PHYS 241 Recitation

1. PHYS 241 Recitation Kevin Ralphs Week 4

2. Overview • HW Questions • Potential • Quiz Questions

3. HW Questions Ask away….

4. Potential • What does it tell me? • The change in potential energy per unit charge an object has when moved between two points • Why do I care? • The energy in a system is preserved unless there is some kind of dissipative force • So the potential allows you to use all the conservation of energy tools from previous courses (i.e. quick path to getting the velocity of a particle after it has moved through a potential difference)

5. Potential • Why do I care? (cont.) • If you have the potential defined over a small area, the potential function encodes the information about the electric field in the derivative

6. Potential • Word of caution: • Potential is not the same as potential energy, but they are intimately related • Electrostatic potential energy is not the same as potential energy of a particle. The former is the work to construct the entire configuration, while the later is the work required to bring that one particle in from infinity • There is no physical meaning to a potential, only difference in potential matter. This means that you can assign any point as a reference point for the potential • The potential must be continuous

7. Potential • In a closed system with no dissipative forces • The work done is due to the electric force so

8. Potential • The change in potential is the change in potential energy per unit charge • For charge distributions obeying Coulomb’s law we get the following:

9. Potential Although vectors hold more information than scalars, special kinds of vector fields can be “compressed” into a scalar field where the change of the field in a certain direction tells you the component of the field in that direction.

10. Potential • Gradient • The gradient is a vector operator that gives two pieces of information about a scalar function • Direction of steepest ascent • How much the function is changing in that direction • It transforms a scalar function into a vector field where every vector is perpendicular to the function’s isolines

11. Potential • We recover the electric field from the potential using the gradient • The isolines (or isosurfaces) of the potential are called equipotentials • So the electric field is perpendicular to the equipotential lines (surfaces)