Mathcad Community Challenge March 2025 - Magnetism!

[DaveMartin]

This month’s challenge is based on magnetism. Create a Mathcad worksheet to answer any or all of the following:
Basic Challenge:

1. What is the magnetic field strength of 15 Ampere current in a wire at a distance of 0.25 meters?
2. How many turns of wire will be needed to create an electromagnet capable of lifting 1 kilogram of ferrous material if the current is 0.25 Amperes, the lifting face of the magnet is a circle with a diameter of 5 cm, and the length of the coil is 0.1 m? Assume a relative magnetic permeability of 750.
3. What is the total magnetic energy of the Earth? (Assume a magnetic field strength between 0.22 and 0.67 Gauss.)

One resource for the equations to solve these problems is NASA’s Magnetic Math ebook.

Graphing Challenge
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? (Seriously, I have no idea how I would approach this.)

Advanced Challenge
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%?

Mathcad Prime 10 Challenge
Incorporate an advanced input control (e.g., sliders, radio buttons, list boxes) into any of the above challenges.

Find the Mathcad Community Challenge Guidelines here!

[terryhendicott]

Hi David,

Creative hard challenge: can you represent a magnetic field in a plot or chart in Mathcad? (Seriously, I have no idea how I would approach this.)

First attempt

Cheers

Terry

[Werner_E]

Well done!

How about adding arrow heads ?

Orientation is taken from your matrix B

Choose between different arrowhead styles

BTW, when opening your sheet, Prime moans about a region (seems to be one at the bottom) being damaged.

[terryhendicott]

The moans about a region is I cited my source by copying and  pasting text but this included some unprintable characters.

New file has the citation without these characters at the start of the file.

Regards

Terry

[ttokoro]

Make flux lines.

[ttokoro]

Prime 10 with AI hints.

[ttokoro]

Assuming inside of the coil also filled by material. If not, needs 750*48 turns.

However, Q2 in basic challenge must need more check by others.

[ttokoro]

Version 2. Trying to plot line current and its magnetic field lines in 3D.

[ttokoro]

Version 3. Trying to plot Terry and Werner's dipole magnetic field lines in 3D.

FN=1 to 3 changes the start points of flux displayed.

M can change the magnitude of magnetic dipole of Terry's equation.

[ttokoro]

[ttokoro]

Version 3b2. Trying to plot Terry and Werner's dipole magnetic field lines in 3D for 3 types of SN=1, 2 and 3.

n_flux can change the density of magnetic flux.

dL can change the resolution of calculation.
M can change the magnitude of Magnetic dipole moment.

N can change the size of n*n calculation field.
flux_plot can on/off to plot flux lines.   etc..
3D plot of each element must <40000, so if exceed it red boundary line appears.

[ttokoro]

[ttokoro]

The challenge will be extended to the end of this week instead of ending today!

This means more challenge requests to the users! So, the Ver. 4 is 3D plot of toroidal coil magnetic fluxes.

How to plot the coil and curved arrow in 3D are the challenges. And also change the color and size of plots that changed by advanced input controls are good tips.

How to change the direction setting which is under the plot, without using global definition, is also good tips.

[DaveMartin]

I came up with 48 turns as well. But I realize the question was a bit ambiguous regarding the construction of the electromagnet. 

[DJNewman]

Howdy all,

Good news: The challenge will be extended to the end of this week instead of ending today!

[DJNewman]

Sorry for the delays; here is the write-up solution blog!

https://www.mathcad.com/en/blogs/community-challenge-magnetism

And y'all have badges (that look a bit different than before, for the better) now too.

I'm currently looking over the May challenge prompt; should be fun.