Confusion In Electrostatics In electrostatics, we deal with charge configurations which are at rest. I find this statement a little confusing. The charges are at rest, but in what frame of reference? Are they at rest with respect to an inertial frame? I flipped through various books but couldn't find a satisfactory answer to this question.
 A: Yes, they are at rest relative to an inertial frame, and you're describing the forces applied to them and the accelerations they experience in that frame.
If you looked at the exact same charges from a moving frame, there would be magnetic fields.
In an accelerating or rotating frame, the charges would experience accelerations not described by Coulomb's law.
A: Charges at rest for some observer $S$ will be moving for an observer $S'$ that is moving at some speed $v$ with respect to $S$. In fact, you can find the expressions of the electric and magnetic fields for such an observer :
$$ \mathbf{E}' = \gamma(\mathbf{E}+\mathbf{\beta}\times\mathbf{B})-\frac{\gamma^2}{\gamma+1}\mathbf{\beta}(\mathbf{\beta}\cdot\mathbf{E})$$
$$\mathbf{B}' = \gamma(\mathbf{B}-\mathbf{\beta}\times\mathbf{E})-\frac{\gamma^2}{\gamma+1}\mathbf{\beta}(\mathbf{\beta}\cdot\mathbf{B})$$
Where $\gamma = \frac{1}{\sqrt{1-\frac{v^{2}}{c^{2}}}}$. You see that if $\mathbf{B}=0$ in $S$ (charges at rest for instant), then $\mathbf{B}'$ is not necessarily equal to zero.
A: This is something that confused me a lot when I started studying electromagnetism, as well: two charges that are rest with regard to each other experience only electric force, but two charges that are at motion in the same direction experience both electric and magnetic force. Later in electromagnetism, you will learn about how you use Maxwell's Laws to transform between electric and magnetic fields in moving frames of reference.
