Jump to content
  • entries
    31
  • comments
    29
  • views
    4,738

Gauss's Law - for both Electricity and Gravity?

nathanstack15

Entry posted by nathanstack15 ·

1,463 views

 Share

This past week in physics, we learned about Gauss's Law for electricity. It states that the electric flux, or the amount of electric field penetrating a surface, is proportional to the charge enclosed within the surface. Interestingly, Gauss's Law does not only apply to electricity: it also applies to gravity. According to Wikipedia, gravitational flux is a surface integral of the gravitational field over a closed surface. This is analogous to electric flux, equivalent to the surface integral of the electric field over a closed surface. Gauss's Law for gravity is mathematically represented by this equation:  \oiint{\displaystyle \scriptstyle \partial V}\scriptstyle \partial V {\displaystyle \mathbf {g} \cdot d\mathbf {A} =-4\pi GM}\mathbf {g} \cdot d\mathbf {A} =-4\pi GM , where \oiint represents a surface integral over a closed surface. Gauss's Law for electric fields states that:

\Phi_E = \frac{Q}{\varepsilon_0} = \oiint{\displaystyle \scriptstyle _{S}}{\displaystyle \scriptstyle _{S}} {\displaystyle \mathbf {E} \cdot \mathrm {d} \mathbf {A} }\mathbf{E} \cdot \mathrm{d}\mathbf{A} . Electric flux can also be represented by 4 pi k Q. Since G is the gravitational constant analogous to k for electricity, and since M is analogous to charge, it makes sense that total gravitational flux is equivalent to -4 pi GM. Gravitational flux is negative because gravitation fields always attract, where electric flux can be positive or negative depending on the enclosed charge.

 Share

1 Comment

Recommended Comments

Shadoof

Looks like this needs a little bit more work on the formatting, but it is interesting that these two are very similar to each other.

Link to comment
Guest
Add a comment...

×   Pasted as rich text.   Paste as plain text instead

  Only 75 emoji are allowed.

×   Your link has been automatically embedded.   Display as a link instead

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.

×

Terms of Use

The pages of APlusPhysics.com, Physics in Action podcasts, and other online media at this site are made available as a service to physics students, instructors, and others. Their use is encouraged and is free of charge. Teachers who wish to use materials either in a classroom demonstration format or as part of an interactive activity/lesson are granted permission (and encouraged) to do so. Linking to information on this site is allowed and encouraged, but content from APlusPhysics may not be made available elsewhere on the Internet without the author's written permission.

Copyright Notice

APlusPhysics.com, Silly Beagle Productions and Physics In Action materials are copyright protected and the author restricts their use to online usage through a live internet connection. Any downloading of files to other storage devices (hard drives, web servers, school servers, CDs, etc.) with the exception of Physics In Action podcast episodes is prohibited. The use of images, text and animations in other projects (including non-profit endeavors) is also prohibited. Requests for permission to use such material on other projects may be submitted in writing to info@aplusphysics.com. Licensing of the content of APlusPhysics.com for other uses may be considered in the future.

APlusPhysics Books

APlusPhysics Books

×
×
  • Create New...