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PHYS 241 Recitation

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PHYS 241 Recitation

Kevin Ralphs

Week 4

- HW Questions
- Potential
- Quiz Questions

Ask away….

- 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)

- 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

- 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

- In a closed system with no dissipative forces
- The work done is due to the electric force so

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

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.

- 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

- The gradient is a vector operator that gives two pieces of information about a scalar function

- 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)