What is the difference between electrical potential and electric potential energy?

Introduction

To grasp the nuances of electrical phenomena, it’s important to understand the concepts of electric potential and electric potential energy. Both are central to electromagnetism and play a vital role in describing how electric charges interact within electric fields. However, despite being closely related, these terms are not interchangeable.

Electric Potential Energy

Electric potential energy is a form of potential energy that results from the interaction of charged objects due to their positions or arrangements. Similar to gravitational potential energy, which depends on the mass of an object and its height in a gravitational field, electric potential energy depends on the charge of an object and its position in an electric field.

Consider two charges in space. The electric potential energy of the system is the work done to assemble this system of charges from infinity. If the charges are alike (both positive or both negative), work must be done to overcome the electrostatic repulsion as they’re brought together. This work is stored as electric potential energy. If the charges are unlike, they naturally attract each other, and work must be done to separate them; again, this work is stored as electric potential energy.

In a system of more than two charges, the total electric potential energy is the sum of the electric potential energy of each pair of charges. The electric potential energy is a scalar quantity, meaning it has magnitude but no direction. It is typically measured in joules (J).

Electric Potential

Electric potential, on the other hand, is the amount of electric potential energy per unit charge. In other words, it’s the work done by an external force to bring a positive unit test charge from infinity to a specific point in the electric field without any acceleration.

It’s important to note that electric potential is not the same as potential energy. Rather, it is the ‘potential’ for creating electric potential energy. Just as gravitational potential energy per unit mass gives gravitational potential, electric potential energy per unit charge gives electric potential.

Electric potential is a scalar quantity and is measured in volts (V), where 1 V = 1 Joule/Coulomb. It is often described as the electric potential ‘at a point’, emphasizing its spatially variant property.

The Connection and Differences

Electric potential and electric potential energy are closely related. For a charge q in an electric field, the electric potential energy U is given by U=qV, where V is the electric potential at the charge’s location. Essentially, the electric potential energy of a system is the amount of ‘potential’ for doing work, while the electric potential is a way of quantifying this potential energy per unit charge.

The key difference between them is what they describe: electric potential energy is concerned with the energy of a specific system of charges, while electric potential relates to the electric field itself, independent of the presence of any particular charges.

Another difference is that electric potential energy is associated with a pair or a system of charges, while electric potential is associated with a point in the electric field.

Conclusion

Understanding electric potential and electric potential energy is essential in electromagnetism, enabling us to analyze the behavior of charges in electric fields and the energy transformations that occur in these systems. Although these terms are related, they describe different aspects of electrical phenomena and must be used correctly to accurately describe physical systems. As you continue your study of electromagnetism, you will see these concepts in action in a variety of situations, from the operation of capacitors in electronic circuits to the dynamics of particles in high-energy physics experiments.