# Are Coulomb's Law and Lorentz force always true for all phenomenon in physics?

I saw two equation about charge:

• Coulomb's law

$$\mathbf F=k \frac{q_1q_2}{ r_{12}^{2} }\, \mathbf{\hat r}$$

• and magnetic Force

$$\mathbf F=q \, \mathbf v\times \mathbf B$$

My question is:

Are these equations true for all cases, for example:

• like very fast movement?
• very tiny particle like basic particles?
• Coulomb's Law is true only for statics; Lorentz force relation is always true. – user36790 Apr 4 '16 at 5:37
• Then you have to use the more general Maxwell's equations with Lorentz force. – user36790 Apr 4 '16 at 5:44
• your means is formula on this post physics.stackexchange.com/questions/238559/… – stackprogramer Apr 4 '16 at 5:46
• I've seen Timaeus' ans.... Jefimenko's is one particular explicit solution of Maxwell's equation. In general, you've to use Maxwell's equations. – user36790 Apr 4 '16 at 5:53

## 1 Answer

These are classical equations of electromagnetism and hold for classical dimensions, i.e. where the Heisenberg's Uncertainty Principle is ignorable because $h$ is actually zero as far as measurements go. Coulomb's law is a law discovered in static conditions, and the Lorentz force in charge moving in a magnetic field. Maxwell's equations combine these and other phenomena in a coherent theory which is used for classical dimensions to describe and predict the behavior of charges and magnetic fields.

For elementary particles the concept of force is substituted by the concept of "interaction". In this case electromagnetic interaction, and is in the realm of quantum mechanics. See the answer in this question here.

• IMO, you should mention the validity of Coulomb's Law only in statics. – user36790 Apr 4 '16 at 5:40
• @user36790 thanks for the observation. I edited – anna v Apr 4 '16 at 5:52