Electric field visualization

Coulomb's law, published in 1785, describes the force between point charges: it is proportional to the product of the charges and inversely proportional to the square of the distance between them. From this single law, the entire structure of the electric field follows. The field at any point is the vector sum of contributions from all charges, and the field lines you see here are curves whose tangent at every point matches the field direction.

Field lines begin on positive charges and end on negative charges (or extend to infinity if the net charge is nonzero). They never cross, because the field has a unique direction at every point. The density of field lines is proportional to the field strength, so regions where lines bunch together represent strong fields, and regions where they spread apart represent weak ones. This geometric representation, invented by Michael Faraday in the 1830s, remains one of the most powerful tools for visualizing electromagnetic phenomena.

Equipotential contours connect points of equal electric potential (voltage). They are always perpendicular to field lines, forming a complementary picture of the field. Near a positive charge, potential is high; near a negative charge, it is low. The spacing of equipotential lines indicates the rate at which potential changes with distance — closely spaced contours mean a strong field (steep potential gradient), while widely spaced contours mean a weak field.

The vector field view shows the field as arrows at a grid of sample points. Each arrow points in the direction of the field and its length represents the field magnitude (capped for readability). Together, these three visualizations — field lines, equipotentials, and vector arrows — provide a complete picture of the electrostatic field from any configuration of point charges.