The most recent Mathcad challenge was based on magnetism:
Create a 3D plot of the force generated by an electromagnet as a function of electrical current and surface area of the lifting face of the electromagnet. (Choose any values you want for the other parameters of the electromagnet.) Creative hard challenge: can you represent a magnetic field in a plot or chart in Mathcad?
The earth’s magnetic field currently decays approximately 6.3% per century. How many years is it until earth’s magnetic field will be 50% of its current strength assuming (1) linear decay and (2) exponential decay? How long until 25%, 10%, and 1%?
Incorporate an advanced input control (e.g., sliders, radio buttons, list boxes) into any of the above challenges.
This month we had multiple submissions from frequent contributors Terry Hendicott and Professor Tokoro, with Werner E (and Professor Tokoro) building on Terry’s worksheet. Interestingly, they mostly chose to go right for the hardest challenge: plotting a magnetic field. I added this at the last minute, not expecting anyone to address it, because I had no clue how to approach the problem. Once again, the community rose to the challenge.
Terry submitted the first worksheet. He cites an article from the European Journal of Physics on “Modelling the Magnetic Dipole.” His worksheet uses two programs to facilitate the XY Plot of the magnetic field. This plot, as well as a couple other XY Plots visible in the draft view of the worksheet, are impressive, but a little more use of text boxes could help others follow the flow. Another program creates the basis for a beautiful color Contour Plot of the magnetic field. Kudos on going above and beyond on research and incorporating underutilized Contour Plots in your solution.
The challenge is a community challenge, so Werner E built on Terry’s worksheet by adding a function and modifying the second program to incorporate arrows onto the depiction of the magnetic field. This definitely helps visualize the field lines.
Like the previous challenge, Professor Tokoro submitted multiple worksheets – five in total this time, building on his previous work. The first one addressed the basic challenges, using symbolic evaluation with keywords to solve the problems. I like the use of documentation and color formatting to guide the user. He used symbolic evaluation again to solve the advanced challenge to determine when the Earth’s magnetic field will be half its current strength. I like the use of XY plots with vertical markers to depict the answers, which frankly scares me and shows the opposite of my intuition. Assuming linear decay, the field strength will halve in just under 800 years. Assuming exponential decay, that value increases to 1065 years.
Professor Tokoro takes on both the “simpler” graphing challenge and the Prime 10 challenge by plotting the force and current on 3D plots. It uses both the Checkbox and Slider advanced inputs to allow the user to change the plot parameters. I like the use of multiple Z-axis inputs to the 3D plot, which is a very nice technique I had not really considered before.
The second worksheet depicts the magnetic field in the wire from the basic challenge and magnetic flux density for the electromagnet in 3D, with slider controls. Wow. This makes for a great teaching tool for both physics and Mathcad. The third worksheet version takes on displaying a magnetic field with both an XY Plot and a 3D Plot. It has great use of color and looks very pretty. Reflecting once again the community concept, it incorporates Terry’s original work. If you’re wondering how he captures all this in a single page, he has collapsed Areas making use of the new “hide borders” functionality.
The fourth submission builds on this worksheet with even more input controls and a Contour Plot. The additional variations include radically different scenarios for the magnets: a single bar with two dipoles, dipoles at a distance but “facing” each other, and two magnets of the same polarity “facing” each other. This is truly impressive work.
The fifth worksheet depicts solenoids in 3D that can be updated with a Combo Box, Checkbox, and Slider. The graphing of the arrows intrigues me as it turns 3D Plots in Mathcad into graphic artistry. The programs in the collapsed Area show a high level of complexity.
My biggest takeaways from this month’s submissions are (1) Mathcad has incredible power to communicate concepts and results graphically through plots, and (2) the community is a great resource for learning and collaborating. If you want to take your worksheets to the next level, I strongly suggest you take a look at the techniques employed by our contributors.
In the challenge, I referenced a NASA book made for school students. The equations there were made to minimize or avoid the use of units. If you’re performing math for magnetism in the real world, though, you absolutely need to use units for quantities of magnetic flux density, force, and distance. Speaking of units, our challenge next month will be heavily dependent on that aspect of Mathcad functionality. Early adopters of Mathcad Prime 11 will appreciate one of the major enhancements in that version: custom unit systems. The next challenge should also appeal to people who love science fiction, movies, and video games. Stay tuned!
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