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. LCSphysicist

    I'm not understanding how to calculate the magnetic field of a sphere

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  2. yucheng

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  3. Russ Edmonds

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  4. eric11201120

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  5. P

    Solving Sphere in Cone Problem w/Semivertical Angle

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  6. Drakkith

    B Mass and Surface Gravity of a Dyson Sphere

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  7. RodolfoM

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    I tried to find the charge distribution using the given potential but couldn't produce the correct result. Also, Gauss's Law doesn't help, as the electric flux is 0 but we don't have any symmetry. Can someone please shine a light on this? Thanks in advance..
  8. P

    Moment of Inertia of a sphere about an axis

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  9. E

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  10. J

    I Is the Surface of a Sphere Locally Flat?

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  11. Eagle9

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  12. S

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  13. AN630078

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  14. J

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  15. H

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  16. P

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  17. P

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  18. P

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  19. A

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  20. A

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  21. H

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  22. brotherbobby

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  23. A

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  24. .Scott

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  25. LCSphysicist

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  27. .Scott

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  28. E

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  29. cwill53

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  30. B

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  31. Haorong Wu

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  32. G

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  33. Chris Miller

    B Shape of Hubble sphere at relativistic velocity

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  34. TheGreatDeadOne

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  35. S

    Deriving relations for a hard sphere phase diagram

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  36. E

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  37. agnimusayoti

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    Well, in this problem, I try to use $$d \tau '= \mu ^2 \sin {\theta} {d\mu} {d\theta} {d\phi}$$ With these domain integration: $$0<\mu<r$$ $$0<\theta<\pi$$ $$0<\phi<2\pi$$ , I get $$V=\frac{1}{4\pi \epsilon_0} \frac{3Qr^2}{2R^3}$$ This result is wrong because doesn't match with Prob 2.21, which...
  38. B

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    I used the potential at the surface of the sphere for my reference point for computing the potential at a point r < R in the sphere. The potential at the surface of the sphere is ## V(R) = k \frac {Q} {R} ##. To find the potential inside the sphere, I used the Electric field inside of an...
  39. E

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  40. A

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  41. Tony Hau

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  42. P

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  43. preachingpirate24

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  44. brotherbobby

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    I draw a sketch of the diagram to the right. The body has a radius of ##r_B = 0.2## m. The volume of the body is given by ##V_B = \frac{4}{3}\times \pi \times 0.2^3 = 0.034\;\text{m}^3##. The mass of the body : ##w_B = \rho_B V_B = 400\times 0.034 = 13.37\,\text{kg}##. Hence the mass of the...
  45. R

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  46. M

    Integrating ##\sigma=\chi\int{dA/A}## for a sphere

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  47. rxh140630

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  48. Amitkumarr

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  49. omar558

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  50. Nexus99

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