A topic in the Open Knowledge Graph — a free, open map of 15,290 topics and the order to learn them in.
Electric field lines are curves whose tangent at any point is parallel to the electric field vector. The density of field lines is proportional to field strength. Field lines originate on positive charges and terminate on negative charges, providing a powerful visual representation of electric fields.
Sketch field line patterns for simple distributions (point charge, dipole, parallel plates) and verify tangents match expected field direction. Use computational tools to visualize patterns for complex distributions.
You already understand the electric field as a vector quantity — at each point in space it has a magnitude and a direction. The challenge is that a vector field fills all of space, and plotting an arrow at every point produces an illegible thicket. Electric field lines are a clever encoding: instead of arrows everywhere, draw a continuous curve such that at every point along the curve, the tangent to the curve points in the direction of the local electric field. One curve traces out the "direction story" of the field along its path.
The density rule encodes magnitude: pack the lines close together where the field is strong, spread them apart where it is weak. Near a point charge the field falls off as 1/r², so the lines, which start radially inward or outward from the charge, naturally spread apart as they travel outward — the area of a sphere grows as r², exactly compensating the 1/r² falloff. This is not a coincidence; it is the geometric content of Gauss's law built right into the picture.
The directionality convention is that lines originate on positive charges and terminate on negative charges (or go to infinity for net-charge configurations). For a dipole, you can apply the superposition principle you know: the total field at any point is the vector sum of the fields from the positive and negative charges. The field lines you draw are the integrated paths of this combined vector field, curving around from the positive charge toward the negative charge. Where the positive and negative contributions cancel exactly, the field is zero — and a zero-field point is where lines converge and then cannot continue; these saddle points between like charges are places where the field lines approach from multiple directions and then scatter apart.
Three strict rules govern every valid field-line diagram: (1) lines never cross — if they did, the field at that point would have two directions simultaneously, which is impossible; (2) lines never form closed loops in electrostatics — a closed-loop field would allow you to move a charge around the loop and gain energy indefinitely, violating energy conservation; (3) the number of lines leaving a charge is proportional to that charge's magnitude. Armed with these rules you can sketch field patterns for any charge distribution and immediately read off where the field is strong, which direction it points, and where charges would be pushed — without solving a single equation.