Electric Field Lines and Field Maps

A field line is drawn so that at every point along it, the line is tangent to the electric field vector there. Lines start on positive charges (or infinity) and end on negative charges (or infinity), spreading out as they leave a charge and bunching up as they approach one. That spacing is not decoration: the density of lines through a patch of space represents the magnitude of E. Near a point charge the lines are packed tightly close in, where the field is strong, and they spread apart farther out, where the field is weaker, matching the 1/r² falloff.

Because E has exactly one direction at any given point, two field lines can never cross. A crossing would mean the field points two different ways at the same spot, which is meaningless. For the same reason, a charged particle released in a curved field does not slide along a line like a bead on a wire. At the instant it's released it accelerates along the local field direction, but as it moves it enters a region where the field points a slightly different way, so its actual path peels away from the original line's curve. The line only ever tells you the instantaneous push, not the future route.

This topic sets up Gauss's law, the next big idea in the unit. Field maps make flux visible: where lines pass through a surface densely, flux is high, and counting lines through a closed surface is the qualitative version of the integral Gauss's law computes exactly. Seeing the dipole map, or two like charges pushing lines apart between them, builds the geometric intuition that symmetry arguments later formalize.