The electric field,
seen from an angle
Every line here is traced by stepping through Coulomb's law in three dimensions, then flattened onto the page. Spin the plane, move the charges, and watch the lines rearrange themselves.
whatTwo charges and the field lines threading between them. Each line is traced by walking along the summed Coulomb field in 3D, so the picture is a solution, not a sketch.
lawE = kq/r², summed over every charge. Lines start on positive charges, end on negative ones, and never cross.
tryAdd a second positive charge and drag it toward the existing pair.
noticeA null point appears where the pushes cancel — the probe reads near zero there, and lines steer around it rather than through it.
in lifePhotocopiers and laser printers steer toner with exactly this field pattern.
found byCoulomb measured the inverse-square law in 1785; Faraday introduced field lines in the 1830s and Maxwell gave them equations.