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Gauss's Law

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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.

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Related Experiment Video

Updated: Jun 10, 2026

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

Absorbing filter to flatten gaussian beams.

S K Dew, R R Parsons

|August 21, 2010

Summary

Researchers developed a novel absorbing filter to flatten laser beam intensity profiles. This tantalum film filter achieves a uniform output, crucial for laser applications.

Area of Science:

Optics and Photonics
Materials Science

Background:

Laser beams often exhibit a Gaussian intensity profile, which can be undesirable for certain applications.
Uniform laser beam profiles are essential for precise laser processing and measurement.

Purpose of the Study:

To develop an absorbing filter capable of flattening the Gaussian intensity profile of a laser beam.
To fabricate and characterize a thin tantalum film filter for laser beam shaping.

Main Methods:

Fabrication of a thin tantalum film using direct current (dc) magnetron sputtering.
Utilized substrate masking and motion during sputtering to control film thickness and profile.
Developed a predictive model for filter production, correlating process parameters with film characteristics.

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Single Molecule Fluorescence Microscopy on Planar Supported Bilayers

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Last Updated: Jun 10, 2026

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

Single Molecule Fluorescence Microscopy on Planar Supported Bilayers

Single Molecule Fluorescence Microscopy on Planar Supported Bilayers

Published on: October 31, 2015

Main Results:

Achieved a filter with a flat output profile within +/-3% uniformity over a 2.2 mm diameter.
The filter demonstrated a transmission of 60% of the peak intensity of the original Gaussian beam.
The developed model accurately predicted the film profile and filter performance.

Conclusions:

The developed dc magnetron sputtering technique with masking and motion is effective for creating laser beam-flattening filters.
The fabricated tantalum filters provide a highly uniform intensity profile, suitable for advanced laser applications.
The predictive model aids in optimizing the filter fabrication process for desired performance.