Voltage

What happens when a charged body moves or is moved from one point to another in an electric field? How can this be expressed mathematically?

Its potential energy changes, work is done on the charge by the field. This is expressed V = W/q

What is electrical potential energy?

a form of energy that is stored in an electric field. Work is done on/by the field when a charged particle is forced to move against/within the field.

What is voltage of an electrical source (e.g. a battery)?

Voltage (or EMF, electromotive force) is a measure of the energy supplied to each coulomb of charge passing through it. Hence a source such as a battery supplies electrical potential energy.

Describe the electrical field between two parallel plates

The electric field is uniform. As a charged particle moves through such a field, the force from one plate increases while that from the other plate decreases so that the total force remains constant.

What happens when a charged object moves against the direction it would naturally move in an electric field?

Work is done on the field

What happens when a charged object moves in the direction it would naturally move in an electric field?

The field would do work on the object/particle