Electric Potential and Work (Electrostatics) - MCAT

What is electric potential? By definition, electric potential is the potential energy per unit charge. The unit for electric potential is the volt (V). According to the definition of electric potential, the unit can also be expressed as (J/C). This is very important because the MCAT may use both interchangeably. So, what exactly does electric potential mean? The best way to explain electric potential is to use the concepts that govern the macroscopic world and to apply them to the microscopic world of charges. Objects possess some charge that can be positive, negative or neutral. The charge which constitutes the objects sets up an electric field around the object that acts as a “detector.” This electric field is what allows the object to detect neighboring objects or fields. If the field points outward than the object has a positive net charge and if the field points inward the object has a negative net charge. If another charged object were to enter the field, an electric force would act on the object accelerating it in some direction. Which direction? The direction of the net force acting on the charged object—this is what Newton’s second law tells us. But, how do you determine direction? Imagine that you have a positive source charge. The direction of the electric field for the source charge will be outward. Now, you place a positive test charge in the electric field. What happens? The direction of the net force acting on the test charge is outward since it will repel the source charge. Thus, it will accelerate in the direction of the field. The opposite will happen with a negative test charge—it will accelerate in the direction opposite of the electric field. You can calculate the magnitude of the force using the following equation:

F=qE

Where q is the test charge and E is the magnitude of the electric field of the source charge.

The electric field is a vector approach to explain the behavior of charged objects (similar to velocity and moving objects). Electric potential is a scalar approach to explain the behavior of charged objects (similar to kinetic energy and moving objects). From Newton’s second law, if an object moves in the direction of the net force acting on it, the velocity of the object will increase. This means the kinetic energy will increase. Conversely, if the object moves opposite the direction of the net force acting on it, the kinetic energy will decrease. For charged objects, the electric potential explains the energy of an object with respect to its position in some electric field. So, how do you explain the potential and kinetic energy of a charged object? Consider the macroscopic world. If you were to lift a book from the ground over your head, what kind of energy does the book gain? It gains potential energy. If you were to then drop the book from above your head, what happens? The potential energy translates into kinetic energy. When you lift the book over your head, you are doing something the book would not normally do. When you drop the book from the top of your head, the book is doing what it wants to do—to move in the direction of gravity and to the floor. This means that when an object does something it “naturally” will not do, it will gain potential energy. When an object does something it “naturally” wants to do, it will gain kinetic energy (This makes sense according to Newton’s first law). This same idea can be applied to the microscopic world. When a positive test charges moves in the direction of the electric field due to a positive source charge, the test charge is doing something it naturally wants to do, potential energy is lost and kinetic energy is gained. This means for the system to gain potential energy some external agent needs to act on the system to push the two “like” charges near one another. Only then will potential energy be gained.

In a nutshell:

• When two like charges repel, this is a natural tendency. Thus potential energy is lost and kinetic energy is gained.

• When opposite charges attract, this is a natural tendency. Thus potential energy is lost and kinetic energy is gained.

• In order to move two like charges near one another, this will not naturally happen because they will repel, external work needs to be done on the system. This means potential energy is gained and kinetic energy is lost.

So now that the concepts are explained, let me introduce some equations. The mathematical representation for electric potential is:

V = U/q

Where V is the electric potential, U is the potential energy and q is the charge.

The potential energy of a test charge is:

U = qV.
This will be negative when potential energy is lost and positive when potential energy is gained. This is a very important point for the MCAT because when asked to calculate the potential energy of the system, you can knock out choices you know are wrong based on what you know of the tendency of the system. This saves time on the test and prevents unnecessary calculations. Work is defined as:

W = -ΔU

Thus negative work means a positive change in potential energy. This is another important point for the MCAT.