# Coulomb's law universal or not?

## Main Question or Discussion Point

What exactly is meant by universal law? I have read in a book a that Ohm's law is not a univeral law. I somewhat understood that as Ohm's law is not obeyed by all materials and not always. But I read now in another book that Coulomb's law is also not a universal law. Now I am beginning to wonder what is a univeral law.

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Coulomb's law only works for a point charge, and not for all charge distributions. As it only works in certain situations (as does Ohm's Law), then it is not universal. A universal law will work in any situations.

I did not get what you mean by the law not applicable to charge distributions. For charge distributions too we can still apply the law individually for each charge and get the results. Like we have the force calculations for a line charge or sheet of charge. Even the gravitational law consider bodies with masses as particles, so is gravitational law too not universal. You must be right, but I think I am missing a point. If you can elaborate, that will help.

nicksauce
Homework Helper
Well you can't just blindly apply Coulomb's law if the charges in question have a velocity or an acceleration.

Dale
Mentor
Coulomb's law is a simplification of Maxwell's equations under specific conditions (electrostatic = no moving charges). The universal law is Maxwell's equations which are hard to solve sometimes. So you use the simpler Coulomb's law where you can and the more complicated but universal Maxwell's equations when you need to.

PS Coulomb's law is not the only simplified form of Maxwell's equations that is in widespread use, but it is the first one that you encounter in a typical course of study.

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So why does Coulomb's Law not work for charges in Motion?

-Ataman

Dale
Mentor
Coulomb's law gives you the electric field. If a charge is moving you need to consider the magnetic field also.

Friends,
I agree with you all. I am now convinced/enlightened why the law is not universal. Thanks.

cepheid
Staff Emeritus
Gold Member
Am I to understand that, in contrast, Gauss' law IS universal. In other words, although you can derive it from Coulomb's law in the context of electrostatics, it is actually applicable outside of that context as well?

nicksauce
Homework Helper
Well Gauss's law is one of Maxwell's equations, which are universal, whereas Coulomb's law is not.

rbj
Coulomb's law is a simplification of Maxwell's equations under specific conditions (electrostatic = no moving charges). The universal law is Maxwell's equations which are hard to solve sometimes. So you use the simpler Coulomb's law where you can and the more complicated but universal Maxwell's equations when you need to.

PS Coulomb's law is not the only simplified form of Maxwell's equations that is in widespread use, but it is the first one that you encounter in a typical course of study.
Well Gauss's law is one of Maxwell's equations, which are universal, whereas Coulomb's law is not.
there seems to be something wrong with this thread. Gauss's Law is a direct consequence of any inverse-square law. if it's inverse-square (and additive, i.e. superposition applies), then Gauss's Law applies.

so is the implication here that Coulomb's Law is not inverse-square?

BTW, from a POV of classical, non-relativistic physics, yes Coulomb's law is lacking because it does not describe the electromagnetic interaction. but if Special Relativity is considered, that plus Coulomb's Law suffices, i think.

i would say that the premise of the question (and many of the responses) is wrong. Coulmb's Law is quite universal. but like other universal laws, it's not the only one.

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Dale
Mentor
Am I to understand that, in contrast, Gauss' law IS universal. In other words, although you can derive it from Coulomb's law in the context of electrostatics, it is actually applicable outside of that context as well?
Well Gauss's law is one of Maxwell's equations, which are universal, whereas Coulomb's law is not.
Gauss's law and Coulomb's law are equivalent. You can derive either from the other quite easily. By "not universal" I simply meant to imply that Gauss/Coulomb is only one part of Maxwell, which is the "universal" law. Gauss/Coulomb always applies, but whenever you have moving charges it is insufficient to predict the behavior without the other Maxwell equations.

Coulmb's Law is quite universal. but like other universal laws, it's not the only one.
OK, I am fine with that too. "Universal" but not "complete".

nicksauce
Homework Helper
"
there seems to be something wrong with this thread. Gauss's Law is a direct consequence of any inverse-square law. if it's inverse-square (and additive, i.e. superposition applies), then Gauss's Law applies."

Sorry the point I was trying to make was that Gauss's Law always applies as it is one of Maxwell's equation, and Coulomb's law is only a solution of the Maxwell equations when things aren't changing with time. Does that make it not universal? It depends on what one means by universal.

rbj
Sorry the point I was trying to make was that Gauss's Law always applies as it is one of Maxwell's equation, and Coulomb's law is only a solution of the Maxwell equations when things aren't changing with time.
it is not that either. it is what is usually enumerated as the first of Maxwell's equations.

$$\nabla \cdot \mathbf{E} = \frac {\rho} {\epsilon_0}$$

is the differential expression of

$$\oint_S \mathbf{E} \cdot \mathrm{d}\mathbf{A} = \frac {Q_S}{\epsilon_0}$$

while that is a direct expression of Gauss's Law, that expression follows directly from the fact that Coulomb's Law is inverse-square and submits itself to superposition.

Does that make it not universal? It depends on what one means by universal.
what i usually mean by "universal" is that it is as applicable to the aliens on the planet Zog as it is to us here.

nicksauce
Homework Helper
Ok sure, but if $$\frac{\partial \rho}{\partial t} \neq 0$$, then $$\vec{E} = \frac{q}{4\pi\epsilon_0r^2}\vec{r}$$ will not be a solution of Maxwell's equations. The impression I got from the initial post was that 'universal' is to mean 'always applies'.

Dale
Mentor
what i usually mean by "universal" is that it is as applicable to the aliens on the planet Zog as it is to us here.
I think that is too liberal a definition. By that definition Ohm's law is universal too.

To the OP: I think these last few posts make it clear that there is no clear definition of a "universal" law.

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