Electric Force

Coulomb's law, developed in the 1780s by French physicist Charles Augustin de Coulomb, may be stated as follows:

Coulomb's Law

The magnitude of the electrostatic force between two point electric charges is directly proportional to the product of the magnitudes of each charge and inversely proportional to the square of the distance between the charges.

The direction of that force is directed towards a point between them if they are of opposite charge to each other, and away from it if they are both of the same type of charge.


The definition of the Coulomb Force is represented by this equation:

The electric force Fe (that acts on charges):



ε0 is the permitivitty of free space,

Q1 and Q2 are the charges and

r is the distance they are apart

The Coulomb force is a force - so it is a vector!

A positive result indicates a repulsive force (two negative charges or two positives will result in that).

A negative result indicates an attractive force (one charge of each type will result in that).

Comparison of Electic Force to Gravitational Force

The gravitational force (that acts on masses) is given my the following equation:

(the negative sign shows that the force is always attractive)


G is the gravitational constant,

m1 and m2 are the masses and

r is the distance they are apart.

Can you see the similarity?

The examiners will expect you to be able to...

An example - comparing the forces

Consider two electrons one metre apart:

mass of the electron me = 9.11 x 10-31 kg

charge on the electron Qe = 1.60 x 10-19 C

G = 6.67 x 10-11 m3 kg-1 s-2

o = 8.85 x 10-12 F m-1

The gravitational force acting on the two electrons is 8.3 X 10 -61 N

The coulomb force acting on the two electrons is 2.3 x 10-28 N

Therefore the coulomb force is 1032 times bigger than the gravitational force

100,000,000,000,000,000,000,000,000,000,000 times bigger

.... that's why we have to think of charged particles as being in a 'different dimension' to us.... they experience the 'hills and dales of the electric field' much more strongly than the 'ups and downs' of the gravitational field.... and the effect of gravity on their mass is negligible to the effect of the electric field on their charge.

We have much more mass than net charge - so we are often unaware of electric fields - but very aware of gravity!

See also - electric field, electric potential, electric force, electric intensity (field strenth) and Alpha scattering

LOJ MARCH 2002 - revamped 2023