Electric Potential: Overview

Imagine a universe that only consists of two protons, initiall at rest and very close to each other. We know what will happen, they will repel each other and accelerate away in opposite directions. In the initial state they had zero kinetic energy but that doesn't last. Where did that energy come from? It came from the fact that they have in increased electric potential energy when they start out and that energy is convered into kinetic energy. That's almost at the heart of what potential energy is, a potential to manifest real, tangible, kinetic energy. Since energy is a scalar, their must be a scalar field that can facilitate this interaction. That field is the electric potential. You may have more experience with it than you think because it is measured in Volts.

OpenStax shows some awesome application of the electric potential below.

https://www.youtube.com/watch?v=ZZJ5znGvYAU

Big Ideas

Big Idea 1: Objects and systems have properties such as mass and charge. Systems may have internal structure.

Bid Idea 2: Fields existing in space can be used to explain interactions.

Big Idea 4: Interactions between systems can result in changes in those systems.

Big Idea 5: Changes that occur as a result of interactions are constrained by conservation laws.

Learning Objectives

BoxSand Learning Objectives

Electric-Fields-Potentials.Electric-Potential.LO.BS.1: Understand that the electric potential is a scalar field.

Electric-Fields-Potentials.Electric-Potential.LO.BS.2: Understand the connection between the electric potential and the electric field.

Electric-Fields-Potentials.Electric-Potential.LO.BS.3: Be able to calculate the electric potential from a set of point charges.

Electric-Fields-Potentials.Electric-Potential.LO.BS.4: Be able to use the equation for the electric potential from a point charge to calculate forces on other charged particles.

Electric-Fields-Potentials.Electric-Potential.LO.BS.5: Understand the connection between electric potential and electric potential energy.

Electric-Fields-Potentials.Electric-Potential.LO.BS.6: Understand, qualitatively, the shape of the potential from an electric dipole.

Electric-Fields-Potentials.Electric-Potential.LO.BS.7: Students should understand the concept of electric potential, so they can:

Determine the electric potential in the vicinity of one or more point charges.
Calculate the electrical work done on a charge or use conservation of energy to determine the speed of a charge that moves through a specified potential difference.
Determine the direction and approximate magnitude of the electric field at various positions given a sketch of equipotentials.
Calculate the potential difference between two points in a uniform electric field, and state which point is at the higher potential.
Calculate how much work is required to move a test charge from one location to another in the field of fixed point charges.
Calculate the electrostatic potential energy of a system of two or more point charges, and calculate how much work is required to establish the charge system.

Electric-Fields-Potentials.Electric-Potential.LO.BS.8: Students should understand the definition and function of capacitance, so they can:

Relate stored charge and voltage for a capacitor.
Relate voltage, charge, and stored energy for a capacitor.
Recognize situations in which energy stored in a capacitor is converted to other forms.

Electric-Fields-Potentials.Electric-Potential.LO.BS.9: Students should understand the physics of the parallel-plate capacitor, so they can:

Describe the electric field inside the capacitor, and relate the strength of this field to the potential difference between the plates and the plate separation.
Determine how changes in dimension will affect the value of the capacitance.

College Board Learning Objectives

Electric-Fields-Potentials.Electric-Potential.LO.BS.2.E.1.1: The student is able to construct or interpret visual representations of the isolines of equal gravitational potential energy per unit mass and refer to each line as a gravitational equipotential. [SP 1.4, 6.4, 7.2]

Electric-Fields-Potentials.Electric-Potential.LO.BS.2.E.2.1: The student is able to determine the structure of isolines of electric potential by constructing them in a given electric field. [SP 6.4, 7.2]

Electric-Fields-Potentials.Electric-Potential.LO.BS.2.E.2.2: The student is able to predict the structure of isolines of electric potential by constructing them in a given electric field and make connections between these isolines and those found in a gravitational field. [SP 6.4, 7.2]

Electric-Fields-Potentials.Electric-Potential.LO.BS.2.E.2.3: The student is able to qualitatively use the concept of isolines to construct isolines of electric potential in an electric field and determine the effect of that field on electrically charged objects. [SP 1.4]

Electric-Fields-Potentials.Electric-Potential.LO.BS.2.E.3.1: The student is able to apply mathematical routines to calculate the average value of the magnitude of the electric field in a region from a description of the electric potential in that region using the displacement along the line on which the difference in potential is evaluated. [SP 2.2]

Electric-Fields-Potentials.Electric-Potential.LO.BS.2.E.3.2: The student is able to apply the concept of the isoline representation of electric potential for a given electric charge distribution to predict the average value of the electric field in the region.[SP 1.4, 6.4]

Enduring Understanding and Essential Knowledge

Enduring Understanding	Essential Knowledge
Electric-Fields-Potentials.Electric-Potential.EU.CB.2.E: Physicists often construct a map of isolines connecting points of equal value for some quantity related to a field and use these maps to help visualize the field.	Electric-Fields-Potentials.Electric-Potential.EK.CB.2.E.1: Isolines on a topographic (elevation) map describe lines of approximately equal gravitational potential energy per unit mass (gravitational equipotential). As the distance between two different isolines decreases, the steepness of the surface increases. [Contour lines on topographic maps are useful teaching tools for introducing the concept of equipotential lines. Students are encouraged to use the analogy in their answers when explaining gravitational and electrical potential and potential differences.] Relevant Equation: $U_{G} = - \frac{G m_{1} m_{2}}{r}$ Electric-Fields-Potentials.Electric-Potential.EK.CB.2.E.2: Isolines in a region where an electric field exists represent lines of equal electric potential, referred to as equipotential lines. An isoline map of electric potential can be constructed from an electric field vector map, using the fact that the isolines are perpendicular to the electric field vectors. Since the electric potential has the same value along an isoline, there can be no component of the electric field along the isoline. Relevant Equation: $V = \frac{1}{4 \pi \epsilon_{0}} \frac{q}{r}$ Electric-Fields-Potentials.Electric-Potential.EU.CB.2.E.3: The average value of the electric field in a region equals the change in electric potential across that region divided by the change in position (displacement) in the relevant direction. Relevant Equation: $E = \frac{\Delta V}{\Delta r}$