• entries
31
29
• views
4,666

# Gauss's Law - for both Electricity and Gravity?

1,388 views

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:  {\displaystyle \scriptstyle \partial V} {\displaystyle \mathbf {g} \cdot d\mathbf {A} =-4\pi GM} , where  represents a surface integral over a closed surface. Gauss's Law for electric fields states that:

= {\displaystyle \scriptstyle _{S}} {\displaystyle \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.

## 1 Comment

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

×   Pasted as rich text.   Paste as plain text instead

Only 75 emoji are allowed.