Phys 241 recitation
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PHYS 241 Recitation. Kevin Ralphs Week 4. Overview. HW Questions Potential Quiz Questions. HW Questions. Ask away…. 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?

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PHYS 241 Recitation

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Phys 241 recitation

PHYS 241 Recitation

Kevin Ralphs

Week 4


Overview

Overview

  • HW Questions

  • Potential

  • Quiz Questions


Hw questions

HW Questions

Ask away….


Potential

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)


Potential1

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


Potential2

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


Potential3

Potential

  • In a closed system with no dissipative forces

  • The work done is due to the electric force so


Potential4

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:


Potential5

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.


Potential6

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


Potential7

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)


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