Understanding Coulomb’s Law and Electric Fields

Posted on Mar 10, 2025 in Physics

Coulomb’s Law

Coulomb’s Law states that the force of attraction or repulsion between two point electric charges is directly proportional to the product of the charges and inversely proportional to the square of the distance (r) between them. It is expressed as: F = kQ1Q2 / r2

Electric forces have the following characteristics:

  • The force is directed along the line of junction of the charges.
  • The force is repulsive if the charges have the same sign.
  • If the two charges are of opposite signs, the force vectors will have opposite directions. Two charges of different signs attract.
  • These are forces at a distance; there need not be any material medium between the charges for such force to act.
  • They always come in pairs.
  • If there are three or more point electric charges, the resultant force on one of them is the vector sum of all the other forces exerted on it.

Electric Field

An electric field is the perturbation that a body makes in space due to having an electric charge.

Electric Field Intensity

Electric field intensity at a point in space is the force acting on the unit positive charge placed at that point.

Electric field properties:

  • It is radial and decreases with the square of the distance; it is therefore a central field.
  • Its direction depends on the sign of the charge (q). If the charge is negative, the electric field is directed towards the load; if positive, it is away from it.

F = qE

Electrical Potential Energy

The difference in electrical potential energy of a charge between two points A and B equals the work done by the electric field to shift the charge from A to B. The electric potential energy of a charge q at a point in space is the work performed by the electric field to move the charge q from that point to infinity.

Electric Potential Difference

Electric potential difference between point A and point B equals the work done by the electric field when moving the unit positive charge from A to B. The electric potential at a point in space is the work performed by the electric field to move the unit positive charge from that point to infinity.

Field Work

Positive Field Work (W > 0)

  • The charge q shifts by the action of electric field forces.
  • The q-load’s electrical potential energy decreases.
  • This happens when two charges of the same sign separate or when two charges of opposite signs approach each other.

Negative Field Work (W < 0)

  • The charge q shifts by the action of a force outside the electric field.
  • The q-load’s electrical potential energy increases.
  • This occurs when two charges of the same sign approach each other or when two charges of opposite signs separate.

Field Lines

Field lines are plotted so that the following conditions are met:

  • At each point in space, the electric field intensity vector is tangent to the field lines and has the same direction.
  • The density of field lines is proportional to the magnitude of the electric field. The electric field is more intense in regions where the field lines are closer together.
  • Field lines always originate in positive charges and terminate on negative charges.

Equipotential Surfaces

Equipotential surfaces are obtained by combining points in space that are at the same electric potential. Properties:

  • Equipotential surfaces are perpendicular to the field lines at any point.
  • The work performed by the electric field to move a charge from one point to another in the same equipotential area is zero.
  • For the field created by a point charge, positive or negative, the potential only depends on the distance to the load. Therefore, equipotential surfaces are concentric spheres centered at the load itself.

Electric Flux

The electric field flow, or electric flux, through a surface is a measure of the number of field lines crossing that surface.

Calculation of Electric Flux

  • Uniform field and flat surface: The area is represented by a vector S, perpendicular to the surface, with a magnitude equal to the area. The flux represents the number of electric field lines crossing the surface S.
  • Variable field and any surface: Divide the surface S into infinitesimal elements dS, and define a corresponding surface vector dS perpendicular to the infinitesimal surface dS. The total flux through the surface S is obtained by adding all contributions.