Strip Coulomb’s law of its second charge and you have the field of a point charge itself: radial, and falling away as the inverse square of distance.
A point charge produces a radial field of strength E = Q / (4πε₀r²), pointing outward for a positive charge and inward for a negative one. Like Coulomb’s law and gravitation, it is an inverse-square field.
Field lines stream straight out from a positive charge or straight in to a negative one. Move the test point and read the field strength off the inverse-square curve; halve the distance and the field quadruples.
E = Q / (4πε₀r²) shares its form with Coulomb’s law and Newton’s law of gravitation. The field is a vector, directed radially, so the fields from several charges are added as vectors, not simply as numbers.
Four quick checks on the field of a point charge and its inverse-square form. Each correct answer earns XP and lights this skill on your star map.
The electric field strength a distance r from a point charge Q is:
The field of a point charge varies with distance as:
Halving the distance from a point charge makes the field:
The field of a positive point charge points:
The point-charge field is inverse-square (1/r²), not 1/r, that 1/r form belongs to the potential. The field is radial and is a vector: to combine fields from several charges, add them as vectors, accounting for direction.
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