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Related Concept Videos

Gauss's Law: Spherical Symmetry01:26

Gauss's Law: Spherical Symmetry

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...
Spherical Coordinates01:23

Spherical Coordinates

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...
Surface Area Calculations01:22

Surface Area Calculations

Surface area calculations for a graph z = f(x, y) are fundamental in engineering applications involving curved structures such as satellite dishes. A parabolic dish reflects communication signals efficiently, but engineers must determine its exact curved surface area to estimate coating materials, fabrication costs, and structural requirements. Since the rim of the dish forms a circular boundary, the surface area is calculated over a circular domain in the xy-plane.Parametric Representation of...
Gauss's Law: Cylindrical Symmetry01:20

Gauss's Law: Cylindrical Symmetry

A charge distribution has cylindrical symmetry if the charge density depends only upon the distance from the axis of the cylinder and does not vary along the axis or with the direction about the axis. In other words, if a system varies if it is rotated around the axis or shifted along the axis, it does not have cylindrical symmetry. In real systems, we do not have infinite cylinders; however, if the cylindrical object is considerably longer than the radius from it that we are interested in,...
Spherical and Cylindrical Capacitor01:26

Spherical and Cylindrical Capacitor

A spherical capacitor consists of two concentric conducting spherical shells of radii R1 (inner shell) and R2 (outer shell). The shells have equal and opposite charges of +Q and −Q, respectively. For an isolated conducting spherical capacitor, the radius of the outer shell can be considered to be infinite.
Conventionally, considering the symmetry, the electric field between the concentric shells of a spherical capacitor is directed radially outward. The magnitude of the field, calculated by...
Maxwell-Boltzmann Distribution: Problem Solving01:20

Maxwell-Boltzmann Distribution: Problem Solving

Individual molecules in a gas move in random directions, but a gas containing numerous molecules has a predictable distribution of molecular speeds, which is known as the Maxwell-Boltzmann distribution, f(v).
This distribution function f(v) is defined by saying that the expected number N (v1,v2) of particles with speeds between v1 and v2 is given by

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Related Experiment Video

Updated: Jun 15, 2026

Indoor Experimental Assessment of the Efficiency and Irradiance Spot of the Achromatic Doublet on Glass (ADG) Fresnel Lens for Concentrating Photovoltaics
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Optical simulation for a fixed spherical solar collector.

B Authier, L Hill, M Duban

    Applied Optics
    |March 10, 2010
    PubMed
    Summary
    This summary is machine-generated.

    This study introduces a raytracing optical simulation to determine optimal absorber dimensions for spherical solar collectors. The method accurately calculates incident solar flux and validates findings through moon-based flux measurements.

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    Area of Science:

    • Solar Energy Engineering
    • Optical Physics
    • Geometric Optics

    Background:

    • Accurate absorber design is crucial for efficient spherical solar collector performance.
    • Understanding incident flux distribution is key to optimizing solar energy capture.
    • Existing methods may lack precision in determining absorber dimensions and flux patterns.

    Purpose of the Study:

    • To propose a raytracing optical simulation for calculating absorber dimensions in fixed spherical solar collectors.
    • To describe physical quantities affecting dimensions and associated measurement methods.
    • To validate simulation results by comparing calculated and measured incident flux.

    Main Methods:

    • Development of a raytracing optical simulation program.
    • Identification and description of key physical parameters influencing absorber dimensions.
    • Experimental measurement of incident flux on the absorber surface using the moon as a surrogate light source.

    Main Results:

    • The simulation provides a method to calculate optimal absorber dimensions for spherical solar collectors.
    • Incident flux on the absorber surface can be accurately predicted for various zenith distances.
    • Experimental validation confirmed the simulation's accuracy, identifying high flux zones and areas with multiple reflections.

    Conclusions:

    • Raytracing simulations are effective for designing spherical solar collector absorbers.
    • The proposed method allows for precise calculation of incident flux, aiding performance optimization.
    • Experimental validation using lunar reflection confirms the simulation's reliability for solar collector design.