## Electric Fields

Fundamentally the electric fieldis defined as the forceper unit chargeexperience 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

whereis the unit vector from chargeto the test charge

Then

Dividing bygives

The electric field at the position ofdue to the chargeisso 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