Connection for ap® courses

In Electric Charge and Electric Field, we just scratched the surface (or at least rubbed it) of electrical phenomena. Two of the most familiar aspects of electricity are its energy and voltage . We know, for example, that great amounts of electrical energy can be stored in batteries, are transmitted cross-country through power lines, and may jump from clouds to explode the sap of trees. In a similar manner, at molecular levels, ions cross cell membranes and transfer information. We also know about voltages associated with electricity. Batteries are typically a few volts, the outlets in your home produce 120 volts, and power lines can be as high as hundreds of thousands of volts. But energy and voltage are not the same thing. A motorcycle battery, for example, is small and would not be very successful in replacing the much larger battery in a car, yet each has the same voltage. In this chapter, we shall examine the relationship between voltage and electrical energy and begin to explore some of the many applications of electricity. We do so by introducing the concept of electric potential and describing the relationship between electric field and electric potential.

This chapter presents the concept of equipotential lines (lines of equal potential) as a way to visualize the electric field (Enduring Understanding 2.E, Essential Knowledge 2.E.2). An analogy between the isolines on topographic maps for gravitational field and equipotential lines for the electric field is used to develop a conceptual understanding of equipotential lines (Essential Knowledge 2.E.1). The relationship between the magnitude of an electric field, change in electric potential, and displacement is stated for a uniform field and extended for the more general case using the concept of the “average value” of the electric field (Essential Knowledge 2.E.3).

The concept that an electric field is caused by charged objects (Enduring Understanding 2.C) supports Big Idea 2, that fields exist in space and can be used to explain interactions. The relationship between the electric field, electric charge, and electric force (Essential Knowledge 2.C.1) is used to describe the behavior of charged particles. The uniformity of the electric field between two oppositely charged parallel plates with uniformly distributed electric charge (Essential Knowledge 2.C.5), as well as the properties of materials and their geometry, are used to develop understanding of the capacitance of a capacitor (Essential Knowledge 4.E.4).

This chapter also supports Big Idea 4, that interactions between systems result in changes in those systems. This idea is applied to electric properties of various systems of charged objects, demonstrating the effect of electric interactions on electric properties of systems (Enduring Understanding 4.E). This fact in turn supports Big Idea 5, that changes due to interactions are governed by conservation laws. In particular, the energy of a system is conserved (Enduring Understanding 5.B). Any system that has internal structure can have internal energy. For a system of charged objects, internal energy can change as a result of changes in the arrangement of charges and their geometric configuration as long as work is done on, or by, the system (Essential Knowledge 5.B.2). When objects within the system interact with conservative forces, such as electric forces, the internal energy is defined by the potential energy of that interaction (Essential Knowledge 5.B.3). In general, the internal energy of a system is the sum of the kinetic energies of all its objects and the potential energy of interaction between the objects within the system (Essential Knowledge 5.B.4).