PHYS 241 Recitation Kevin Ralphs Week 3

Overview HW Questions A Bit of History Flux Gauss’s Law Electrostatics Conductors vs Insulators

A Bit of History History – The 18 th 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

Flux

For the case of a flat surface and uniform velocity, it looks like this:

Flux

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 – Flux through a closed surface and enclosed charge are easily exchanged

3 Considerations for Gaussian Surfaces Gauss’s law is true for any imaginary, closed surface and any charge distribution no matter how bizarre. It may not be useful, however. 1.The point you are evaluating the electric field at needs to be on your surface 2.Choose a surface that cuts perpendicularly to the electric field (i.e. an equipotential surface) 3.Choose a surface where the field is constant on the surface *Note this requires an idea of what the field should look like

Common Gauss’s Law Pitfalls Universal

Electrostatics It may not have been explicit at this point, but we have been operating under some assumptions We have assumed that all of our charges are either stationary or in a state of dynamic equilibrium We do this because it simplifies the electric fields we are dealing with and eliminates the presence of magnetic fields This has some consequences for conductors

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, but only apply in the electrostatic approximation

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