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Potential energy (PE) is stored energy that is associated with the position of an object within a force field, such as the gravitational field or an electric field. In the context of charged particles, PE is the energy that a charge possesses due to its position in an electric field.

The formula PE = qV represents the potential energy of a charge in an electric field, where 'q' denotes the charge, and 'V' signifies the potential difference (voltage) across the field. Consider an example where an electron is lifted within an electric field; as it moves against the field's direction, it gains potential energy. This potential energy can be converted into kinetic energy if the electron is allowed to accelerate back through the field.

Kinetic energy (KE) is the energy that an object possesses due to its motion. Unveiling the relation between kinetic energy and charges in electric fields, a charged particle accelerates when subjected to an electric field, thereby converting its potential energy into kinetic energy.

In our textbook exercise, the charged ion's kinetic energy is equal to the potential energy it acquired from the electric field, as indicated by the principle of energy conservation. If we know the kinetic energy a particle has acquired, we can deduce the potential energy it must have had before being accelerated.

An electric field is a vector field that surrounds electric charges, exerting a force on other charges within the field. The strength of this invisible field determines how strongly a charge would be acted upon. It is often visualized with field lines spreading out from a positive charge or converging onto a negative charge.

Electric Field Direction

The direction of the electric field is defined as the direction of the force on a positive test charge. Accordingly, the field lines are directed away from positive charges and toward negative charges.

Electric Field Intensity

The field's intensity is quantified as force per unit charge, with the SI unit being volts per meter (V/m). As the force acting on a charge increases, or as the charge's distance from the source charge decreases, the electric field strength similarly increases.

Charge is an intrinsic property of subatomic particles that causes them to experience a force when placed in an electric or magnetic field. Charges come in two varieties—positive and negative. Like charges repel each other, while unlike charges attract each other.

Charges are measured in coulombs (C), and the force between charges is described by Coulomb's law. In our problem, we encounter a doubly charged ion, which implies that the ion carries twice the elementary charge of an electron (approximately 1.602 x 10^-19 C). The interaction of this charge with the electric field between the plates is what propels the ion and alters its energy states.

Potential difference, also known as voltage, represents the work done per unit charge to move a charge from one point to another within an electric field. It is the driving 'force' that facilitates the movement of charges in a circuit or between two points in space.

The potential difference is what we calculate when we want to determine the change in potential energy per unit charge for an electric field. In our scenario, this voltage propels the doubly charged ion from a state of lower potential energy to a state of higher kinetic energy as it accelerates between the parallel conducting plates. The relationship voltage (V) = energy (E) / charge (q) is pivotal for understanding how electric fields do work on charges.