## Electric Fields

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 by gives The electric field at the position of due to the charge is 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  