PHYS 220 — Homework #8
[Solution]
For this homework assignment, you'll need the results
of Lab #8.
This homework is due Monday, 20 April.
- Explain the discrepancies between your results and the theoretical
values for B in the middle and at the ends of the solenoid for the
various N & h parameters in #2 of Lab #8.
- The theoretical results are obtained under the
assumption that N
& h → ∞. As N & h get larger, the discrepancy between
the obtained result and theory diminish. For Δθ =
π/10, N = 1000 and h = 100,
our results are off by a mere 0.02% and 0.2% at the center and ends,
respectively. See the table in the
solution for Lab #8
- For an ideal, long solenoid, the B-field inside is uniform and
zero outside. Explain the results depicted in the top panel of
my visualization
script.
- See figure at bottom of this page. Since this is a short, non-ideal solenoid, we expect some
asymmetries (as seen). Still, the field near the center appears
uniform and the field strength is greatly diminished, but non-zero,
outside the
solenoid.
- In lines #60–#64 of
my visualization script, the
B-field is set to zero if the point lies within 5 units of the
origin. This was done for strictly for visualization purposes.
Explain.
- Outside the solenoid, the field is very weak, so
to visualize the
field "far" from the solenoid, we use this technique to mask the
effects of the strong fields near & inside the solenoid.
- Does the B-field depicted in the bottom panel of
my visualization script make
sense physically? Explain.
- Yes, there is a net current into the x-y
plane, so the
field should circulate as shown (RHR).
- Describe an exceedingly simply physical system that would give
results qualitatively similar to those depicted in the bottom
panel.
- A wire along the z axis, with current moving in
the -z direction
would produce this effect.
- Explain the asymmetry in the bottom panel of
my visualization
script.
- The number of turns in the solenoid is finite, and
the current
begins & ends abruptly, causing the asymmetries.
