What is Sphere: Definition and 1000 Discussions

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. H

    Why V=max inside a charged sphere?

    Inside a charged sphere, the electric field strength is zero because there are electrostatic forces from all directions. I can't understand why electric potential inside the charged sphere is maximum ?
  2. D

    Light reflecting off sphere -- Momentum transfer

    Homework Statement Suppose light of momentum -P\hat{\textbf{k}} is shone on a sphere of radius R. What is the momentum transferred onto the sphere? Homework Equations The Attempt at a Solution I think the transferred momentum upon reflection is given by (-2P\hat{\textbf{k}} \cdot...
  3. J

    Density: Cube of Aluminum to Copper Sphere

    Homework Statement What is the diameter of a copper sphere that has the same mass as a 9.00 cm× 9.00 cm× 9.00 cm cube of aluminum? Density of Aluminum = P(al) = 2.70g/cm3 Density of Copper = P(cu) = 8.96 g/cm3 Volume of Aluminum Cube = Vcube = 729 cm3 Homework Equations Volume of a Sphere =...
  4. olgerm

    Troubleshooting N-Spherical Cap Area Formula

    I am trying to understand N-spherical cap area formula (surface area of blue part), but it seems to give wrong answers. for 1 dimensional cap obviously ## \frac{l_{cap}}{l_{sphere}}=\frac{l_{arc}}{l_{circle}}=\frac{r*θ}{r*2π}=\frac{θ}{2π} ## But according to wikipedia formula...
  5. G Cooke

    Maximum negative voltage of a sphere?

    I would like to know the maximum voltage that a metal sphere can hold from applying negative charge to it. My thoughts are that the maximum voltage is the breakdown voltage of the surrounding medium (air in this case). I assume that at that voltage, electrons would arc from the sphere to the...
  6. 24forChromium

    Non-Euclidean area defined by three points on a sphere

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  7. C0balt

    Upthrust/ how does the weight of a sphere change in water?

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  8. sergiokapone

    Metrics of rotating sphere in GR

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  9. F

    What is the electric field due to hollow sphere at R=z?

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  10. A

    Electromagnetic induction by a rotating sphere

    Homework Statement http://physics.columbia.edu/files/physics/content/Quals2010Sec2.pdf Problem 1 Consider a rigid, ideally conducting sphere of radius R, with total charge zero. The sphere rotates with angular velocity Ω, ΩR<<c. Suppose a dipole magnetic field threads the sphere. the dipole is...
  11. G Cooke

    How is voltage on a sphere affected by edges?

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  12. goonking

    MATLAB How to add normal vectors/quivers to sphere in matlab?

    so I got my sphere, centered at (1,-2,0) with radius 3 how do I put normal vectors/arrows onto my sphere's surface? I tried quiver3(x,y,z)
  13. Ebenshap

    Archimedes' area of a sphere proof; proposition 2

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  14. J

    Derivation of moment of inertia of a solid sphere

    Homework Statement I need to know why my derivation does not work. I am attempting to derive I=2/5 mR^2Homework Equations I have seen people derive it using disks but my question is why do the shells not work? Where in my set up did I go wrong? Thanks The Attempt at a Solution I am attempting...
  15. T

    Surface area of a sphere with calculus and integrals

    Homework Statement How do I find the surface area of a sphere (r=15) with integrals. Homework Equations Surface area for cylinder and sphere A=4*pi*r2. The Attempt at a Solution I draw the graph for y=f(x)=√(152-x2). A circle for for positive y values which I rotate. I will create infinite...
  16. jcruise322

    Why Do We Use Ramp Length Instead of Height in Rolling Sphere Calculations?

    Homework Statement A sphere of radius .06 m and mass .5 kg rolls down a ramp that is angled 30 degrees down the incline. It starts rolling from a height of 7 feet and does not slip What is its final linear velocity? Now, I used mgh=translational +rotational KE and found that the final velocity...
  17. I

    The limiting sphere in crystallography

    Hello there ! I am writing here, because I could not find any good explanation in the literature and on the web Going straightaway to the point, my question is connected to Ewald's sphere and so called the limiting sphere. I red that limiting sphere is such a construction that appoints the...
  18. C

    Buoyant Force acting on a sphere

    Homework Statement A sphere of radius 10.0 cm floats in equilibrium partially submerged in water with its lowest point 5.00 cm below the water's surface. (a) What is the buoyant force acting on the sphere? Homework Equations F = pvg The Attempt at a Solution F= 1000 * v * 9.8 V=...
  19. AsadaShino92

