Experiments with Magnetic Fields                       Latest change 2024-11-03
 
In brief:
Reversing the magnet in the bob (and reversing all coil connections to maintain the signal polarities) had no noticible effect on its own.
At my location the natural GeoMagnetic Field (GMF) has a strength of around 20 μT in northern direction and 50 μT poinitng downwards.
I applied an external more-or-less homegenic magnetic field of approximately 100 uT in all directions North, South, East, West, Up and Down. The experiments with Up and Down field were also done with the bob's magnet reversed.
No noticible effects were seen with the horizontal fields. With the vertically applied fields changes were seen in the behaviour of the elliptical path and in the period time. These effects reversed more or less with the reversal of the bob's magnet.
At the end of this chapter you will find some details about the GMF and the construction of the coilset used.

Reversing the bob's magnet.
Currently the bob has a southhpole pointing downwards and the ellipse is going CW in the quadrants 1 and 3 and CCW in 2 and 4.
On 2024-08-27 around 15:10 I reversed the magnet in the bob and also reversed the connections on the coilset, such that all signals have the original polarity. Because the coilset had to be taken out for that action I had to recenter it.
Around 16:00 it was already clear: No change in elliptical direction. Sure this also tells us something, but I have no idea what.
For the time being I leave the situation what it is now.
A few days after this I tried to rotate the top unit back such that the ellipse transitions are on N-S-E-W of the compass scale again. For this to happen I had to rotate it substantially more in CCW direction than before. (this was after the "rotate top unit" experiment)
And walking around the bob with an ordinary compass told me that there are some sources of magnetic field in the vicinity: a cast-iron wood stove and a loudspeakerbox with a big woofer.
Conclusion:
There is a small effect of reversing the bobs magnet: the ellipse transitions have shifted some 15 degrees in western direction.
One of these days I'll repeat the experiment to be sure.


Apply a magnetic field.

The Geo Magnetic Field (GMF) at my location is approx. 20 μT horizontal pointing north and 50 μT vertical pointing down.
Experiments have been done with an extra applied more-or-less uniform field of 20 and 100 μT pointing west and east.
The set of coils to generate these fields is described at the end of this page.

Here a video  Starting with the power supply showing constant curent of 1A giving 20 μT, then follows the cable to the CubiCoil with the bob.


Fig 1 shows the first 3 experiments with magnetic fields.  (click for larger)

Legend:
  Yellow staircase: time of the day in hour steps 0..23,
  light blue: Foucault plane, +180 to -180 deg, 0 = East.
  white: Amplitude of minor axis, 45 mm/ div. + = CCW, - = CW.

Time line:

Graph starts at 2024-09-13_05:00
13_09:13:
   Coilset was placed around the floor unit, floorunit was recentered.
   The E-W coil was engaged at 1A West, giving approx 20 μT West, resulting in 28 μT pointing NW.
15_08:14
   The E-W coil was reverse connected resulting in approx. 20 μT NE.
17_16:30
   The current in the E-W coil increased to 5A, giving approx 100 μT pointing East.
18_23:00 end of test (fttb)

Zero crossing intervals of Foucault Precession:
13_19:34 to 14_11:05 gives 15:31 for half FP.
14_11:05 to 15_03:17 gives 16:12, full FP = 31:42.
15_03:17 to 15_17:55 gives 14:38, full FP = 30:50.
15_17:55 to 16_09:50 gives 15:55, full FP = 30:33.
16_09:50 to 17_00:44 gives 14:54, full FP = 30:49.
17_00:44 to 17_15:52 gives 15:08, full FP = 30:04.
17_15:52 to 18_07:03 gives 15:11, full FP = 30:19.
18_07:03 to 18_22:16 gives 15:13. full FP = 30:24.

Conclusion:
This picture shows that there is hardly any effect on the amplitude and phase of the ellipse's minor axis and the total time of the Foucault Precession.

