PHYS 221 Recitation

1. PHYS 221 Recitation Kevin Ralphs Week 2

2. Overview • HW Questions • Gauss’s Law • Conductors vs Insulators • Work-Energy Theorem with Electric Forces • Potential

3. HW Questions Ask Away….

4. Flux/Gauss’s Law • History • The 18th century was very productive for the development of fluid mechanics • This lead physicists to use the language of fluid mechanics to describe other physical phenomena • Mixed Results • Caloric theory of heat failed • Electrodynamics wildly successful

5. Gauss’s Law • What does it tell me? • The electric flux (flow) through a closed surface is proportional to the enclosed charge • Why do I care? • You can use this to determine the magnitude of the electric field in highly symmetric instances; The symmetries of the charge distribution are reflected in the field they create • Flux through a closed surface and enclosed charge are easily exchanged

6. Conductors vs Insulators • Conductors • All charge resides on the surface, spread out to reduce the energy of the configuration • The electric field inside is zero • The potential on a conductor is constant (i.e. the conductor is an equipotential) • The electric field near the surface is perpendicular to the surface Note: These are all logically equivalent statements

7. Conductors vs Insulators • Insulators • Charge may reside anywhere within the volume or on the surface and it will not move • Electric fields are often non-zero inside so the potential is changing throughout • Electric fields can make any angle with the surface

8. Potential Energy • In a closed system with no dissipative forces • The work done is due to the electric force so This formula assume the following: • is constant in both magnitude and direction • The displacement is parallel to • WARNING: Since charge can be negative, and might point in opposite directions (this is called antiparallel) which would change the sign of W • This can be combined with the work-energy theorem to obtain the velocity a charged particle has after moving through an electric field

9. 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)

10. 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

11. Tying it Together Multiply by q Electric Field Electric Force Vectors Multiply by -Δx Multiply by -Δx Change in Potential Change in PE Scalars Multiply by q

12. Analogies with Gravity • Electricity and magnetism can feel very abstract because we don’t usually recognize how much we interact with these forces • There are many similarities between gravitational and electric forces • The major difference is that the electric force can be repulsive • Gravity even has a version of Gauss’s law