    Charge and energy of a conducting sphere

    Homework Statement A conducting sphere of radius 100cm is charged to a potential of 30 volts. a) What is the charge on the sphere? b) What is the energy stored in the field? c) If the sphere is connected to a second identical uncharged sphere by a long wire, what is the final energy in the...
  20. A

    Sphere with dipole in a dialectric

    Homework Statement Evaluate the electric field of a hollow sphere with a dipolo , in a dialectric. See left figure.. Homework Equations $$\alpha \vec{p}$$ The Attempt at a Solution I don't understad why at the field electric "in" there is a term of form $$\alpha \vec{p}$$ , and term $$\beta$$...
  21. I

    Sphere Rolling Down Hill into Projectile Motion

    Homework Statement Mountaineers are simulating a massive avalanche snowball by using a big Styrofoam ball (m = 75 kg; r = 1.50 m).They give it an initial impulse of 1500 kg m/sto start it rolling down the hill without slipping (no snow sticks to the ball, and ignore air resistance). Near the...
  22. Titan97

    Field inside a charged sphere

    What is the direction of field inside a charged non-conducting sphere? Using gauss law, I can find the magnitude of electric field inside the shell by assuming a spherical Gaussian surface. But how can I find its direction? Also, if electric field exists inside a charged sphere, wouldn't the...
  23. S

    Electric field due to a Solid Non-Conducting Sphere

    Homework Statement "Find the electric field due to a solid conducting sphere of uniform charge distribution using Coulomb's law and brute force integration only. Use Gauss' Law to verify the result. Homework Equations Coulomb's law for element field dE[/B] The Attempt at a Solution I...
  24. A

    Collision of two rolling bodies

    Homework Statement A solid sphere is rolling without slipping on rough ground with an angular velocity w and linear velocity v. It collides elastically with an another identical sphere at rest. Radius of each sphere is R and mass m. What is the linear velocity of the first sphere after it...
  25. faradayscat

    Dynamics/kinematics of rotating sphere

    I'm wondering about how one would describe the dynamics of a rotating sphere. Consider this: a solid sphere of mass "m" and radius "r" is set to rotate about a tangent to its surface. If it is released from the horizontal position such that it swings like a pendulum, what would be the force...
  26. M

    Sphere Volume to Surface Area, Why not for Cone?

    Homework Statement Wikipedia tells me that I can obtain the surface area of a sphere by realizing that the volume of a sphere is equivalent to the infinite sum of the surface areas of hollow, nested spheres, sort of like little Russian dolls. That makes sense, and then differentiating both...
  27. G

    Force between charged and neutral sphere after scaling

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  28. A

    Self-Capacitance of an Insulating vs. Conductive Sphere

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  29. P

    Finding volume of a modified sphere using integrals

    Hello guys, new member here. I've got a calculus project due Tuesday that I could use some help on. I won't bore you with the all details of the project, but first let's imagine an olive in the shape of a perfect sphere (with a radius always bigger than 6mm) that goes through a set of blades...
  30. E

    Electrostatic force between two halves of sphere

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  31. Titan97

    Finding potential of conducting sphere

    Homework Statement Find the potential at the centre and at P of a hollow uncharged conducting spherical shell if a charge q is placed at a distance of 2r from centre of shell. (r is the radius) Homework Equations All the charge induced on the sphere has to reside on the sphere's outer...
  32. gracy

    E=0 inside the conducting sphere Always?

    An uncharged metal sphere suspended by a silk thread is placed in a uniform external electric field E.(a)What is the magnitude of the electric field of points inside the sphere?(b)Is your answer changed if the sphere carries a charge? I would have asked this in homework forum but it does not...
  33. F

    What is the method for deriving Stokes' law for drag around a sphere?

    So you can solve the Stokes equation for flow around a sphere to obtain the pressure in the fluid: p=p0-3nuacosθ/2r2 where n is the viscosity, u is the speed of the fluid (along the z axis) far away from the sphere, a is the radius of the sphere and r,θ are the usual spherical polar coordinates...
  34. S

    How Does Replacing a Sphere Affect Water Level in a Bowl?

