What is the potential energy of
this system?
PEe = 2.16×10^10 J
24.4 - Electric potential
Electric potential: The electric potential energy
of a test charge at a given point in a field,
divided by the test charge.
The electric potential of a location in an electric field is the measure of how much
electric potential energy will be generated by placing a charge at that point. It is
analogous to the concept of electric field. Just as the concept of electric field provides a
way to determine how much electric force any charge will encounter at a given location,
the concept of electric potential is used to determine how much potential energy placing
the charge in a field will generate.
The term “electric potential” may seem confusing, since we are already using the
related term “electric potential energy.” The formula in Equation 1 provides a direct way
to calculate electric potential. The electric potential at a point in a field is calculated by
placing a test charge in a field, determining the potential energy of the system created
by introducing the charge at that location, and then dividing by the test charge.
The electric potential at any point is unique, which means it has only one value. This
reflects the fact that the electrostatic force is conservative, and any configuration of
charges has just one value for its potential energy. Electric potential has no direction,
only a magnitude, making it a scalar. In Concept 1, you see a graph of the electric
potential around a positive point charge, and in Concept 2, you see the graph of the
electric potential around a negative point charge. Note how the electric potential
increases near the positive point charge, and becomes increasingly negative near the
negative point charge. This reflects how the PEe of a positive test charge will increase
near a positive charge, and take on larger negative values near a negative charge.
The graphs on the right provide metaphors for electric potential. The positive charge
creates a potential peak, a mountain to be scaled, while the negative charge creates a
potential well, a hole to be climbed out of.
You should remember that, just like electric fields, real potential peaks and wells exist
around charges in three-dimensional space. They would require four dimensions to properly graph! The three-dimensional graphs in Concepts
1 and 2 only show the electric potential at locations lying in a plane around a point charge.
The equation for calculating the electric potential at locations around a point charge is shown in Equation 2. The equation can be derived from
the equation for the PEe of a pair of charges. The PEe created by placing a test charge in the field is calculated, and then the PEe is divided
by the test charge, which means the test charge factor cancels out of the equation. Like the equation for potential energy from which it comes,
this equation assumes there is zero potential energy when there is an infinite separation between the charges. This is the same as stating that
the electric potential infinitely far away from a point charge is zero, as suggested by the graphs of the potential peak and the potential well.
The unit of electric potential is the volt. A volt is defined as one joule per coulomb, or energy per unit charge. It is named after Alessandro Volta
(1745-1827), the Italian inventor of the system that underlies the design of most batteries.
Electric potential
Reflects ability of fields to create PE
Calculated as electric PE / test chargeElectric potential
Potential can be positive or negative