### Project: 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:

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.

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)

#### 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

Conceptual questions:

- What is the dl vector and how is it different from the r_sep vector?
- How can you use right hand rule to determine the direction of the B-field from the current loop?
- Why is the magnetic field smaller on the outside of the ring compared to the inside?
- In the real world, why would we want to use a current ring instead of a permanent magnet if we need a B-field?
- The current in this problem is 5000 A. Is that big or small? Is it realistic? How would you create this kind of electromagnet in real life? (Like in the video)
- Why would having a magnetic field from a ring of current attract the chunks of metal from the truck?
- How does the set up from the code compare to the integral set up from Wednesday? Write out the steps that the code takes and compare those to your steps from Wednesday.