Write the vector form of force acting between two charges q 1 and q 2 having r 1 → and r 2 → as their position vectors respectively.

Consider two positive point charges q 1 and q 2 placed in vacuum at distance r from each other. In vector form, Force on charge q 2 due to q 1 is F → 21 = 1 4 π ε 0 ⋅ q 1 q 2 r 2 r ^ 12 Where r ^ 12 is a unit vector in the direction from q 1 to q 2 Similarly, Force on charge q 1 due to q 2 is F → 12 = 1 4 π ε 0 ⋅ q 1 q 2 r 2 r ^ 21 Where r ^ 21 is a unit vector in the direction from q 2 to q 1 .

State Coulomb's law in vector form and prove that F → 21 = − F → 12 where letters have their usual meanings.

Consider two positive point charges q 1 and q 2 placed in vacuum at distance r from each other. Coulomb's law: Magnitude electrostatic force between two point charges separated by a distance, (iv) is directly proportional to product of magnitude of two charges (v) is inversely proportional to square of the distance between them (vi) will act along the line joining two charges. F = 1 4 π ε 0 q 1 q 2 r 2 In vector form, Force on charge q 2 due to q 1 is F → 21 = 1 4 π ε 0 ⋅ q 1 q 2 r 2 r ^ 12 Where r ^ 12 is a unit vector in the direction from q 1 to q 2 Similarly, Force on charge q 1 due to q 2 is F → 12 = 1 4 π ε 0 ⋅ q 1 q 2 r 2 r ^ 21 Where r ^ 21 is a unit vector in the direction from q 2 to q 1 The Colomb forces between unlike charges ( q 1 q 2 < 0 ) are attractive, as shown in the figure As r ^ 21 = − r ^ 12 , therefore F → 21 = − F → 12 . This means that the two charges exert equal and opposite forces on each other. So Coulomb forces obey Newton’s third of motion.