2
$\begingroup$

Coulomb's law is typically described as being for two stationary, isolated charges.

Coulomb's law, or Coulomb's inverse-square law, is a law of physics that describes force interacting between static electrically charged particles.

"Coulomb's law", Wikipedia

Even though it's primarily intended for stationary charges, can Coulomb's law ever be used with moving charges? If so, why?

I'm looking for an intuitive explanation, one concerning more of physics and less of mathematics.

$\endgroup$
  • 1
    $\begingroup$ It also works in the "quasi-static" regime where the charges have velocities much less than the speed of light. If $v\approx c$, then one must use relativistic electrodynamics. $\endgroup$ – ZeroTheHero May 2 '18 at 17:50
  • $\begingroup$ Related: "Is Coulomb's law accurate for moving charges?". $\endgroup$ – Nat May 6 '18 at 23:25
4
$\begingroup$

Coulomb's law is not equally applicable to charged particles in motion. The reason is that moving charged particles give rise to magnetic fields in addition to electric fields. In a system of moving charged particles, to calculate the net force on any particular charged particle we use a different force law (the Lorentz force):

$$\vec{F} = q(\vec{E} + \vec{v}\times\vec{B}),$$

where $q$ is the particle's charge and $\vec{v}$ is its velocity, and $\vec{E}$ and $\vec{B}$ are the (vector) values of the electric and magnetic fields due to all the other moving charged particles at the location of the charge in question. This is the force at one instant of time (think of a single frame in a motion picture). Because all the charged particles are moving, $\vec{E} \text{ and }\vec{B}$ will be continuously changing.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.