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

    What happens if you put a sphere (ball) on the top of a pyramid?

    I was wondering what happens if you put a perfect sphere (a ball) on the top of a perfect pyramid. To which side will the ball fall and why? It is random? An if it is, does a pattern emerge after many attempts?
  2. G

    Modulus of the electric field created by a sphere

    I think the right solution is c). I'll pass on my reasoning to you: R=6\, \textrm{cm}=0'06\, \textrm{m} \sigma =\dfrac{10}{\pi} \, \textrm{nC/m}^2=\dfrac{1\cdot 10^{-8}}{\pi}\, \textrm{C/m}^2 P=0'03\, \textrm{m} P'=10\, \textrm{cm}=0,1\, \textrm{m} Point P: \left. \phi =\oint E\cdot...
  3. P

    Electric field at the center of a sphere

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  4. A

    Rotational Mechanics -- A solid sphere is rolled on a rough surface

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  5. M

    Work done by pushing a proton into the sphere with non-uniform charge

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  6. Z

    B Would a Dyson sphere need a "relief valve?"

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  7. O

    How to create a uniformly charged sphere?

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  8. F

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  9. G

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  10. G

    I Visualizing the cotangent space to a sphere

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  11. G

    Electric field around a sphere with an internal charge distribution

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  12. Edward Candle

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  13. Z

    Electric field direction on a grounded conducting sphere

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  14. Mounice

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  15. Leo Liu

    Understanding the Electric Field of a Charged Sphere

    This page claims that "[t]he electric field outside the sphere is given by: ##{E} = {{kQ} \over {r^2}}##, just like a point charge". I would like to know the reason we should treat the sphere as a point charge, even if the charges are uniformly distributed throughout the surface of the...
  16. F

    B Is εσT⁴ hemispherical or full sphere?

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  17. Adrian555

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  18. S

    Potential difference between the surface of a sphere and a point far away

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  19. S

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  20. karush

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    ?
  21. B

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  22. G

    Gauss-Theorem on a solid dielectric sphere

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  23. Z

    Find the electric field on the surface of a sphere using Coulomb's law

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  24. Saptarshi Sarkar

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  25. fisher garry

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  26. B

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  27. Luke Tan

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  28. E

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  29. D

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  30. Heyxyz

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  31. M

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    I'm a bit confused about the notation used in the exercise statement, but if I'm not misunderstanding we have $$\begin{align*}(\psi^+_1)^{-1}:\begin{array}{rcl} \{\lambda^1,\lambda^2\in [a,b]\mid (\lambda^1)^2+(\lambda^2)^2<1\}&\longrightarrow& \{\pm x_1>0\}\subset \mathbb{S}^2\\...
  32. Arman777

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    I tried to use ##W = ε_0/2 \int E^2d\tau## for all space. So I find that ##E = \frac{(R^3 - b^3)\rho}{3ε_0r^2}## where ##\rho## is the charge denisty. So from here when I plug the equation I get something like $$W = \frac{(R^3 - b^3)^2\rho^2 4 \ pi}{18ε_0} \int_{?}^{\inf}1/r^2dr$$ Is this...
  33. E

    Line charge inside a conducting sphere?

  34. S

    Force on a sphere due to a conducting plate

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  35. A

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    Homework Statement: A perfect hemisphere of frictionless ice has radius R=6.5 meters. Sitting on the top of the ice, motionless, is a box of mass m=6 kg. The box starts to slide to the right, down the sloping surface of the ice. After it has moved by an angle 20 degrees from the top, how much...
  36. S

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  37. sdefresco

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  38. snatchingthepi

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    So I got an assignment returned to me with fewer marks than I had expected. One part in particular is confusing to me. The professor is only available on Monday for a tutorial, but I'd like to see what is wrong before then. Can anyone spot why this is incorrect?
  39. bob012345

    A What is the solution for two electrons on a sphere?

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  40. Celso

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    Honestly I don't know where to begin. I started differentiating alpha trying to show that its absolute value is constant, but the equation got complicated and didn't seem right.
  41. F

    Why is the magnitude of the electric field in a sphere the same?

    I was looking at a sphere that has a positive point charge at the center of a sphere with radius R. Now, I understand that the electric field is pointing outwards (in the direction of dA), so $$d\phi = EdA$$ However, I am told that since the magnitude electrical field is the same because the...
  42. Kaushik

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  43. K

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  44. George Keeling

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  45. George Keeling

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  46. Kaushik

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  47. elisagroup

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  48. G

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  49. N

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  50. confusedhome

    I Amount of energy inside a sphere of radius 1au around the Sun

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