    A small solid sphere of mass M0, of radius R0, and of uniform density ρ0 is placed in a large bowl containing water. It floats and the level of the water in the dish is L. Given the information below, determine the possible effects on the water level L, (R-Rises, F-Falls, U-Unchanged), when that...
  35. gracy

    Potential due to a uniformly charged sphere

    http://www.phys.uri.edu/gerhard/PHY204/tsl93.pdf To find electrical potential at r<R I want to know why should we subtract ##V##=-##\int_∞^R\frac{kQ}{r^2}\,dr##-##\int_R^r(0)\,dr##=##\frac{kQ}{R}## I don't know why are we subtracting these two?
  36. C

    B Do curves, circles and spheres really exist?

    Obviously, they exist as mathematical concepts, and those concepts are real, but in physical reality, everything is made up of subatomic particles and, if the theory is ever verified, strings. So if you try to construct a curve, circle or sphere, you are necessarily stacking a bunch of subatomic...
  37. S

    Potential inside a sphere with two regions

    Homework Statement Suppose a charge is distributed in a lower half region of a sphere and the upper half has zero charge. What is the potential inside? Homework Equations Poisson Equation? The Attempt at a Solution My problem here is I don't know how to start, I think laplace equation can't...
  38. imadrea

    How to devise moment of inertia formula of solid sphere?

    Homework Statement how to divide moment of inertia of solid sphere about its central axis?. Solid sphere has radius R, mass M. Homework Equations I=∫r2dm 2/5 MR^2 The Attempt at a Solution https://photos.google.com/search/_tra_/photo/AF1QipPoXyad0q1Y3yisc0LeeJHGApkIrGbitK6kAk5p i try to...
  39. F

    Gauss' Theorem - Divergence Theorem for Sphere

    Homework Statement Using the fact that \nabla \cdot r^3 \vec{r} = 6 r^2 (where \vec{F(\vec{r})} = r^3 \vec{r}) where S is the surface of a sphere of radius R centred at the origin. Homework Equations \int \int \int_V \nabla \cdot \vec{F} dV =\int \int_S \vec{F} \cdot d \vec{S} That is meant...
  40. Y

    Solid sphere and hollow sphere rolled down an inclined plane

    A solid sphere and a hollow one of same mass and radii are rolled down a rough inclined plane. Which of the following is true? (A) solid sphere reaches bottom with greater speed. (B) solid sphere reaches the bottom with greater kinetic energy. ( I know that option A is correct.Thus I felt that...
  41. S

    Potential inside a grounded conducting sphere

    Homework Statement Hi, I'm currently answering a problem in Jackson's electrodynamics. The question is: Given a point charge q inside a hollow. grounded, conducting sphere of inner radius a. Find the potential inside. This can be solved by placing an image charge outside the sphere, and...
  42. Justice Hunter

    B What Are the Physical Limitations of a Dyson Sphere?

    So the popular internet news outlets are ringing with articles about a possible Dyson sphere, or alien mega-structure around a star (KIC 8462852) 1500 light years away. Here is one such article : http://www.space.com/30855-alien-life-search-kepler-megastructure.html I'd like to know, since i...
  43. goonking

    Finding the Electric Field Inside a Charged Sphere

    Homework Statement Homework EquationsThe Attempt at a Solution so plugging in the variables, the density should be 0.002 with density known, and the volume of the sphere with radius 10, we can find the mass. (density x volume = mass) mass is about 16.75 kg it states the amount of charge...
  44. E

    Moving an iron sphere along a path with an electromagnet

    Hello, So I am working on a project that requires the movement of iron nanoparticles (let's assume 25nm in diameter, and let's assume the sphere is uniform and pure iron) through a (non-magnetic) gel using an externally applied magnetic field. Let's assume the total distance I want to move the...
  45. j3dwards

    Electrostatic potential inside/outside sphere

    Homework Statement A sphere of radius R carries an electric charge Q, uniformly distributed inside its volume. (a) Using the expression for the electric field given in the lectures, compute the electrostatic potential V (r) inside and outside the sphere. Homework Equations E[/B] = -∇V The...
  46. F

    Find a normal vector to a unit sphere using cartesian coordinates

    Homework Statement Consider a unit sphere centered at the origin. In terms of the Cartesian unit vectors i, j and k, find the unit normal vector on the surface Homework Equations A dot B = AB cos(theta) A cross B = AB (normal vector) sin(theta) Unit sphere radius = 1 The Attempt at a...
  47. 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...
  48. S

    Electric field inside a sphere

    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...
  49. 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...
  50. 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...
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