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. N

    What Charge Must a Wooden Sphere Have to Float Above the Earth?

    Hello, everyone :-) We have a wooden sphere at a height of h = 1 m above the surface of the Earth which has a perimeter of RZ = 6 378 km and a weight of MZ = 5.97 · 10^24 kg. The sphere has a perimeter of r = 1 cm and is made of a wood which has the density of ρ = 550 kg·m − 3. Assume that...
  2. S

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  3. Saitama

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  4. K

    Circle Expansion on Expanding Sphere

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  5. Superposed_Cat

    Volume of n-dimensional sphere

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  6. M

    A small lump of ice sliding down a large, smooth sphere.

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  7. B

    Comoving redshift and area of sphere

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  8. T

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  9. S

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  10. S

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  11. V

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  12. B

    Calculating Flux through a Sphere using Cylindrical Coordinates

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  13. B

    Flux Through Sphere: Cylindrical Coordinates

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  14. Philosophaie

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  15. C

    Calculus of Variation - Shortest path on the surface of a sphere

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  16. C

    E-field & hollow non-conducting sphere

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  17. U

    Minimum linear velocity attained by sphere

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  18. Q

    Calculating Change in Volume of a Shrinking Sphere

    Homework Statement http://i.minus.com/jbxIzu0P7sTqP0.png Homework Equations V(sphere) = 4/3(pi)(r^3) V = 36pi in^3 dr = -0.2 in dV = ? The Attempt at a Solution I basically solved for the radius, and took the derivative and plugged in the value of the radius and the...
  19. J

    Electrostatics - hollow charged sphere

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  20. M

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  21. PsychonautQQ

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  22. PsychonautQQ

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  23. PsychonautQQ

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  24. ShayanJ

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  25. L

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  26. B

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  27. B

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  28. J

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  29. M

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  30. B

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  31. R

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  32. N

    Sphere Volume Calculation: Bore Hole of Radius r in Sphere of Radius R

    Homework Statement A hole of radius r is bored through the center of a sphere of radius R. Find the volume V of the remaining portion of the sphere. Homework Equations The Attempt at a Solution Wouldn't is be (4/3)∏(R^3-r^3)?
  33. M

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    Homework Statement A beam of parallel light rays from a laser is incident on a solid transparent sphere of index of refraction n1 (see figure). (a) If a point image is produced at the back of the sphere, what is the index of refraction of the sphere? (b)What index of refraction, if any, will...
  34. J

    Accelerated charge inside sphere (again)

    Sorry to go on about this scenario again but I think something is going on here. Imagine a stationary charge ##q##, with mass ##m##, at the center of a stationary hollow spherical dielectric shell with radius ##R##, mass ##M## and total charge ##-Q##. I apply a force ##\mathbf{F}## to charge...
  35. C

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  36. B

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  37. C

    Help with magnetic field in sphere problem

    Homework Statement Consider a polycrystalline sample of Subscript[CaSO, 4]\[CenterDot]2 Subscript[H, 2]O in an external magnetic field Overscript[B, \[RightVector]] in the z direction. The internal magnetic field (in the z direction) produced at the position of a given proton in the...
  38. Z

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  39. T

    Why integrate at these points? (Electric potential of a sphere)

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  40. O

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  41. M

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  42. P

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  43. J

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  44. atyy

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  45. K

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  46. M

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  47. T

    Find Electric Field Around a Non-Conducting Sphere

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  48. H

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  49. D

    Finding Electric Field from an insulating sphere

    An insulating sphere with a radius of (3.3E-2) m has a uniform charge density of (6.74E-6) C/m^3 throughout its volume. (1)Find the magnitude of the electric field at a point (5.7E-2) m from the center of the sphere. (2) Find the magnitude of the electric field at the surface of the...
  50. B

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    Homework Statement Standard E field problem where I'm to find the field at 3 positions of a hollow sphere that has a charge density k/r^2 r ≤ a a ≤ r < b b ≤ r Homework Equations ∫Eda=Q/ε The Attempt at a Solution I guess the thing that is tripping me up are the limits. I know...
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