A few notes:
At the up-going zero crossings of the minor axis we see sometimes a small sudden jump. Most likely this is related to a timing error in the data acquisition. This has my attention.
From 09-13_11:00 to 09-14_01:00 a little bump can be seen. Most likely this is related to watching video in the same room, using a beamer, which may produce a steady airflow. On a few other days I've seen such coincidences in the evenings, and we know now that the pendulum is very sensitive to systemic airflows.
Applying a vertical magnetic field does have influence. See below.
Stil to do: Horizontal fields pointing north and south.


Vertical Field.
While applying a vertical magnetic field to the area where the bob moves it became very soon clear that the there were noticible effects.
Therefore a set of experiments was done, with all 4 combinations of the field pointing up or down and the magnet in the bob with the northpole up or down. It was also found that there was a small but noticible change in the period time, caused by the fact that the magnetic field produces a small force on the magnet in the bob.

Below are pictures of the 4 combinations. Compare them with the picture without an extra field.
The natural vertical component of the GMF at my location is 50 μT pointing down. (I have a magnetic south pole under my feet)
I have added a field of either +100 μT or - 100 μT so it adds to +50 μT or -150 μT.
When the bob has its magnet with the north pole down it experiences a force of

Applied field
None
Up
Down
Up
Down
Resulting field   μT -50
+50
-150
+50
-150
Magnet in Bob
Up
Down
Period Time
Normal
- 10-5 
+ 10-5 - 10-5 - 10-5
Picture
Fig 2-normal
Fig 2A
Fig 2B
Fig 2D
Fig 2C

Legend for all graphs:
Yellow staircase: Time of the day in hour steps 0..23
Light Blue: Angle of Swinging Plane, +180 deg to - 180 deg.
White: amplitude of ellipse's minor axis. + = CCW, - = CW, scale 45 mm / div
Green: Period time, offset : 4.1275 sec, scale 45 usec / div.


Fig 2-normal. No extra field applied. "normal" situation, magnet in bob upwards..
Source: 2024-09-16_08:00 .. 2024_09-18_23:59.
During the evening hours some irregularities are visuble in the period time.
Most likely due to the beamer for watching video which produced some air draught.


Fig 2A. Extra field 100 μT upwards, resulting field 50 μT upwards. Magnet in Bob upwards.
Source: 2024-09-19_11:53 .. 2024-09-21_03:30
At 09-21_00:30 the field was changed to downwards for the next experiment. Visible by the jump in period time.


Fig 2B. Extra field 100 μT downwards, resulting field 150 μT downwards. Magnet in Bob upwards.
Source: 2024-09-20_20:00 .. 2014-09-23_11:45.
In the period time trace we can see the jumps when the field was switched from up to down, and back to up.


Fig 2C. Extra field 100 μT upwards, resulting field 50 μT downwards. Magnet in Bob downwards.
Source: 2024-09-26_10:00 .. 2024-09-28_14:20.
In the Period Time trace we can see the flippping of the bob's magnet left at 12:52,
and switching the field to minus, right at 12:10.
The dip around 09-26 midnight is unexplained, and did not repeat.


Fig 2D. Extra field 100 μT upwards, resulting field 50 μT downwards. Magnet in Bob downwards.
Source: 2024-09-29_09:00 .. 2024-09-02_09:00
At 2024-09-29_12:10 the field was switched to downwards, at 2024-10-02_07:45 is was switched off.


The next table gives an overiew / timeline of the experiments with a vertical applied magnetic field.
The field of + or - 100 μT added or subtracted from the natural vertical field of -50 μT at my location.
Also the magnet in the bob was reversed halfway, so we have 4 combinations

Day
sept ´24
Events
Field
Applied
μT
Field
Resulting
μT
Magnet
in
Bob
Effect
on Bob
μT
FP cross
Zero
FP Half
Swing
Time
FP Full
Swing
Time
Picture
Remark
th 19
11:53
+100
+50
+
+50 13:54
-----

