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Gauss's Law

Gauss's Law

If a closed surface does not have any charge inside where an electric field line can terminate, then the electric field line entering the surface at one point must necessarily exit at some other point of the surface. Therefore, if a closed surface does not have any charges inside the enclosed volume, then the electric flux through the surface is zero. What happens to the electric flux if there are some charges inside the enclosed volume? Gauss's law gives a quantitative answer to this question.

Gauss's Law: Spherical Symmetry

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...

Gauss's Law: Cylindrical Symmetry

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,...

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Related Experiment Video

Updated: Dec 25, 2025

The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry

The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry

Published on: August 12, 2013

Incoherent detection sensor design approach using Gaussian optics.

|April 1, 2020

Summary

This summary is machine-generated.

This study presents a top-level design approach for incoherent optical detection sensors, drawing inspiration from radar systems. The goal is to optimize performance in a stochastic manner for remote sensing applications.

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Last Updated: Dec 25, 2025

The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry

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Published on: August 12, 2013

Characterization of SiN Integrated Optical Phased Arrays on a Wafer-Scale Test Station

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Area of Science:

Optics and Photonics
Remote Sensing
Sensor Technology

Background:

Incoherent optical detection sensors (direct detection sensors) are valuable for remote sensing.
While less robust than coherent sensors in clutter, they offer simplicity and performance advantages.
Optimizing their design for stochastic requirements is crucial.

Purpose of the Study:

To develop a sensor- or top-level design approach for incoherent optical detection sensors.
To leverage decades of research from radar systems for optical sensor design.
To meet performance requirements in a stochastic fashion.

Main Methods:

Adapting design principles from established radar systems.
Focusing on a top-level, sensor-centric design methodology.
Applying stochastic optimization techniques.

Main Results:

A framework for designing incoherent optical detection sensors is proposed.
The design approach integrates radar system methodologies.
Guidance for optimizing sensor performance under uncertainty is provided.

Conclusions:

The proposed design approach offers a viable path for developing advanced incoherent optical sensors.
Borrowing from radar research provides a robust foundation for optical sensor design.
This work facilitates improved performance of direct detection sensors in various applications.