# 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

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.