 A
Field +
fr 20

,,
+50 ,,
+50 05:20
20:56
15:26
15:36

31:02
 A

sa 21
00:30
-100
-150
,,
-150 12:00
15:04
30:40

Field -
su 22

,,
-150 ,,
-150 03:33
18:33
15:33
15:00
30:37
30:33


mo 23
11:45
,,
+50 ,,
+50 10:18
15:45
30:45


tu 24

,,
+50 ,,
+50 01:37
17:32
15:19
15:55
31:04
31:14
B

we 25

,,
+50 ,,
+50 09:02
15:30
31:25
B

th 26

,,
+50 ,,
+50 01:30
16:38
16:28
15:08
31:58
31:36
B
1/
fr 27
12:52
,,
+50 Flip
to -
-50 08:34
**
15:56
31:04
C
Flip Bob
2/
sa 28

,,
+50 ,,
-50 03:57
19:20
-----
15:23

C

su 29
12:10
-100
-150 ,,
+150
11:38
16:18 31:41
C
Field -
mo 30

,,
-150 ,,
+150
05:45
21:36
18:07
15:51
34:25
33:58
D
3/
oct '24



,,






tu 01
07:45
,,
-150 ,,
+150
13:20
15:44
31:35
D

we 02

+100
+50 ,,
-50 06:08
21:15
16:48
15:07
32:32
31:55
D
Field +
th 03

,, +50 ,,
-50 13:59
16:44
31:51


fr 04
23:13
0 -50 ,,
+50 05:27
20:21
15:28
14:54
32:12
30:24

Field off
sa 05

,, -50 ,,
+50 12:49
15:28
30:24


su 06

,, -50 ,,
+50 04:13
19:23
15:24
15:10
30:52
30:34



Remarks:
1/ from 18:00 to 22:00 we had an irregularity of unknown origine, which elongated the FP
2/ because of flipping the magnet in the bob we had to relaunch it.
3/ on sept 29 late we had an unexplained delay in the FP.

Discussion:
The natural vertical field at my location is 50 μT downpointing. I call this direction negative.
The extra field is ca. 100 μT and adds or subtracts to -150 μT when down or + 50 μT when up.
We see a substantial different behaviour of the ellipse's minor axis. With the resulting field of +50 μT we have a slight flattening at CCW and a bit more ellipse when CW (fig. 2A).
With the field down, or -150 μT, we see a strong flattening at CW and a shorter time for CCW. (fig 2B).
When the magnet in the bob is reversed this pattern reverses too. (fig 2C and 2D).
In all cases the linearity of the Foucault Precession is almost unchanged, but the Foucault Period tends to be somewhat longer, never shorter.

At this moment I have no explanation for the periodic changes in the period time. It looks like an anticorrelation with the ellipse.
It can however be also caused by an unroundness or not being perfectly horizontal of the Rim coil, which defines the pendulum's amplitude.

The mechanism by which the period time changes with the magnetic field is not yet understood. My first thought was that the field pulls the bob a little bit up or down, as if gravity changes a bit, but that is wrong. A magnet in a homogeneous field experiences only a rotational force when the magnet is not aligned with the field. For a pulling force a field gradient is required.
But: near the extremes of the amplitude the bob's magnet is rotated over Θ and experiences a rotational force. Maybe that is the mechanism.


Update 2024-10-27.
The experiments with the horizontal field in N-S and S-N direction are now finished.
I applied 100 uT pointing North or South for a few full periods of the Foucault Plane.
The message is: No noticible effects were seen.

Zero crossing intervals of Foucault Precession in the period 2024-10-06 to 2024-10-23:

06_04:11 to 06_19:19 gives 15:08
06_19:19 to 07_11:18 gives 15:59, full FP = 31:07
07_11:18 to 08_04:14 gives 16:56, full FP = 32:07

On 2024-10-08 there was an interruption because of installing new software and a relaunch.

