2. Coulomb's Law and the Electric Field

Coulomb's Law

Coulomb's law, given by Charles-Augustin de Coulomb in 1785, states that the force of attraction or repulsion between two point electric charges is directly proportional to the product of the magnitudes of the two charges and inversely proportional to the square of the distance between them. This force acts along the straight line joining the two charges. Mathematically:

F = k · q₁ · q₂ / r²

Here, F is the electrostatic force, q₁ and q₂ are the magnitudes of the two charges, r is the distance between them, and k is a constant of proportionality called the electrostatic force constant, whose value in a vacuum is approximately 9 × 10⁹ N·m²/C². This law is structurally identical in form to Newton's law of gravitation, with electric charge playing the role that mass plays in gravitation — a comparison that is a favourite of exam-setters. Note the key qualitative results that follow from the law: doubling either charge doubles the force; doubling the distance between the charges reduces the force to one quarter of its original value (because of the inverse-square dependence).

Electric Field

An electric field is the region of space around a charged object within which another charge would experience a force. It is a useful way of describing how a charge modifies the space around it, so that any other charge brought into that space 'feels' the presence of the first charge without direct contact. The electric field at a point is defined as the force experienced by a unit positive test charge placed at that point, and its SI unit is newton per coulomb (N/C), which is equivalent to volt per metre (V/m). Electric field lines are drawn to visualise the field: they point away from a positive charge (radially outward) and point toward a negative charge (radially inward); the density of field lines represents the strength of the field, with lines closer together indicating a stronger field.