# Background Story

I wanted to measure the magnetic field B of this permanent magnet, to see if it's strong enough to use for DYI NMR (Nuclear Magnetic Resonance).

# Theory

The idea was that most of the magnetic field lines are concentrated between the two iron spacers that link the two magnets together.  If a probe is placed between the two spacers, the probe will feel most of the B.  If the probe is removed (ideally to an infinite distance) the magnetic field seen by the probe will be zero.

If our probe is a coil, some voltage will be generated while pulling it out from the B magnetic field.

The coil has 17 turns made out of solid Cu wire from a former LAN cable.  The blue white wire on the exterior is unconnected, just for mechanical consolidation of the whole donut.  The coil is initially put in the middle of the two iron spacers, then the orange wire is slapped down over the edge of the table in order to quickly move the coil outside the iron spacers and thus to a zero B field.

From Faraday's induction law, the induced voltage V in an N turns coil will be:

where Φ is the magnetic flux

B being the magnetic field and A being the area.  Combining the two formulas,

If we integrate over the time required to pull the measuring coil out of the B magnetic field, we get

# Practice

Rigol DS1054Z can calculate and display for us the area of a waveform (the integral).  Let's check if the area indeed stays the same.  The next 3 screen captures show 3 different measurements.  In all 3 the area is almost the same, about 355 microvolt-seconds.

And constant area it is, indeed!

The shape of the induced voltage waveform differs for each measurement, yet the measured area is about the same, as predicted by theory.

At a closer look at the magnets, there is a washer between each of the two iron spacers and the magnets:

Let's remove the washers (in the hope that thus we can slightly increase the magnetic field) and measure again, 3 more times:

Strangely, the magnetic field seems to be slightly smaller without the washers, any ideas why?

Now, let's plug the numerical values into the last formula and see how many Tesla we have between the two iron spacers:

B = 1/(17 turns * 3.14 * 0.01 m * 0.01 m) * 355E-06 Vs = 0.066470 Tesla = 66.5mT

Not bad, 66.5 mT for 2 magnets bought for less than \$10 from the LIDL supermarket.

If it were to use them for NMR (Nuclear Magnetic Resonance) experiments, the Larmor precessional frequency of 1H protons will be at about 2.83 MHz.

The magnet is pretty strong when used as intended, as a clamping device.  Once clamped to a ferrous material it is almost impossible to remove with only one hand.  It was sold as a "20Kg holding magnet" for keeping in place ferrous materials while welding or assembling them.

Just out of curiosity, the inside of the two magnets looks like this: