Which law is more fundamental, Gauss's law or Coulomb's Law?

Question

I think Coulomb's law because forces are more fundamental than fields (are they?) but Coulomb's law can be derived from Gauss's law.

@garyp I would understand it the following way: A theorem/law $A$ is less fundamental than $B$ if it can be derived from $A$. For example the equations of uniform motion are less fundamental than Newton's laws because they can be derived from them. Likewise General Relativity would be more fundamental than Newton's laws etc. That's at least how I think the term "fundamental" is commonly understood. — Jannik Pitt, May 26 '17 at 17:49

score 1 · Answer 1 · answered May 26 '17 at 17:08

First of all, you can write Coulomb's law in terms of fields: $$ E(r) = k_e\frac{q}{r^2} $$ in this formulation, it is equivalent to Gauss's law applied to a point charge.

Second, you may want to further ask whether forces are more fundamental than fields. The answer is that fields turn out to be more fundamental. How do we tell? Consider the following experiment. Put a charge $Q$ in the origin. At a large distance $R$, we have initially no charge, and at time $t=0$, we place a charge $q$. If the fundamental version of Coulomb's law is the force one, then the force will be in place only when the two charges have had the opportunity to interact, which will take at least $R/c$. But that's not the case. The particle $q$ feels the force immediately, which means that there was something already there, which doesn't need to be communicated from $Q$ after $q$ is placed: the field.

So if one uses the force format, special relativity has to be invoked. — anna v, May 27 '17 at 03:34

anna v · Answer 2 · 2017-05-27T11:14:44.400

Laws in physics were called so because they were like axioms, not provable, but assumed so as to build mathematical models which fit existing data and predict future behaviors.

Electromagnetism is elegantly described by Maxwell's equations in all its aspects, and has as postulates what to start with were experimentally found as "laws". See the answer here for how Coulomb's law can be derived from Gauss' law and Lorenz transformations , so it is not necessary as a postulate for Maxwell's equations.

As with mathematical axioms , when it is possible to take a proven theorem as an axiom and make the original axiom a provable theorem, so with the laws of electrodynamics. Usually one chooses the simplest form. As Gauss' law has a clear correspondence with one of Maxwell's equations and includes non static electricity, it is reasonable to take it as an "axiom" of the physical theory.

score -3 · Answer 3 · edited May 26 '17 at 17:34

Gauss's Law can also be derived from Coulomb's Law (with some assumptions though).Check this out :" https://en.wikipedia.org/wiki/Gauss%27_law#Deriving_Coulomb.27s_law_from_Gauss.27_law " No Law is more fundamental to the other law.

At times most of the laws are mere consequences of each other.

Nothing can be said in particular.Forces seem more fundamental than fields though both forces and fields are terms given by us only. Both are significant in their respective uses.

Which law is more fundamental, Gauss's law or Coulomb's Law?

3 Answers3