Gaussthe field between charges, drawn line by line.
Every charge bends the space around it, but the field itself is invisible. Place a positive or negative charge and watch the lines spring from plus to minus, the equipotential rings nest, and a released test charge fall along a field it can never see. Drag a pole and the whole field re-knits in real time.
Positive lines
Field of a positive charge, pointing outward. Arrows follow the direction a positive test charge would move.
Negative lines
Lines converging inward onto a negative charge — the sink where the field terminates.
Equipotentials
Rings of equal potential. Where they crowd, the field is strong; where they spread, it is weak.
The zero divide
The dashed contour is the zero-potential line — the balance point between opposite charges.
Test charge
A released probe, accelerating along the field it falls through, tracing the invisible force as a path.
The field is real; only its picture is a choice.
Michael Faraday drew lines of force to reason about a thing he could not touch. A field line is the path a free positive charge would take, released from rest: it leaves every positive charge and lands on a negative one, and it never crosses another line.
Line density is not decoration. Pack the lines together and the field is strong; let them fan apart and it weakens with the square of distance. The same information sits in the equipotential rings — always perpendicular to the lines, tightest where the field bites hardest.
Here the lines are integrated numerically, step by step, straight through the vector field the charges make — the same sum Gauss wrote down, evaluated a few thousand times a second as you drag.