09_11:21 to 10_04:13 gives 16:52
10_04:13 to 10_19:26 gives 15:13, full FP = 32:05
10_19:26 to 11_11:55 gives 16:29, full FP = 32:02
11_11:55 to 12_03:27 gives 15:33, full FP = 31:05
12_03:27 to 12_18:05 gives 15:38, full FP = 31:11
12_03:27 to 12_18:05 gives 15:28, full FP = 31:06
12_18:05 to 13_09:48 gives 15:45, full FP = 31:13
13_09:48 to 14_02:38 gives 16:56, full FP = 32:33
14_02:38 to 14_17:32 gives 14:54, full FP = 31:50
14_17:32 to 15_09:35 gives 16:17, full FP = 31:11
15_09:35 to 16_00:42 gives 15:05, full FP = 31:22
16_00:42 to 16_16:06 gives 15:24, full FP = 30:29
16_16:06 to 17_07:53 gives 15:43, full FP = 31:07   17:15 field 120 uT North
17_07:53 to 17_23:39 gives 16:14, full FP = 31:57
17_23:39 to 18_15:14 gives 15:35, full FP = 31:49
18_15:14 to 19_06:13 gives 14:59, full FP = 30:36
19_06:13 to 19_21:49 gives 15:36, full FP = 30:37
19_21:49 to 20_13:43 gives 15:34, full FP = 31:10
20_13:43 to 21_05:12 gives 15:25, full FP = 30:59    18:12 field 80 uT South
21_05:12 to 21_20:29 gives 15:17, full FP = 30:42
21_20:29 to 22_11:51 gives 15:12, full FP = 30:29
22_11:51 to 23_03:21 gives 15:30, full FP = 30:42
23_03:21 to 23_18:11 gives 14:50, full FP = 30:20   11:38 field to normal 20 uT North
23_18:11 to 24_09:57 gives 15:46, full FP = 30:36




About the Geo Magnetic Field, GMF.

Also see:  https://en.wikipedia.org/wiki/Earth%27s_magnetic_field


Fig 3 The earth and its magnetic field.  (simplified model)
The convention is to draw the magnetic field lines with arrows as if they exit the NORTH pole of the magnet or solenoid where the field is made.
Here we see the GMF as if there were a big magnet inside the earth. The axis of this magnet is tilted approx. 180 + 11 degrees w.r.t. the earth's axis of rotation, indicated by GNP = Geographical North Pole, and GSP = Geographical South Pole. EQ identifies the equator.
MNP and MSP identify the magnetic north and south poles.
The confusing definition of the GMF North pole being on the southern hemisphere results from a historical mistake, before it was understood that opposite poles attract each other, whlle equal poles repell each orther.
The magnetic southpole of the earth sits somewhere in the Canadian arctic.
Remember: The North pointing hand of a compass is a Northpole and is attracted to the South pole of a magnet if you bring one close by.

At my location in the Netherlands (red dot) the field has a horizontal component of 20 μT pointing North within 2 degrees, and a vertical component of 50 μT pointing downwards.



Constucting A coilset for the magnetic field tests.

Feasibility.

The idea was to construct a set of 3 coil-pairs forming the sides of a cube. I set the size to 70 x 70 x 70 cm.
The question was: Can I make a magnetic field with a strength in the order of the local GMF inside that cube? Well, for that we have to do some calculations.

In magnetism we have to deal with two concepts which are often confused: magnetic field strength and magnetic induction.
The field strength H is expressed in Ampere per meter. It is a.o. what is generated by an electric current flowing through a solenoid.
The Induction B is the resulting magnetism expressed in Tesla, or Newton per Ampere-meter.
The relation between the two is the permeability, μ, which is generally split up in two parts, μ0 and μr. μ0 is a physics constant (*) with the value 4 * pi * 10-7 Newton-meter per Ampere-squared, and μr is a dimensionless value, specific for the material in the magnetic circuit. For example Iron can have a μr of 100 to 30000, while air = 1. This makes electromagnets with an iron core so much stronger than without the iron.
The formulas are simply B = μ * H,  or H = B / μ,  or μ = B / H.
In our case we only have to deal with air, so μr = 1.

