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.

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  1. Z

    Flux Through a Sphere Containing a Dipole

    So I am probably understanding something wrong but would gauss's law \frac{Qinside}{\epsilon0} for a sphere surrounding an electric dipole, with a point charge just outside of the sphere. If you imagine this scenario without the outside charge, the field lines through the surface all come...
  2. D

    Integral on the surface of a sphere - course notes

    Hello, In my electrodynamics course, there's a "maths" introduction and there's something i don't get ! Homework Statement It says that : the integral on the surface of a sphere is ∫1/r da = 4πr'/3 with r=|r'-R|, R the vector from the element da to the center. r'=r'*z^ The Attempt...
  3. H

    Puck on a sphere, energy & Newton's 2nd

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  4. Y

    Electric Field of a Conducting Sphere

    Homework Statement At a distance of 0.206cm from the center of a charged conducting sphere with radius 0.100cm, the electric field is 485N/C . What is the electric field 0.612cm from the center of the sphere? Homework Equations E(r)=1/4∏ε_0 * qr/R^3 where r is radius of the Gaussian...
  5. M

    How can the surface area of a sphere be derived using integration of circles?

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  6. andyrk

    Charged Spherical Shell and Solid Sphere

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  7. andyrk

    Why Does Earthing a Charged Sphere Neutralize Its Charge?

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  8. E

    Field of a grounded sphere - Scilab

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  9. O

    Average distance to surface of sphere

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  10. G

    Mie scattering for sphere with constant dipole moment

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  11. T

    Electric field in a hollow charged sphere

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  12. Ackbach

    MoI of a Sphere using Spherical Coordinates

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  13. Astrum

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  14. G

    Greens function and the conducting sphere

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  15. P

    Sphere has the minimum surface area?

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  16. Crazymechanic

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  17. R136a1

    Are Maps on a Sphere Homotopic if They Avoid Antipodal Points?

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  18. mesa

    How to derive the surface area of a sphere?

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  19. X

    How do you create a perfect sphere?

    the formula for the surface area of a sphere is SA = 4 (pi) r2, with pi = 22/7 and r = radius of the sphere. for example the SA for Earth with a radius of 6,378 km is 510,065,600 km2 what would the radius be in order that for you to lay a grid of perfect square on the surface of the sphere?
  20. Z

    Would a big enough manmade metal sphere have gravity?

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  21. 6

    Torque on a point on a sphere in a fluid/finding pressure?

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  22. Saitama

    Ray optics - Reflection from sphere

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  23. D

    What is the mass of the sphere?

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  24. F

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  25. Feodalherren

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  26. C

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  27. K

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  28. H

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  29. M

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  30. A

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  31. D

    Slipping Sphere on Steep Incline

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  32. B

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  33. andyrk

    Oblique Impact of a smooth sphere against a fixed plane

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  34. A

    Dielectric Sphere in Uniform Field

    Hi, One of the boundary conditions when solving for the potential, \Phi, outside a dielectric sphere placed within a uniform electric field is \lim_{r→0}\Phi(r,θ)<\infty Can anyone explain/prove why this so. Thanks,
  35. J

    Optimization: maximum curved surface area of a cylinder in sphere

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  36. S

    Finding the volume of a sphere with a double integral

    Homework Statement I know how to find the volume of a sphere just by adding the areas of circles, so I decided to do a double integral to find the same volume, just for fun. Here's what I've set up. I put 8 out front and designed the integrals to find an eighth of a sphere that has its center...
  37. S

    Type of curvature of gradient force from edge to center of a sphere

    I was doing some simple physics with a ball resting on a table and I made this curve (0,0) (25, 6.8) (50, 27.51) (75, 63.4) (100, 112.34) (125, 175.7) (150, 253.3) (175, 345.4) I was wondering if anyone could identify what sort of curve it is? I am just curious. This is not a homework...
  38. R

