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My class was learning the magnetic effects of current and one of the things we learnt was that the magnetic field strength produced by some conductor is going to be directly proportional to the current flowing through it.

Now, by Ohm's Law, we also know that V = IR. So, if we do some temperature changes, R should change and so the current flowing in the conductor should change. As a result, the strength of the magnetic field should change.

However, this is more of a mathematical reason. What I desire is an explanation that is more theory oriented - What exactly does the temperature change do that causes the field strength to change?

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  • $\begingroup$ I have now updated my answer to its final form. Hope you will find it helpful. $\endgroup$
    – Markoul11
    Jan 21 at 10:46

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The reason you are assuming Is correct that on Changing the temperature the magnetic field is going to change as well in both permanent magnets and electromagnets now understand the reason behind this and let's make it more theory oriented as well.

First of all you should be aware of the terms drift velocity and relaxation time of the electrons I'll assume that you are!

So when there is change in temperature then there must be transfer of heat between the conductor and the surroundings and let's say the conductor is at the lower temperature than the surroundings then what will happen the heat will travel from surroundings to our conductor and this energy will get converted into the kinetic energy of the electrons (there is already some velocity in the electrons but as the temperature difference becomes bigger the heat energy will more and more get converted into the kinetic energy). So this will result in more collisions with their vacancies, other atoms and other free electrons and with this the electrons under the influence of the electric force because of the closed circuit (potential difference is applied) will not be able to totally decelerate the electrons earlier and change the direction of velocity quickly as it was doing before which were moving in the direction of electric field (in general they should move opposite to the direction of electric field because they are negatively charged but because of these more strong collisions this will deflect the electrons from the direction in which they should actually move, not significantly but yes, electron will gain more velocity in the direction of electric field as compared to normal conditions) will result in the decrement of the drift velocity and current as well because current and drift velocity are directly related to each other according to the equation $I = V_d enA$ Where $V_d$ is drift velocity and remaining are the constants.

Now let us understand with this equation:-

$R = \frac{ml}{ne^2τA}$

Just focusing $τ$ here is the relaxation time, and $n$ is the number of free electrons per unit volume.

From the above equation keeping all the constants beside such as length, area, mass and charge of an electron we can see that the resistance is inversely proportional to the relaxation time and the $n$ As the temperature increases the number of free electrons increases as well but there is not significant increase because there are already enough free electrons inside the conductor. And the main reason to increase the resistance here is the decrement in the relaxation time of the electrons because of increased velocity in random directions of the electrons due to conversion of the thermal energy. So this is how the resistance increases with increase in temperature and according to the ohms law i.e $V = IR$ the resistance increases which will lead to decrement in current and as the current is directly proportional to the magnetic field strenght hence it will decrease as well.

Hope it helps.

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    $\begingroup$ You're assuming you have a constant voltage source. Coz if it's a current source, your conclusion doesn't hold. $\endgroup$ Jan 20 at 14:21
  • $\begingroup$ @AccidentalBismuthTransform yes it's for constant voltage. $\endgroup$ Jan 20 at 15:44
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If you increase the temperature of the wire, it means that the random motion of electrons is raised inside the wire. Now, the electrons collide more frequently than before, which means that the scattering time is decreased. This, in turn, means the conductivity is reduced. The average velocity (drift velocity) of electrons is reduced. Therefore, the magnetic field is also decreased.

In short, The temperature decreases the speed of particles (and so the current), decreasing the strength of the magnetic field.

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    $\begingroup$ You're assuming a constant voltage source produces the current. Otherwise your conclusion doesn't necessarily hold. $\endgroup$ Jan 20 at 14:22
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Answer Updated 21 Jan 2022

To understand temperature effects, we need to look at the atomic structure of the elements that make up the magnet. Temperature affects magnetism by either strengthening or weakening a magnet’s attractive force. A magnet subjected to heat experiences a reduction in its magnetic field as the particles within the magnet are moving at an increasingly faster and more sporadic rate. This jumbling confuses and misaligns the magnetic domains, causing the magnetism to decrease. Conversely, when the same magnet is exposed to low temperatures, its magnetic property is enhanced and the strength increases.

source

Similar regarding this question about relation of magnetic field generated on an electric current carrying conductor wire for example, with temperature:

Increase of entropy (i.e. temperature) leads to partial misalignment of the discrete magnetic moments of the uniform directional flowing electron's current and therefore to a reduction of the generated corresponding magnetic field.

In theory, a conductor wire with higher resistivity $ρ$ will generate the same magnetic field strength $B$ around it with distance $r$, with a lower resistivity wire as long as both have the same current value $I$:

Magnetic field around wire

$$\mathrm{B}=\frac{\mu_{0} \mathrm{I}}{2 \pi \mathrm{r}}$$

However in a higher resistivity wire the atoms inside will scatter more electrons of the current and generate more heat (i.e. increase of entropy of current's uniform flow) therefore the number of electrons passing through the cross-section of the wire per unit of time will decrease thus also the current value $I$ will start to decrease as the wire heats up which will result in the reduction of the magnetic field assuming a fixed voltage value applied to the wire.

So you see the magnetic field is always analogue to the current but a higher resistivity $ρ$ wire conductor for a given cross-section of the wire, will result to a larger drop of current with time for the same voltage applied. The higher the temperature increase on the wire the larger the reduction of its magnetic field. Magnetic field strength reduces with current reduction and temperature increase because there are less number of uniform direction flowing electrons and therefore less number of aligned discrete magnetic moments of electrons exist per unit of time which lessens therefore the magnetic field strength generated around the wire (i.e. magnetism is all about coherence, alignment and uniformity).

Two identical dimensions wires one from gold and the other from silver, with compensated applied voltage for their different resistivity $ρ$, will initially generate the same current value in both conductors but with time the gold wire will increase more in temperature due its higher resistivity and experience a larger current drop and magnetic field strength drop than the silver.

Also, resistivity $ρ$ of material of conductor does not remain fixed but increases with temperature which makes things even worse. The best solution is too keep things cool using higher cross-section wires.

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    $\begingroup$ The question was for electrically-induced magnetic fields in a current-carrying conductor, and your answer addresses peranent magnets. $\endgroup$ Jan 20 at 13:56
  • $\begingroup$ Answer updated similar to magnetic field generated by a conductive wire. $\endgroup$
    – Markoul11
    Jan 21 at 9:13
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Just for reference: magnetic fields are not influenced by temperature.

What you have is something, here an electrical circuit, that generates a magnetic field. And this circuit is temperature dependent, e.g. the resistance changes. Depending on how this circuit reacts to the change in resistance you can then measure a change in the generated magnetic field.

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