CHARLES AUGUSTIN DE COULOMB ( – ) Since force is a vector, it is better to write Coulomb’s law in the vector notation. Let the position vectors of charges q and q be r and r respectively [see Fig. . (a)].
We denote force on q due to q by F and force on q due to q by F . The two point charges q and q have been numbered and for convenience and the vector leading from to is denoted by r : r = r – r In the same way, the vector leading from to is denoted by r : r = r – r = – r The magnitude of the vectors r and r is denoted by r and r , respectively ( r = r ). The direction of a vector is specified by a unit vector along the vector. To denote the direction from to (or from to ), we define the unit vectors: ˆ = r , ˆ ˆ ˆ , Coulomb’s force law between two point charges q and q located at r and r is then expressed as ˆ o F ( .
) Some remarks on Eq. ( . ) are relevant: • Equation ( . ) is valid for any sign of q and q whether positive or negative.
If q and q are of the same sign (either both positive or both negative), F is along ˆ r , which denotes repulsion, as it should be for like charges. If q and q are of opposite signs, F is along – ˆ r (= ˆ r ), which denotes attraction, as expected for unlike charges. Thus, we do not have to write separate equations for the cases of like and unlike charges. Equation ( .
) takes care of both cases correctly [Fig. . (b)]. • The force F on charge q due to charge q , is obtained from Eq.
( . ), by simply interchanging and , i.e., ˆ = − F F Thus, Coulomb’s law agrees with the Newton’s third law. • Coulomb’s law [Eq. ( .
)] gives the force between two charges q and q in vacuum. If the charges are placed in matter or the intervening space has matter, the situation gets complicated due to the presence of charged constituents of matter. We shall consider electrostatics in matter in the next chapter. FIGURE .
(a) Geometry and (b) Forces between charges.