A charge of \(3.1 \mathrm{C}\) moves from the positive to the negative terminal of a \(9.0-\mathrm{V}\) battery. How much energy does the battery impart to the charge?

Electric charge is one of the fundamental properties of particles that determines their electromagnetic interactions. Fundamentally, there are two types of electric charges: positive and negative. Opposite charges attract each other, while like charges repel. The standard unit for measuring electric charge is the Coulomb (C), which is a relatively large unit in the realm of particles and everyday objects. It’s important for students to understand that electric charges are conserved; they can be transferred from one object to another but cannot be created or destroyed.

In practical terms, objects or particles become charged when they gain or lose electrons, which carry a negative charge. The electric charge's role in the problem above is pivotal since it’s the quantity of charge that is moving through the electrical potential created by the battery, resulting in the work being done or energy transferred.

The electric potential difference, also known as voltage, is a representation of the work required to move a unit charge from one point to another in an electric field. It's measured in Volts (V) and can be thought of as the electric 'pressure' that drives charge through a circuit. A higher potential difference means more energy per unit charge is available to be transferred.

Understanding the concept of electric potential difference is crucial when analyzing electrical circuits. In the given exercise, the battery provides a potential difference of 9.0 volts, which determines how much energy each Coulomb of charge acquires as it moves from the positive to the negative terminal of the battery. This concept helps explain why household batteries have different voltages, such as 1.5V, 9V, or 12V, each designed for specific applications where different amounts of energy transfer are required.

The work done by a battery on an electric charge is the amount of energy the battery imparts to the charge as it moves through the circuit. This concept is closely related to electric potential energy, which is the potential energy a charged particle has due to its position in an electric field. The work done by a battery is calculated by multiplying the charge (in Coulombs) by the electric potential difference (in Volts) the battery provides, expressed by the equation \( W = QV \).

When a charge moves against the electric potential difference, the battery is doing work on the charge, increasing its electric potential energy. In our exercise, a charge of 3.1 Coulombs moving through a 9.0-Volt potential difference means the battery does 27.9 Joules of work on the charge. This calculation shows how energy is conserved and transformed from chemical energy in the battery into electric potential energy of the charge.