Crude estimation of a magnetic quadrupole

[peripatein]

Hi,

Homework Statement

I ran an experiment to determine B_r(r), where B_r was the radial magnetic field produced by a magnetic dipole. Having found the magnetic moment of the dipole, I would now like to determine the contribution to the magnetic field of the next order in the expansion (viz. the quadrupole). I have no information on the magnetic moment itself of the quadrupole nor do I possesses any information on the current density J. I am interested in a very crude estimation, if possible. I do, however, know that the ratio (magnet's size : distance from Hall's magnetic sensor) was ~1:6, on average.

Homework Equations

See attachment. First moment is that of the dipole. Second is of the quadrupole.

The Attempt at a Solution

Using the formulae in the attachment, I estimated the ratio B_D/B_Q to be 3. Hence, the contribution of the dipole order to the magnetic field was 3 times that of the quadrupole order. I performed the estimation thus:
B_D = 2*1/2*m_D/R³, whereas B_Q = 3/2R³ * 2 * 4/3 * m_D * 1/6
It seems too small a ratio to me. Could anyone please help me determine whether this is indeed reasonable? I'd truly appreciate some prompt advice.

 

[BigJDubs]

The ratio you found is reasonable given the information that you have. The 1:6 ratio suggests that the magnet's size is much smaller than the distance from the Hall's magnetic sensor, which means that the contribution of the quadrupole order will be much smaller than that of the dipole order. This is reflected in your calculation, where the ratio of BD/BQ is 3.