Differences

This shows you the differences between two versions of the page.

--- course_planning:184_projects:f18_project_8 [2018/10/23 16:39] – [Project 8A: Lakeview's Mystery] tallpaul
+++ course_planning:184_projects:f18_project_8 [2018/10/25 16:41] (current) – [Project 8A: Lakeview's Mystery] tallpaul
@@ Line 12: / Line 12: @@
   * Explain what the pieces of the integral are ( $d\vec{l}$ ,  $\vec{r}$ , and limits) and how you determined them for your solution.
   * Relate the magnetic field from a current to the magnetic field from a single moving charge - explain how these are similar and/or different.
+</WRAP>
+==== Project 8B: Magnets 'n' Junk ====
+Task force S.P.A.R.T.A.N has been given some much-needed downtime. Your team goes for a walk around town in order to get to know some members of the community and find the best coffee in town. As you are strolling around town, you hear a holler. "Aya!!! Hey, howdy!! Come check out this ol' piece of junk I got right here, y'all!" It's Dr. Daryn McPaddel, the town inventor/engineer who is always showing her neighbors' strange contraptions that she has made, and also happens to live adjacent to Lakeview's scrapyard, which allows her to tinker and invent to her heart's delight. This is what you see:
+{{youtube>lSmuqLtmuwg?large}}
+As you observe Dr. McPaddel's magnetic crane-thing at work you notice that there are a bunch of kids on a field trip in the scrap yard. This seems like an odd place for a field trip but then again nobody can really leave the town so there might not be a load of options. The teacher with the field trip, identifying you from all your work around town approaches you and says: "Hey, you know about electricity and magnets and whatnot, can you explain what's going on?" You agree to explain in detail how the thing works since you are concerned what crazy old Dr. Daryn McPaddel will say. The best way would probably be with a visual, and Dr. McPaddel has already created a visual of the coil of wire inside the contraption. All that's left to do is show what the magnetic field looks like.
+<code python>
+GlowScript 2.7 VPython
+xaxis = cylinder(pos = vec(-3, 0, 0), axis = vec(6, 0, 0), radius = 0.01, color = color.white)
+yaxis = cylinder(pos = vec(0, -3, 0), axis = vec(0, 6, 0), radius = 0.01, color = color.white)
+zaxis = cylinder(pos = vec(0, 0, -3), axis = vec(0, 0, 6), radius = 0.01, color = color.white)
+## Setting up the constants
+mu0 = 4 * pi * 10 ** -7    # magnetic constant in standard units
+I = 5000                   # current in ring
+R = 1                      # radius of ring
+thickness = 0.05           # thickness of ring
+## Drawing the ring
+ring = ring(pos = vec(0, 0, 0), axis = vec(0, 0, 1), size = vec(thickness, 2 * R, 2 * R), color = color.blue)
+## Splitting the ring into little pieces
+N = 100                    # number of little pieces
+dtheta = 2 * pi / N        # angle between adjacent little pieces
+theta = 0
+little_pieces = []
+## Determining dl and the location for each little piece
+while theta < 2 * pi:
+    r_source = vec(0, 0, 0)
+    dl = vec(0, 0, 0)
+    little_piece = arrow(pos = r_source, axis = dl, color = color.green)
+    little_pieces.append(little_piece)
+    theta = theta + dtheta
+## Picking some points to observe the magnetic field
+observation_radii = [0, 0.4, 0.8, 1.2, 1.6]
+observation_angles = [0, pi/2, pi, 3*pi/2]
+observation_heights = [0]
+r_obs_vectors = []
+## Putting the observation points into a list
+for rad in observation_radii:
+    for angle in observation_angles:
+        for height in observation_heights:
+            r_obs = vec(rad * cos(angle), rad * sin(angle), height)
+            r_obs_vectors.append(r_obs)
+## Visualizing the magnetic field
+for r_obs in r_obs_vectors:
+    B_total = vec(0, 0, 0)
+    for little_piece in little_pieces:
+        r_source = little_piece.pos
+        dl = little_piece.axis
+        r_sep = vec(0, 0, 0)
+        B_little_piece = vec(0, 0, 0)
+        B_total = B_total + B_little_piece
+    arrow(pos = r_obs, axis = B_total, color = color.yellow)
+</code>
+<WRAP Info>
+=== Learning Goals ===
+  * Practice the right hand rule, and make predictions for what magnetic field looks like from a ring of current
+  * Relate superposition in the code to how an integral is constructed
+  * Investigate the physical meaning of how an integral splits up a wire into "little pieces"
+  * Practice setting up an integral for a different shape than a straight line
+  * Gain some experience working in cylindrical coordinates
 </WRAP>