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An approximation for the volume of a thin spherical shell is the surface area of the inner sphere multiplied by the thickness t of the shell: [2], when t is very small compared to r (). The total surface area of the spherical shell is .
The gravitational field of a spherically symmetric mass distribution like a mass point, a spherical shell or a homogeneous sphere must also be spherically symmetric. If n ^ {\displaystyle {\hat {\mathbf {n} }}} is a unit vector in the direction from the point of symmetry to another point the gravitational field at this other point must therefore be
In geometry, a spherical cap or spherical dome is a portion of a sphere or of a ball cut off by a plane. It is also a spherical segment of one base, i.e., bounded by a single plane. If the plane passes through the center of the sphere (forming a great circle), so that the height of the cap is equal to the radius of the sphere, the spherical cap ...
The total volume is the summation of all shell volumes: ... This can be found from the volume element in spherical coordinates with r held constant. [9]
In geometry, a spherical sector, [1] also known as a spherical cone, [2] is a portion of a sphere or of a ball defined by a conical boundary with apex at the center of the sphere. It can be described as the union of a spherical cap and the cone formed by the center of the sphere and the base of the cap. It is the three-dimensional analogue of ...
Terminology for spherical segments. In geometry, a spherical segment is the solid defined by cutting a sphere or a ball with a pair of parallel planes. It can be thought of as a spherical cap with the top truncated, and so it corresponds to a spherical frustum. The surface of the spherical segment (excluding the bases) is called spherical zone.
A spherical Gaussian surface is used when finding the electric field or the flux produced by any of the following: [3] a point charge; a uniformly distributed spherical shell of charge; any other charge distribution with spherical symmetry; The spherical Gaussian surface is chosen so that it is concentric with the charge distribution.
Ellipsoid. An ellipsoid is a surface that can be obtained from a sphere by deforming it by means of directional scalings, or more generally, of an affine transformation. An ellipsoid is a quadric surface; that is, a surface that may be defined as the zero set of a polynomial of degree two in three variables.