Inverse square law and superposition.

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Discussion Overview

The discussion centers on the relationship between the inverse square law and the principle of superposition in the context of electromagnetism and gravity. Participants explore the implications of the inverse square law for linearity in field equations and the conditions under which superposition applies.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant questions why the /r^2 dependence guarantees the applicability of superposition, suggesting there may be deeper arguments beyond the simple reasoning provided in their textbook.
  • Another participant asserts that superposition is possible because the equations governing electromagnetism and gravity are linear, implying a connection between the inverse square law and linear equations.
  • A participant mentions that a linear field equation can be derived from the inverse square law, which supports the use of superposition.
  • There is a reiteration of the equivalence between Gauss's law and Coulomb's law, emphasizing the derivation of linear field equations from the inverse square law.
  • One participant acknowledges the source of their understanding as Purcell's book and expresses interest in further contemplating the distinction between linear and nonlinear fields.

Areas of Agreement / Disagreement

Participants express various viewpoints on the connection between the inverse square law and superposition, with some agreeing on the linearity of the equations involved, while others seek deeper understanding. The discussion remains unresolved regarding the specific implications of these relationships.

Contextual Notes

Participants reference the need for a deeper understanding of linear versus nonlinear fields and the implications of the curl of the field, indicating potential limitations in their current explanations.

DukeofDuke
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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.
 
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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?
 
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.
 

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