# Magnetic Field induced by Electricity in Wire depends on Voltage or Current?

I'm attempting to understand the very basics of how a magnetic field induced by electricity flowing through a straight copper wire is generated, and how to properly measure it.

I'm a novice in the field of electricity and magnetism, I only took one introductory class on the subject.

It is my understanding that a magnetic field is when electricity flows through any conductive material, such as a copper wire (feel free to correct me at any point in this post if my understand is flawed or incorrect). In the case of a wire, I understand that the right-hand thumb rule is used to delineate the magnetic field and it's direction based off of the direction of the current flowing through the wire.

It is also my understanding that we are able to calculate the estimated magnetic field at a distance $$r$$ from the center of the conductive wire via the following formula:

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

where $$B$$ is the strength of the magnetic field measured in units of Tesla, $$\mu_{o}$$ is the permeability of the free space between the wire and point at radius $$r$$, and $$I$$ is the current flowing through the wire measured in Amperes.

Simply looking at this formula would lead me to believe that the strength of the magnetic field generated by electricity flowing through the wire would depend only on the current of the electricity. However, when I searched the web regarding my question, I found some answers that suggest that it could be the voltage as well, such as this post. I understand that in order for electric current to be present in the first place there needs to be some potential difference in the form of voltage between the source and destination of electrons, however I want to know whether the magnetic field would be more powerful if a higher voltage is applied to the current flowing through a wire, or whether it will not be affected by the voltage.

Alongside my main question above, I also would like to learn about what the proper way to measure the strenght of the magnetic field induced by electricity in a wire is. Would a device such as this be of use? Is there a specific type of magnetic field detectors that are used for wires specifically?

Thanks for reading my post, any guidance is appreciated.