How do point charges generate electric fields around them?

Point charges generate electric fields by exerting a force that either attracts or repels other charged particles.

In more detail, a point charge is a charge that is considered to be concentrated at a single point in space. This is an idealisation, as real charges have a spatial extent, but it is a useful model for many situations. The electric field generated by a point charge is a region around it where another charged particle would experience a force.

The direction of the electric field at any point in space is the direction in which a positive test charge would be pushed or pulled if it were placed at that point. If the point charge is positive, it repels the positive test charge, so the electric field points away from the point charge. If the point charge is negative, it attracts the positive test charge, so the electric field points towards the point charge.

The strength of the electric field at any point in space is defined as the force experienced by a positive test charge divided by the magnitude of the test charge. This is given by Coulomb's law, which states that the force between two charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. Therefore, the electric field E generated by a point charge Q at a distance r from the charge is given by E = kQ/r^2, where k is Coulomb's constant.

The electric field is a vector field, which means it has both a magnitude and a direction at every point in space. The electric field lines are a visual representation of the electric field. They start at positive charges and end at negative charges, and their density at any point represents the strength of the electric field at that point. The direction of the electric field at any point is tangent to the electric field line passing through that point.

In summary, point charges generate electric fields by exerting a force on other charged particles, and this force is described by Coulomb's law. The electric field is a vector field that represents the force a positive test charge would experience at any point in space due to the point charge.