Coulomb's Law and the Electric Field
Coulomb's law gives the force between static point charges and defines the electric field as the force per unit test charge.
Definition
Coulomb's law states that the force between two point charges acts along the line joining them with magnitude proportional to the product of the charges and inversely proportional to the square of their separation; the electric field is the resulting force per unit positive test charge at each point in space.
Scope
This topic covers the inverse-square force law between point charges, the principle of superposition, the definition of the electric field as a vector field surrounding charge distributions, and the calculation of fields from discrete and continuous charge distributions. It includes experimental tests of the inverse-square exponent and the field of simple geometries such as lines, sheets, and spheres of charge.
Core questions
- How does the electrostatic force depend on charge magnitude and separation?
- How is the field of a continuous charge distribution computed by superposition?
- How accurately has the inverse-square exponent been verified experimentally?
Key concepts
- point charge
- inverse-square law
- superposition
- electric field vector
- test charge
- continuous charge distribution
Key theories
- Inverse-square force law
- The force between point charges falls off as the inverse square of distance; high-precision experiments constrain the exponent to deviate from 2 by less than a part in a billion, equivalent to bounding the photon mass.
- Superposition principle
- The total field from many charges is the vector sum of the fields of each charge taken individually, which underlies the integral expressions for the field of continuous distributions.
Clinical relevance
The field concept and Coulomb interactions are the basis for understanding particle accelerators, mass spectrometry, electrospray ionization, and electrostatic forces between charged molecules.
History
Coulomb published his torsion-balance results in 1785, though Cavendish had earlier inferred the inverse-square law from the absence of charge inside a charged conductor. Faraday's field-line picture in the 1830s reframed action-at-a-distance as a local field, a view consolidated by Maxwell.
Key figures
- Charles-Augustin de Coulomb
- Henry Cavendish
- Michael Faraday
Related topics
Seminal works
- jackson1998
- williams1971
Frequently asked questions
- What is the difference between the electric force and the electric field?
- The electric field is a property of space created by source charges, defined as force per unit charge; the electric force is what a specific charge actually experiences when placed in that field, equal to its charge times the field.
- How precisely is the inverse-square law known?
- Modern experiments constrain any deviation of the exponent from exactly 2 to below about one part in 10^9, which also places a stringent upper bound on the rest mass of the photon.