  ### Author Topic: Measure a magnet's B field with a Rigol DS1054Z oscilloscope and a piece of wire  (Read 310 times)

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#### RoGeorge ##### Measure a magnet's B field with a Rigol DS1054Z oscilloscope and a piece of wire
« on: July 02, 2019, 08:47:57 am »
I wanted to find out the magnetic field, B, for this permanent magnet. 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:

$V = -N\frac{\vartriangle \Phi}{\vartriangle t}$

where $\Phi$ is the magnetic flux

$\Phi = BA$

$B$ being the magnetic field and $A$ being the area.

To be precise,

$V = -N\frac{d\Phi}{dt} = -NA\frac{dB}{dt}$

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

$\int_{t_0}^{t_{\infty}} V dt = -NA (B_{t_{\infty}} - B_{t_0})$

where
$B_{t_{\infty}}$ is $B$ outside the two iron spacers, so zero
$B_{t_0}$ is the magnetic field $B$ between the two iron spacers, the value we try to find out

In conclusion,

$B = \frac{1}{NA} \int V dt$

If we look at the voltage waveform with an oscilloscope while extracting the coil probe out of our unknown $B$ field, then the $\int V dt$ term is nothing but the area of the voltage waveform seen on the oscilloscope.

According to the last formula for $B$, no mater the speed we pull the coil out from the field, and no matter the shape of the voltage waveform induced in the coil, the area seen on the oscilloscope should be about the same, because area is dictated by the initial magnetic field $B$, which is constant.

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.   Constant area it is! 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:   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.

On the inside, each of the two magnets looks like that: The following users thanked this post: Rerouter, JPortici, snarkysparky, bd139

#### snarkysparky

• Regular Contributor
• • Posts: 162
• Country:  ##### Re: Measure a magnet's B field with a Rigol DS1054Z oscilloscope and a piece of wire
« Reply #1 on: July 03, 2019, 12:55:06 am »
Also independent of the spatial distribution of the field if I understand correctly.

Very interesting post.

Thanks

#### RoGeorge ##### Re: Measure a magnet's B field with a Rigol DS1054Z oscilloscope and a piece of wire
« Reply #2 on: July 03, 2019, 07:22:40 pm »
Indeed, the spatial distribution doesn't matter either.

It matter only the values of the initial and the final $B$.  In other words, a static magnetic field is a conservative field, so the path of a line integral doesn't matter.  Only the start and the destination points matters.

Same thing said in yet another way:  In a conservative field any closed path integral is zero, meaning that if you start from a point then wonder around no matter what path, when you came back to the point you started, the integral will be zero.

https://en.wikipedia.org/wiki/Conservative_vector_field

Note that
- a static magnetic field is a conservative field, but
- a variable magnetic field is NOT conservative.

That's why the 2nd law of Kirchhoff (sum of voltages in a closed loop is zero) is NOT true if the circuit we want to apply that 2nd law is inside a non-conservative field (is inside a variable magnetic field).  From here, the whole drama steered by professor Walter Lewin when he said "Kirchhoff's law is for the birds!". The professor is correct, by the way, and that is why we need to fix the 2nd law of Kirchhoff by adding to the schematic virtual voltage sources for the induced voltages, when a circuit functions inside a variable magnetic field.  And yes, two voltmeter connected at the same measuring points can indicate different voltages, it can even be that one indicates a negative voltage and the other indicates a positive voltage! Again, both voltmeters connected at the same points.  Sounds crazy, but it's true. « Last Edit: July 03, 2019, 07:38:35 pm by RoGeorge »

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