Spherical Symmetry
Spherical Symmetry - Related Videos
01:26
Gauss's Law: Spherical Symmetry
0 Views •
2023
A charge distribution has spherical symmetry if the density of charge depends only on the distance from a point in space and not on the direction. In other words, if the system is rotated, it doesn't look different. For instance, if a sphere of radius R is uniformly charged with charge density ρ0, then the distribution has spherical symmetry. On the other hand, if a sphere of radius R is charged so that the top half of the sphere has a uniform charge density ρ1 and the bottom half has a uniform...
01:23
Spherical Coordinates
0 Views •
2023
Spherical coordinate systems are preferred over Cartesian, polar, or cylindrical coordinates for systems with spherical symmetry. For example, to describe the surface of a sphere, Cartesian coordinates require all three coordinates. On the other hand, the spherical coordinate system requires only one parameter: the sphere's radius. As a result, the complicated mathematical calculations become simple. Spherical coordinates are used in science and engineering applications like electric and...
01:26
Symmetry
0 Views •
2025
The equation of an ellipse centered at the origin defines all points whose distances from the center maintain a constant ratio between the horizontal and vertical axes. This equation results in a smooth, closed curve that extends further along the x-axis than the y-axis, giving it a horizontal orientation. Such an ellipse demonstrates three kinds of symmetry: across the x-axis, across the y-axis, and about the origin. These symmetries are essential in understanding the graph's structure and...
01:27
Gauss's Law: Planar Symmetry
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2023
A planar symmetry of charge density is obtained when charges are uniformly spread over a large flat surface. In planar symmetry, all points in a plane parallel to the plane of charge are identical with respect to the charges. Suppose the plane of the charge distribution is the xy-plane, and the electric field at a space point P with coordinates (x, y, z) is to be determined. Since the charge density is the same at all (x, y) - coordinates in the z = 0 plane, by symmetry, the electric field at P...
10:52
Reconstitution of Basic Mitotic Spindles in Spherical Emulsion Droplets
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Cited by 19 •
2016
The assembly and positioning of the mitotic spindle depend on the combined forces generated by microtubule dynamics, motor proteins and cross-linkers. Here we present our recently developed methods in which the geometrical confinement of spherical emulsion droplets is used for the bottom-up reconstitution of basic mitotic spindles.
FAQs
Once the system has a central point and no angular variation, the field’s value is determined by distance from that point alone. The angular coordinates no longer change the result, so the governing description can be reduced from three spatial dimensions to one radial dimension, simplifying the relevant differential equations.
Spherical symmetry matters for conservation laws because radial dependence is the only spatial variation that remains. A conservation principle can therefore be incorporated into equations that track how a field or distribution changes with radius, rather than with three independent coordinates. This reduction preserves the physical law while making its mathematical expression more manageable.
It can serve as an idealization rather than a claim that every object is perfectly uniform in all directions. The source material includes approximately spherical objects, so the model is useful when a radial description captures the main behavior while more detailed angular structure is not the focus of the analysis.
First identify the relevant central point and determine whether the system’s properties can be represented using radius alone. Next, express the gravitational, electric, pressure, or other field in terms of radial distance, then formulate the corresponding one-dimensional differential equations. Solving those equations yields a radial description rather than a full angular map.
The approach is valuable when the main goal is to determine how a field or pressure distribution changes outward from a center. Examples include gravitational fields around planets or stars, electric fields from isolated charges, pressure in fluid droplets, and hydrostatic equilibrium. It also supports modeling spacetime around approximately spherical objects.
A radial solution provides profiles of quantities such as gravitational or electric fields, pressure distributions, and other properties that vary with distance from the center. In hydrostatic-equilibrium problems, it helps frame how pressure is represented across radius; in spacetime models, it supports a description around an approximately spherical object.