PHYS 241 Recitation

Kevin RalphsWeek 3

Overview

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

A Bit of History

• 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

Flux• Flux, from the Latin word for “flow,” quantifies the amount

of a substance that flows through a surface each second• It makes sense that we could use the velocity of the

substance at each point to calculate the flow• Obviously we only want the part of the vector normal to

the surface, , to contribute because the parallel portion is flowing “along” the surface

• Intuitively then we expect the flux to then be proportional to both the area of the surface and the magnitude of

Flux

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

Flux

• For curved surfaces and varying flows, if we chop the surface up into small enough pieces so that the surface is flat and the velocity uniform, then we can use an integral to sum up all the little “pieces” of 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

• Your surface must be closed• The charge you use in the formula is the

charge enclosed by your surface• The Gaussian surface need not be a physical

surface• Start from the definition of flux and simplify

only if your surface/field allows it 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 surfaceNote: 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