# What Is The Relationship Between Temperature and Magnetic Force?

## Main Question or Discussion Point

Hi All,
In an experiment I ran to determine the trend between distance and magnetic force (produced by an electromagnet) the result showed that the trend was either an inverse quartic or inverse quintic function. Such a result was unexpected as the trend is documented as being an inverse cubic function. When trying to justify why such a result occurred it was proposed that the trend was a combination of the inverse cubic function for magnetism and the relationship between temperature and magnetic force (produced by an electromagnet). (This was thought due to errors within the experimental design which ultimately resulted in the temperature as distance decreased, increasing). I however do not know the trend which relates temperature and magnetic force (and after searching the internet for the better part of an hour still do not know). I attempted working out what the relationship should be using some crazy combination of Biot-Savart Law, Ohm’s Law and Joules First Law however I couldn’t understand how to correctly do this. Could someone please tell me what this relationship between temperature and magnetic force (produced by an electromagnet) is preferably with some kind of proof using formulae?

Thanks,
Z.C

(Edited to make magnetic force that of an electromagnet)

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K^2
Inverse-quintic function is the name. And there shouldn't be much of a change in magnetic properties until you reach a threshold temperature known as Curie Temperature.

At large distances, the behavior should be inverse-cubic. But if you included data points where magnets are close, geometry of the magnets could have thrown things off.

There is one more important factor is that you generally shouldn't be trying to use the fit curve to determine the power law of the system, because a lot of higher-order curves can give you good fits. Often, better fits, because they tend to be better at absorbing errors.

Inverse-quintic function is the name.
Thank you :)

And there shouldn't be much of a change in magnetic properties until you reach a threshold temperature known as Curie Temperature.
Sorry I forgot to state that the magnet is actually an electromagnet not a permanent magnet. Does your statement that there shouldn't be much of a change in magnetic properties until the threshold temperature is reached apply to both forms of magnets or only a permanent magnet?

At large distances, the behavior should be inverse-cubic. But if you included data points where magnets are close, geometry of the magnets could have thrown things off.
The test was conducted at distances ranging from 1.3 cm - 3.8 cm is this close enough for the geometry of the magnets to have thrown things off? Also by the geometry of the magnet throwing things off, does this occur because the distance from the attractive pole of the magnet to the target object is larger than the distance between the two poles of the magnet?

you generally shouldn't be trying to use the fit curve to determine the power law of the system, because a lot of higher-order curves can give you good fits. Often, better fits, because they tend to be better at absorbing errors.
I'm not entirely sure what you mean by this... The way in which I established the function of the graph was to select the power trend line within Microsoft Excel. Is this using the fit cure to determine the power law of the system? If so how should I determine the trend?

Thanks Again,
Z.C

K^2
Ah, with electromagnets, it can be a factor. If your wire heats up significantly, the resistance will increase, and magnetic field will drop, which might be consistent with your findings. How hot did your coils get?

As for using fits, I'm not sure there is a better way here. It's more of the case of not trusting the results too much. What sort of RMSE do you get for different inverse power curves?

How hot did your coils get?
The temperature of the coils was determined in two ways, one was using a heat gun which returned that the temperature reached was approximately 72°C, while the other was heating a cylinder filled with water with the electromagnet and using Q=mcΔT to determine the temperature: this returned a calculated temperature of approximately 60.5°C.

As for using fits, I'm not sure there is a better way here. It's more of the case of not trusting the results too much. What sort of RMSE do you get for different inverse power curves?
I'm not to sure how to calculate the RMSE in this case... What I did do was graph the force of the magnet against the inverse of distance to different powers ((D = da) Where D is the new set of values, d is the distances from the original experiment and a is a changeable negative integer) against the resultant R2 value for a linear trend. The results of this were;

Power (a) ..... R^2
-1 ...............0.9264
-2 ...............0.9783
-3 ...............0.9771
-4 ...............0.9414
-5 ...............0.8957
-6 ...............0.8516

However I'm not sure whether this is a correct method, how should I calculate the RMSE?

Thanks,
Z.C