A good starting point is to look up the induction of the GMF at your location. For NL I found 20 μT for the horizontal component which is also very well pointing North, and 50 μT for the vertical component.
So we need 20 10-6 / 4 pi 10-7 = 16 A/m for the horizontal component, and 40 A/m for the vertical part.

In my old school books I found the formula H = NI / l for the field strength in the center of a long coil or solenoid. Long means here that the length of the solenoid must be (much) larger than the diameter.  H is the fieldstrength in A/m, N the number of turns, l the length in meters, and I the current in Amperes.
Note that the diameter of the solenoid is irrelevant.


Fig 1. Solenoid.

So to make our 16 A/m takes only 16 windings, and a current of 1 Amp. Easy to to. But there is a twist. We can't have such a coil around the bob's area, we need to split it in two parts. Shift half the windings to the left, and the other half to the right. The assumption is that the change in field strength and in the shape of the field will not be dramatical.

Simulation.
And here comes FEMM, Finite Element Method Magnetics, a freeware software packet to simulate magnetic fields. It is for M$ window$ but it also works well under Linux with Wine.
Unfortunately FEMM is 2D only, and I could not find a method to simulate other than round, axisymmetric coils.
So I made a simulation of the field between two coils of 70 cm diameter, placed parallel at 70 cm distance. Each coil had 1 winding carrying 1A of electrical current. I assumed that the step from round to square coils would not make a dramatic difference.

    
Fig 2  Field strength plot.                             Fig 3.  Legend.

The left side of the plot represents the axis of the coils, we see only the right half, the left half is to be mirrored.
The circle in the center shows the area of 230 mm radius where the bob moves.
There we have around 1.3 μT field strength. In the center of the coilset we have a reasonably homogeneous field.

Yes, the most homogeneous field can be made with the so called Helmholtz setup, where the two identical coils are round and at at a distance of their radius. For my purpose that was a bit inconvenient, because it is difficult to make a cube out of a 3 sets of Helmholtz coils.

By increasing the number of windings and / or the electrical current we can easily reach fields in the order of 20 μT.
A fast test with a single wire loop of ca. 50 cm diameter carriying 10 A showed a compass to deviate some 45 deg from the north. So this simulation is not several orders of magnitude wrong.

The final coil set (I call it the CubiCoil)  was made with 6 square coils of 70 x 70 cm each with 11 windings of wire 1.5 mm2, a type of house installation wire readily available in NL, in boxes of 100 m. This wire can carry at least 10 A continuously without overheating. The sides were reinforced with thin wooden bars. I labeled the vertical coil pairs with red and green cable ties. I connected the coils of each pair in series, using a compass to find out the proper polarity. I used thick red/black loudspeaker cable to connect the coil set to a current regulated power supply.
The 4 standing planes needed a cross of nylon rope to keep the whole thing upright.


Fig 4. The orientation of the planes and fields.
The arrows indicate the north poles, when the red wire of the feeding cable is positive.


Fig 4. The CubiCoil.  (click for larger image)

Check calibration.
In the simulation we had 1.3 μT for 1 A with 1 winding per coil. In the real thing we may expect 14 μT at 1 Amp for the 11 windings per coil.
To do the check I placed the CubiCoil such that the axis of one coil pair was oriented E-W. I placed a compass in the center of the cube on a non magnetic support. The compass pointed north. I turned up the current in that coil pair until the compass was 45 degrees off. That is the 20 μT reference current. I needed 1 Amp to reach that field strength. With this current flowing I moved the compass around some 30 cm to see if there was a serious deviation from the 20 μT. The angle of the compass did not change more than some 10 degrees.


(*) μ0 is even a very basic constant in physics, together with its electrical counterpart ε0, which you need if you do calculations with an electric field.
Nice to know:
When you take the square root of  1 / (μ0 * ε0)  you will find a value of ca. 3 108, with dimension meters per second, being the speed of light.
When you take the square root of μ0 / ε0 you will find a value of ca. 376 with the dimension Ohm. That is the characteristic impedance of the vacuum.