6.2.2 Coulomb’s law

According to Coulomb's law, any two point charges exert an electrostatic (electrical) force on each other that is directly proportional to the product of their charges and inversely proportional to the square of the distance between them:

F ∝ Qq

F ∝ 1/r²

F = kQq/r²

The separation of the charges is 'r'. The magnitudes of the charges are Q and q. The electrostatic force experienced by each point is F. The point charges interact and will exert equal but opposite forces on each other (N3). K is the constant of proportionality:

k = 1/4πε0

NOTE: ε0 is the permittivity of free space ε0 (8.58 x 10^-12 Fm^-1). This means we can write:]

F = Qq/4πε0r²

As we know from 6.2.1, the electric field strength 'E' is equal to F/q:

E = F/q = Qq/4πε0r²q = Q/4πε0r²

From this we can see that electric field strength is directly proportional to the charge Q and is inversely proportional to the square of r. This means that a graph of E against 1/r² will produce a straight line through the origin.

Similarities and differences
Okay so we need to know some similarities and differences between electric and gravitational fields. I took the liberty of making a table:

Gravitational fields	Electric fields
Point masses produce a radial field	Point charges produce a radial field
Masses only produce an attractive field	Charges can produce an attractive or repulsive field
Gravitational field strength is the force per unit mass g = F/m = -GM/r2	Electric field strength is the force per unit positive charge E = F/q = Q/4πε0r2
F ∝ Mm	F ∝ Qq
F ∝1/r2	F ∝1/r2
F = -GMm/r2	F = Qq/4πε0r2

Different fields
It is important to remember that not just electric fields give rise to a force. We also have magnetic, and gravitational fields we cover in this spec!