Electric Force: Coulomb's Law

So far we have discussed the attraction and repulsion between electric charges only qualitatively, Coulomb was the first scientist to write down the force law for attraction and repulsion between electric charges quantitatively.

Coulomb's Law for the magnitude of the electrostatic force between two point charges q₁ and q₂, kept at distance r apart is:

F = k	q₁ q₂

	r²

The value of k depends on the medium in which the charges are placed. In vacuum, the value of k, Coulomb's constant: is

k₀ = 8.9874 $\cdot$ 10⁹ Nm²/C² 9.0 $\cdot$ 10⁹ Nm²/C²

This tells us that the force between two charges, 1 C each, kept at a distance of 1 m in vacuum is almost 10¹⁰ N, a huge force. The Coulomb is a rather large charge unit:

typical charges in electrostatic charging: 10⁹ e = 10⁹ $\cdot$ 1.6$\cdot$ 10^-19 C $\cdot$ 10^-10 C
typical charges in the laboratory: pC to mC
typical charge transfer between a thundercloud and the ground by a lightning bolt: 10 to 100 C.

If the two charges have the same sign, F is positive, denoting a repulsive force. If they have different signs (one positive and the other negative), the sign of F is negative, indicating an attractive force. This will become more clear when we discuss the vector nature of the force:

If ₁₂ is the force on charge 1 due to charge 2, and ₁₂ is the unit vector along the line joining the two from q₂ to q₁, then:

₁₂ = k	q₁ q₂	₁₂

	r²

Now you see that if either of q₁ or q₂ is negative, then ₁₂ is directed along -₁₂ , i.e. toward q₂.

Mutual nature of the forces: ₁₂ and ₂₁, the force on charge 2 due to charge 1, constitute a mutual pair of action-reaction forces, in the sense of Newton's Third Law :

₂₁ = -

₁₂