Points to Ponder

Electrostatics studies forces between stationary charges. However, if a net Coulomb force acts on a charge, it would accelerate. Therefore, when we say a charge is "at rest" in an electrostatic situation, we assume some other unspecified force (e.g., mechanical support) holds it in place, exactly balancing the Coulomb force.

A capacitor is designed to concentrate the electric field lines into a narrow region between its plates. Because the field is confined, even a strong field produces only a small potential difference between the two conductors.

At the surface of a spherical charged shell, the electric field $\mathbf{E}$ is discontinuous: it is zero inside and $\frac{\sigma}{\varepsilon_0} \hat{n}$ outside. In contrast, the electric potential $V$ is continuous across the surface, with value $\frac{q}{4\pi\varepsilon_0 R}$ at the surface.

The torque $\mathbf{p} \times \mathbf{E}$ on an electric dipole causes it to oscillate around the direction of $\mathbf{E}$. Only when a dissipative force (like friction or radiation) is present will the oscillations damp out, and the dipole eventually align with $\mathbf{E}$.

The potential due to a point charge $q$ at its own location is not defined — it becomes infinite. This is because the distance $r$ in $V = \frac{kq}{r}$ goes to zero. …