# Is there an equation for the magnetic field of a conductor attached to a magnet?

Let's say I have a hollow conductive rod, 10mm diameter (O.D.), and I place a magnet of known strength 50mm up the shaft. What is the microTesla (mT) or Gauss (G) of the magnetic field (or flux density, or whatever it would be) of the shaft 50mm away from the magnet attached to it?

Here's what I'm attempting to do:

I want to attach a magnet to my manual transmission's shifter lever, and then use hall effect sensors to detect it's position and display the selected gear on a display. I have the Arduino code written and the display wired. I'm having a problem understanding what sensitivity Hall Effect Sensors to get, what strength and size magnet(s) to get, and how to go about figuring how they relate to each other.

Essentially, I don't want the magnet too close to the 6 Hall Sensors, nor do I want a huge, expensive magnet. I have 216 neodymium buckeyballs I can encircle the shaft with, if I used them would it matter which polarity I had them arranged in? If I used a single magnet, would I place the poles alongside or perpendicular to the rod? How would I go about ball-parking the mT of the magnetic field 50mm (or whatever distance) down the rod, away from the magnet to get an idea of the sensitivity (rated in mV/mT for the hall effect sensors)?

How does a magnetic field propagate through a conductor? How would I position the magnet(s) to maximize the mT down the rod of my shifter? How do I place the Hall Effect Sensors (which read mT perpendicular to their face) to maximize the readings?

Ideally, I'm hoping to place the magnet(s) far enough away that what I'm reading is the transmitted 'magnetism' of the rod itself, is this an improper way to look at it (or even possible)? If it's not, is it the case that I have to bring the actual magnets near the hall effect sensors, and I can't 'transfer' it to the rod?

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