What could cause data to linearize at a higher power than it should?

[djh101]

For our physics lab we found the magnetic field produced by a magnet at different distances. When graphing the data, it was supposed to produce a linear graph when we plot the field strength against 1/r³. However, my graph doesn't become linear until 1/r⁵ (however, it does linearize quite nicely at this power). What are some possible reasons for the data linearizing at a higher power of r than it is supposed to?

 

[berkeman]

For our physics lab we found the magnetic field produced by a magnet at different distances. When graphing the data, it was supposed to produce a linear graph when we plot the field strength against 1/r³. However, my graph doesn't become linear until 1/r⁵ (however, it does linearize quite nicely at this power). What are some possible reasons for the data linearizing at a higher power of r than it is supposed to?

Can you describe your test setup and instrumentation? A photo or drawing would help too.

What makes you think it should follow 1/r³? That may only be for some idealized setups...

 

[djh101]

We measured the magnetic field of a permanent magnet with a Hall probe and took measurements at different distances from the magnet. We are given that B is proportional to the inverse of r cubed. I would understand if the data was a little off and didn't fit exactly, but it linearizes almost perfectly, just not at the right power of 1/r. I'm really just looking for a general explanation as to why a particular set of data might linearize at a different power than theoretically predicted (in this case B ∝ 1/r^3 theoretically but B ∝ 1/r^6 experimentally).

 

[berkeman]

We measured the magnetic field of a permanent magnet with a Hall probe and took measurements at different distances from the magnet. We are given that B is proportional to the inverse of r cubed. I would understand if the data was a little off and didn't fit exactly, but it linearizes almost perfectly, just not at the right power of 1/r. I'm really just looking for a general explanation as to why a particular set of data might linearize at a different power than theoretically predicted (in this case B ∝ 1/r^3 theoretically but B ∝ 1/r^6 experimentally).

Was it a bar magnet, a horseshoe magnet, or some other shape? How big was it? Over what range did you make the measurements? What were the physical dimensions of the Hall probe? how did you remove the bias of the Earth's magnetic field? Can you post your data?

 

[CWatters]

Did you keep the distances short (eg much less than the length of the bar magnet)?

 

[marcusl]

What do you mean "linearize to 1/r^5"? (A power law is not linear unless the exponent is 1.) Did you mean that your data were a good fit to that function?