Fundamentally the electric field
is defined as the force
per unit charge
experience by a small charge – small enough so as not to disturb the field in any way. We can write
or
A electric charge or combination of electric charges produces an electric field – that is, a force is exerted on any electric charge that comes close to these charges. If a 'test charge'– an infinitesimally small charge, so that the distribution of charges is not disturbed and the electric field does not change -is introduced, the force experienced by the test charge will be the sum of the forces exerted by each individual charge in the distribution. We can use Coulomb's Law to write
where
is the unit vector from charge
to the test charge
Then
Dividing bygives
The electric field at the position ofdue to the chargeis
so we can also write
This means that we can find the field due to each charge as a vector and add them.
The technical term is linear – the electric field and the electric force are both linear in the charges