Point charges create electric fields by exerting forces that either attract or repel other charged particles.

To elaborate, a point charge is conceptualized as a charge concentrated at a single point in space. While this is an idealization—since real charges possess a spatial extent—it serves as a valuable model for various scenarios. The electric field produced by a point charge defines a region surrounding it where another charged particle would experience a force.

The direction of the electric field at any given point in space corresponds to the direction in which a positive test charge would be pushed away or pulled closer if placed at that location. If the point charge is positive, it repels the positive test charge, resulting in an electric field that radiates outward from the point charge. Conversely, if the point charge is negative, it attracts the positive test charge, causing the electric field to point toward the point charge.

The strength of the electric field at any point in space is quantified as the force experienced by a positive test charge divided by the magnitude of that test charge. This relationship is encapsulated in Coulomb’s law, which states that the force between two charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them. Consequently, the electric field $E$ generated by a point charge $Q$ at a distance $r$ from the charge can be expressed as:

where $k$ is Coulomb’s constant.

The electric field is classified as a vector field, meaning it possesses both a magnitude and a direction at every point in space. Electric field lines serve as a visual representation of this field: they originate from positive charges and terminate at negative charges. The density of these lines at any point indicates the strength of the electric field at that location. Furthermore, the direction of the electric field at a specific point is tangent to the electric field line that passes through that point.

In summary, point charges generate electric fields that exert forces on other charged particles, a phenomenon accurately described by Coulomb’s law. The electric field represents the force that a positive test charge would encounter at any position in space due to the presence of a point charge.