The magnitude of the electrical force between two stationary charged particles is given by Coulomb’s law, also known as the Coulomb’s inverse square law in electrostatics. According to the law,
“ The electrostatic force of attraction or repulsion between two stationary point charges is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them”
The S.I unit of electric charge is coulomb. A definition of coulomb can be obtained from Coulomb’s law. One coulomb of charge is that charge which when placed at rest in vacuum at a distance of one metre from an equal and similar stationary charge repels it and is repelled by it with a force of 9 x 109 newton.
Direction of the force
The electrostatic force between two stationary point charges is along the straight line joining the two charges. The force is repulsive if both the charges have the same sign and it is attractive if the charges have the opposite sign.
Important Results of Coulomb’s Law
- According to Coulomb’s law force between two charges is mutual. The forces exerted by the charges on each other are equal in magnitude but opposite in direction. These forces form an action and reaction pair in accordance with Newton’s third law of motion.
- The electrostatic force between any two charges is not affected by the presence of other charges in the neighbourhood.
- The principle of superposition holds good for coulomb’s force. When a number of charges are interacting the net force on the given charge is the vector sum of the forces exerted on it by all other charges.
- The equilibrium of a charged particle under the action of Coulombian forces alone can never be stable.
Gauss Theorem or Gauss Law
Gauss law is of fundamental importance in the study of electric fields. It deals with the net electric flux through the closed surface, generally called Gaussian surface and the net charge enclosed by the surface. The electric flux through the surface is defined as the number of lines of force passing normally through the surface. According to Guass theorem the electric flux from any closed surface is only due the charges (positive or negative) enclosed by the surface. Any charges outside the surface do not contribute the electric flux. The Gauss law-Applications and Gauss theorem Formula is only a restatement of Coulomb’s law.
Gauss law states that “ The total electric flux through the hypothetical close surface is always equal to 1/ε0 times the net charge enclosed by the surface.
Applications of Gauss Law
- Electric intensity at the surface of a charged conductor
Applying Gauss law we can find the electric intensity at the surface of the charged conductor. The point outside and near the surface of a charged conductor in equilibrium is directly proportional to the surface density of charge.
E = σ/ε0.
- Electric intensity at a point near a spherical conductor
The electric intensity at a point outside and near a charged spherical conductor is the same as that of a point charge q at the centre of the conductor. If the point is considered infinitesimally close to the surface of the conductor then the electric field intensity is equal to the surface density of the charge.