PHYS 221 Recitation Kevin Ralphs Week 2

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

HW Questions Ask Away….

Flux/Gauss’s Law 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 (pretend the electric field vector is a velocity):

Flux

Gauss’s Law Situational: Closed Surface

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

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

Potential Energy

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

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

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 ChargeForceFieldPE Electricityq Gravitym