Inverse square law and superposition.

[DukeofDuke]

Hey guys,
I'm reading the E&M book from the berkeley physics courses in preparation for my second round of E&M as a junior in undergrad. And they mention some stuff I remember from my intro to E&M class too...namely, that we can use superposition because both gravity and electromagnetism follow inverse square laws.

...Why exactly is the /r^2 a guarantee that superposition works? For some reason it's no longer making sense to me, though I'm sure there are simple arguments as to why it's needed.

Thanks for clearing up the relationship between the two. The book actually gives a simple reason why (basically, you need the /r^2 to cancel out the area your gaussian and any other unit would leave a space dependence on the total flux). But I'm wondering if there are any deeper arguments.

 

[Nabeshin]

At the end of the day you should remember that the reason you can use superposition is because the equations describing electromagnetism (or the analogous field equations for Newtonian gravitation) are linear. I'm not sure of the chain of implication, but that statement seems to say that 1/r^2 => linear equations. Is that from Purcell?

 

[zomgineer]

You can derive a linear field equation from the inverse square law. If it's a linear field then you can do superposition.

Check out http://en.wikipedia.org/wiki/Gauss's_law#Deriving_Gauss.27s_law_from_Coulomb.27s_law" Basically, the two are equivalent.

 

[netheril96]

You can derive a linear field equation from the inverse square law. If it's a linear field then you can do superposition.

Check out http://en.wikipedia.org/wiki/Gauss's_law#Deriving_Gauss.27s_law_from_Coulomb.27s_law" Basically, the two are equivalent.

Not without the curl of the field given.

 

[DukeofDuke]

Yeah, it's from Purcell. It's actually a really cool book.

Thanks everyone, I'll think about what it means to be a "linear field" versus a nonlinear field some more.