From @JohnDenker: I never cease to be horrified by "steering charge" diagrams
such as 31.19. The Sherwood & Chabay book is infested with
the things, and they're all wrong. Your 31.19 is wrong too.
This is analogous to your oft-cited example, namely dribbling
a basketball on Pluto. Somehow people have developed some sort
of theory (which they never explain) that allows them to draw
"steering charge" diagrams. They're so wedded to the alleged
theory that they don't notice that the resulting diagrams are
wildly inconsistent with the laws of physics.
For one thing, assuming the symbols in 31.19(b) are meant
to be consistent with 31.19(a), there is more total voltage
drop in (b) than in (a). That means there's tremendous
amounts of curl in the field, which is a Bad Thing in an
electrostatic problem.
Also the charge distribution in (b) is inconsistent with
Ohm's law.
Also in (a) the charges are shown in the interior, whereas
the text says they should be on the surface, as (roughly!)
indicated in (b).
Also in (b) there is charge shown in one place where you
absolutely know there's no charge, namely the inside
corners.
Sherwood says such diagrams are only "rough" indications,
meant to show "some" aspects of the situation. The problem
is, students have no way of knowing which aspects are meant
to be faithful to reality, and which are not.
Suggestion: Evidently you used some field line tracing
software to prepare the beautiful diagrams such as 24.7.
You could do something similar to prepare the steering
charge diagrams.
May I ask, what field-tracing software have you been using?
Can it handle resistor-wire boundary conditions?
From @JohnDenker: I never cease to be horrified by "steering charge" diagrams such as 31.19. The Sherwood & Chabay book is infested with the things, and they're all wrong. Your 31.19 is wrong too.
This is analogous to your oft-cited example, namely dribbling a basketball on Pluto. Somehow people have developed some sort of theory (which they never explain) that allows them to draw "steering charge" diagrams. They're so wedded to the alleged theory that they don't notice that the resulting diagrams are wildly inconsistent with the laws of physics.
For one thing, assuming the symbols in 31.19(b) are meant to be consistent with 31.19(a), there is more total voltage drop in (b) than in (a). That means there's tremendous amounts of curl in the field, which is a Bad Thing in an electrostatic problem.
Also the charge distribution in (b) is inconsistent with Ohm's law.
Also in (a) the charges are shown in the interior, whereas the text says they should be on the surface, as (roughly!) indicated in (b).
Also in (b) there is charge shown in one place where you absolutely know there's no charge, namely the inside corners.
Sherwood says such diagrams are only "rough" indications, meant to show "some" aspects of the situation. The problem is, students have no way of knowing which aspects are meant to be faithful to reality, and which are not.
Suggestion: Evidently you used some field line tracing software to prepare the beautiful diagrams such as 24.7. You could do something similar to prepare the steering charge diagrams.
May I ask, what field-tracing software have you been using? Can it handle resistor-wire boundary conditions?