Compare the effets of an electric field on a test charge that is moved from a distance of 2.0 cm to 4.0 cm from the field source.
A field in this context refers to any condition in which a force can be applied to an object over a distance with no physical contact. An every day example is gravity. The force of gravity acting on an object works over great distances of separation. The force created in this manner is dependant upon the "field strength". The field strength is measured at a test object located a distance from the object creating the field.
An electric field is created around any object which has an electric charge. The field strength is then measured by placing a test charge at a distance d away and determining the electrostatic force using Coulomb's Law:
Fe = kQq/d^2 where k is Coulomb's Constant, Q is the charge creating the electric field, q is the test charge, and d is the distance of separation. If we regroup this equation we get
Fe =(kQ/d^2)q. The (kQ/d^2) represents the electric field strength.
From this we can see that the field strength follows the inverse square law. That is that the strength is inversely proportional to the square of the distance to the test charge.
When we move from 2.0cm to 4.0cm, we are doubling the distance. The inverse square law predicts that this will reduce the field strength to 1/4 the value at 2.0cm.