Rule 25 of 36 · Chapter IV — Fields & Waves
Charges shape the space around them
Why this rule exists
An electric charge alters the space around it, creating a field that points away from positive and toward negative charge and weakens with the square of distance. Any other charge feels a force from this field alone. The inverse-square falloff follows from the field spreading over spheres whose area grows as r², so a fixed number of field lines must thin accordingly.
In practice
To find the force on a charge, first map the field from all other charges — magnitude kQ/r², directed along the line joining them — then superpose vectorially and multiply by the charge. For many charges or continuous distributions, exploit symmetry and use Gauss's law, which ties the field on a closed surface to the charge enclosed.
When it doesn't apply
The static inverse-square law assumes charges at rest. Moving charges also make magnetic fields, and accelerating ones radiate electromagnetic waves. Inside conductors and materials, other charges rearrange to screen the field, shortening its reach.