    Steady state conduction in a hollow sphere

    Hello, I'm having trouble with a conduction problem, I have access to the answer but not the solution. I did it on my own and my value is half of what the answer is. Now, my calculus is a little rusty, but I don't know where I am going wrong. So the dimensions and temperatures of the sphere...
  39. A

    Classical Limit formula for differential cross section for Hard Sphere

    I am looking for the derivation to an approximation formula for the differential cross section for hard sphere scattering in the limit of high energy. The paper that mentioned this had referred to Methods of Theoretical Physics, PM Morse and H. Feshbach page 1484 but I have no access to the...
  40. J

    Why Does the Disk Method Integrate Only Half the Sphere's Volume?

    Homework Statement Check that the volume of a sphere is 4/3(pi)r^3 (use disk method) So I don't understand it I got stuck so I looked. I still don't get their solution. Chapter 7, section 2, question 59. http://www.calcchat.com/book/Calculus-ETF-5e/ Homework Equations The...
  41. T

    Work Done by an Insulating Sphere on a test charge

    Homework Statement An insulating sphere of radius 0.240 has uniform charge density 6.50×10−9 . A small object that can be treated as a point charge is released from rest just outside the surface of the sphere. The small object has positive charge 4.10×10−6 How much work does the electric...
  42. E

    Mass conservation for pulsating sphere

    Hi, I'm trying to understand the mass conservation equation for a pulsating sphere which has thickness dr. Please refer to the attached solution. \rho = \rho_{0} (ambient density) + \rho' (small deviation) There are two things I don't follow. First, is that to obtain the mass, the area of...
  43. Y

    Intersection of a sphere and plane

    Homework Statement Show that the circle that is the intersection of the plane x + y + z = 0 and the sphere x2 + y2 + z2 = 1 can be expressed as: x(t) = [cos(t)-sqrt(3)sin(t)]/sqrt(6) y(t) = [cos(t)+sqrt(3)sin(t)]/sqrt(6) z(t) = -[2cos(t)]/sqrt(6) Homework Equations The...
  44. A

    How to uniformly charge an insulating sphere?

    In my Physics book there was this problem of finding electric field produced by the sphere, such that electric charge is distributed uniformly throughout the volume of an insulating sphere. I know that excess charge tends to distribute itself on the surfaces, but since this sphere is made...
  45. E

    Rotating disk/ sphere and moving mass along it

    Coriolis effect - In a non-friction system, f I roll something along the surface of the planet from on of the poles to the equator, it will appear to move to the west, it will essentially stay behind the planets rotation and actually rotate it in the opposite direction. Now, if we add friction...
  46. Saitama

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  47. B

    Why does everything in the Universe form a ball or Sphere?

    I want to know why everything in the universe forms a Ball or Sphere? Is gravity the cause of this? If so why? For example, If we were to pick the sphere apart can we see the source of gravity? Is gravity also a ball or sphere and can we grasp and see it? Why do we not ever see square planets or...
  48. P

    Volume of two pieces of a sphere cut by a plane

    Homework Statement Consider the unit sphere x^{2} + y^{2} + z^{2} = 1 Find the volume of the two pieces of the sphere when the sphere is cut by a plane at z=a.The Attempt at a Solution My interpretation is that a is a point on the z-axis that the plane cuts at. So the height of the segment...
  49. J

    Any one interesed in tasking on a formula for the volume of a sphere.

    An alternate one by the by. My approach will be working with a base ten logarithm function(s). I'm going to graph the sphere on a 3d graph. I'm going to give the value of the radius, one unit. I will first look at the ten elevations up and down from the index, establish the area at each...
  50. P

    Finding Radius of Curvature of a Sphere Using Angle Excess

    On the surface of a sphere, we can find the radius of cuvature of the sphere by: angle excess / area = 1/ r_s^2 http://en.wikipedia.org/w/index.php?title=Angle_excess&oldid=543583039 If we use triangles, for instance, the angle excess is the sum of the angles of the triangle minus 180...
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