electric field still Qenc/(e0*4*pi*r^2)?Homework Equations surface integral of E*da=Qenc/e0The Attempt at a Solution If we draw cones out from the charge. the 2 surfaces from the cones' intersection...
  49. Sobe118

    Point movement on a surface of a sphere

    I'm trying to find the resulting location of a point on a sphere in spherical coordinates or Cartesian. Based on velocities from the perspective of an object on the sphere. So given the: location on the sphere (in spherical or Cartesian) zy - plane rotation of the point up direction of the...
  50. jdsconsumer

    Mass, Volume, Density work with a Sphere

    A spherical shell has an outside radius of 2.75 cm and an inside radius of a. The shell wall has uniform thickness and is made of a material with density 4.59 g/cm3. The space inside the shell is filled with a liquid having a density of 1.00 g/cm3. (a) Find the mass m of the sphere, including...
Back
Top