Why an electric field weakens with distance
A charge affects the space around it: place another charge there, and it feels a push or pull. Physicists describe that influence as an electric field. The field is not a spray of material spreading outward; it is a way to specify the force a small test charge would experience at each location.
For an isolated point charge, the field’s strength follows an inverse-square rule: it is proportional to the source charge and inversely proportional to the square of the distance. The sphere picture explains why. At a greater radius, the source’s influence is distributed across more area, while the total amount associated with the source has not changed. The field is therefore weaker at each point on that larger sphere.
The rule predicts force, not direction
The field’s direction tells which way a positive test charge would be pushed. A negative test charge feels force in the opposite direction, so the same field can correspond to attraction or repulsion depending on the charges involved. The inverse-square rule describes how the force’s magnitude changes with separation; it does not decide whether the charges pull together or push apart.
This simple distance rule is useful because it lets scientists predict how changing the spacing between charges changes their interaction without tracking an imagined stream of force. Move a point charge twice as far away, and the force becomes only one-quarter as strong.
