# Homework Help: Crude estimation of a magnetic quadrupole

1. May 27, 2013

### peripatein

Hi,
1. The problem statement, all variables and given/known data
I ran an experiment to determine Br(r), where Br 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 possess 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.

2. Relevant equations

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

3. The attempt at a solution
Using the formulae in the attachment, I estimated the ratio BD/BQ 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:
BD = 2*1/2*mD/R3, whereas BQ = 3/2R3 * 2 * 4/3 * mD * 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.

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Last edited: May 27, 2013