Electric field line ($d\mathbf{r}/ds\parallel \mathbf{E}$)

An oriented curve whose tangent points along the local electric field. Where the field is nonzero, choosing arc length $s$ gives $d\mathbf{r}/ds=\mathbf{E}/|\mathbf{E}|$. These curves visualize the direction of the force on a positive test charge; they are not generally particle trajectories, since a particle can have inertia and initial velocity. In electrostatics, they are normal to equipotential surfaces and cannot form a closed loop in a region with a single-valued potential that strictly decreases along the line. A field null can separate families of lines.