Experimental measurements of relative magnetic permeability

[brybot]

I am trying to measure the relative permeability of a few materials, but the numbers I'm getting don't quite make sense. Maybe someone here can figure out what might be going wrong.

My setup is as follows. I'm making solenoids using 30 AWG magnet wire wrapped around ferrite, steel and wood cores. I'm doing a single layer of wire and I get about 3600 turns per meter, however the solenoids themselves are about 1"L x 1/4"D. I have a hall effect sensor, the Allegro A1324 which has a sensitivity of 5mv/G. I'm placing the end of the solenoid directly against the sensor and measuring the voltage deviation with respect to current in the solenoid.

With the equation B=kμnI where n=N/L~=3600 I'm solving for the relative permeability k. So k=B/(μnI). At 2 amps I get readings of 201, 170, and 15 G for ferrite, steel, and wood respectively. Then solving for the relative permeability I get 2.2, 1.9 and 0.17. Wood should have something close to 1, so I know something is wrong. And the steel/ferrite should be at least 200.

Any ideas? Thanks

 

[NascentOxygen]

Welcome to Physics Forums.

Quite possibly your ampere-turns per meter was excessive, and the magnetic materials were driven into saturation. Repeat using much smaller currents.

 

[nasu]

What value do you get if there is no core in the solenoid?

 

[brybot]

Welcome to Physics Forums.

Quite possibly your ampere-turns per meter was excessive, and the magnetic materials were driven into saturation. Repeat using much smaller currents.

Thanks for your reply. I'm in the linear region, I've verified experimentally. I'm not sure where saturation will occur, but the relationship between B and I is very linear from 0-2A for these solenoids. Also, 3600 turns per meter is a relatively small value as far as I'm aware.

@ Nasu, I used the wood to mimic an air core. The wire is flimsy and would not hold the shape on its own. Wood and air should both be very close to 1.

I did find another equation for non-ideal solenoids where the length and radius are taken into account. The results did not improve much.

 

[sardar]

It's great that you are conducting experiments to measure the relative permeability of different materials. However, it seems like there may be some errors in your setup or calculations that are leading to inaccurate results.

First, it's important to make sure that your solenoids are all the same size and have the same number of turns. Any variation in these parameters can affect the magnetic field strength and thus the readings you are getting.

Secondly, the sensitivity of your hall effect sensor may also be a factor. It's possible that the sensor is not able to accurately measure the small magnetic fields produced by wood, leading to the low reading you are getting. You may want to consider using a more sensitive sensor or adjusting your setup to increase the magnetic field strength.

Additionally, the equation you are using to calculate relative permeability assumes that the magnetic field is uniform within the solenoid. However, this may not be the case for your setup, especially with the smaller solenoids. You may need to account for any variations in the magnetic field within the solenoid when calculating relative permeability.

I would also recommend double-checking your calculations and making sure you are using the correct units for all variables. Sometimes, a simple mistake in units can lead to significant errors in the results.

In summary, to get more accurate results, make sure your setup is consistent and precise, consider using a more sensitive sensor, and be mindful of any variations in the magnetic field within the solenoid. Good luck with your experiments!