I am interested in creating an inductor with a large inductance/large mag field in core. However, when empirically measuring the inductance of the wound core, I calculated a relative permeability ~1000x less than expected (2-6 vs 2000). My question is whether this is due to an error in my setup/calculations/understanding, or due to receiving a core not up to spec.
The ferrite rod has stated relative permeability of ~2000 and B_sat of .49T (4900G). The physical dimensions are 25.66mm height x 6.32mm diam. http://www.ebay.com/itm/5-ea-Ferrite-Rod-Core-0-25x1-00-Fair-Rite-4077276011-2000u-Perm-Plain-Slug-77-/251653543001?hash=item3a97b85459
Given that this is ferrite, the permeability should be fairly linear. The datasheet for the material can be found here: http://www.mouser.com/ds/2/150/4077276011-476454.pdf
I wound the core with ~100 turns of 28AWG mag wire (.321mm diameter), with a DC resistance of 1.0 ohm. The result is quite messy, but the length of the coil extends 11.6mm, and the outer diameter goes up to 10.3mm:
The inductance of the coil was measured experimentally by creating an RL series circuit fed by a signal generator, and increasing the frequency until the Vpp across the RL circuit was twice the Vpp across the resistor alone. See http://www.daycounter.com/Articles/How-To-Measure-Inductance.phtml for an explanation of this method.
For a 100 ohm 1% tolerance resistor, the required frequency was 77kHz, resulting in a measured inductance of 358uH. I used the following equations to calculate relative permeability \$\mu_r\$. The geometry is neither a loop or solenoid, but the equations only differ by a factor of 2-3x in this case.
\$B_{loop,center} = \mu_0\mu_r\frac{NI}{2R}\$
\$B_{solenoid,center} = \mu_0\mu_r\frac{NI}{l}\$
\$L_{loop} \approx \mu_0\mu_rN^2R(ln(\frac{8R}{r})-2)\$, r = wire radius
\$L_{solenoid} = \mu_0\mu_r\frac{N^2A}{l}\$
Because there is at least 150 ohm in serial with the 2Vpp source, the most current that could flow in one direction is 1/150 = 6.7mA. Assuming the relative permeability is 2000 as stated, there shouldn't be any concern of saturation, as the magnetic field in the center of the loop/coil is at most .28T (\$B_{loop,center}\$ with R=3mm). (Also, the scoped sine waves were clean.)
Given the dimensions from above and the measured L of 358uH, \$\mu_r\$ comes out to 2-6, much less than the expected 2000. Why is this?