Earth's magnetic Field

A few pictures (clicking on the thumbnail gives the full scale picture)

Proposed by

Jean-Marie Frère, ULB, Bruxelles,

with the technical  support of

Anastase Karusho , ULB

Thanks to
Jean Tran Thanh Van  (ICISE, VietNam)
Trung Quan Tran
Philippe Léonard, ULB

description :
The purpose of this experiment is to measure the local value of the Earth Magnetic field, or, rather, its horizontal component.
A simple set-up is proposed, suitable for schools or the first years of university.
The goal is to obtain a sufficiently precise measurement to allow for a significant comparison with other groups world-wide.

Interest of the experiment
and collaboration :
The Earth Magnetic field is a relatively easy to measure quantity, whose understanding requires a number of measurements around the Earth: it is thus an excellent school project, if international collaboration can be promoted.

Here is a simple picture, which shows that the intensity of the B field vary around the Earth.
Nearly horizontal in the tropics, the field points sharply downwards at the latitude of Belgium, and upwards in the Southern hemisphere.
Since the proposed measurement is for the horizontal component, sharp differences are expected (see references below, a factor 2 between Belgium and VietNam, for instance).

Outline of the experiment
  • A compass is placed inside a coil. The device is oriented so that the needle is perpendicular to the coil when no current is present.

  • The current is then increased until an angle of 45° is reached, at which point, the coil magnetic field equals in length the horizontal component of the Earth's magnetic field.

  • For the 8mm spacing solenoid, we get

    If we adjust I to get a 45° angle, we get
    In Brussels, we measured (on Sept 15th, 2017)  I = 132 mA, which yields

  • The value obtained is compared to international standards, an entered into a collaborative project.

  • The measurement may also be compared with the one obtained from a "smartphone" (less demonstrative, does not replace the actual experiment, and calibration is not guaranteed ....).
Equipment  needed
  • A good compass (preferably liquid-filled),
  • A few meters (depends on coil chosen: 6 to 12 meters) of copper wire
    (insulated or not; magnet/enameled copper wire is ideal but not necessary,
    ... don't forget to remove the enamel on the ends! )
  • a digital multimeter (standard lab/electrician equipment)
  • a variable resistor (e.g. 50  or 100 ohm potentiometer), (or a choice of fixed
    resistors for optional method)
  • dry cell(s) (small batteries)  as a power supply.  we use 2 reloadable AA cells, but this is not critical .. DO NOT USE a car battery (a short circuit can cause fatal wounds !)
  • some cardboard, glue, .. 
  • a printed version of the proposed templates (available here for 8 mm pitch
    and here for 4 mm pitch) -- be sure to check that the printer prints real size (you may need to disable the "shrink to fit" option)-- or design you own!

  • If you want to perform a local calibration (not necessary if you use the templates) , some standard lab equipment is needed: oscilloscope, LF sine generator.  It is also possible to use a Hall effect probe.
Experimental procedure 
  • assemble the solenoid: print out the chosen template
    (available here for 8 mm pitch and here for 4 mm pitch) making sure that the printer reproduces the correct size (you may need to de-select a "shrink to fit" option) and glue it to some strong cardboard,
    then fold and glue it into shape.
  • wind your wire according to the notches (it helps to make an incision with a cutter at each of the small arrows, so that the wire is trapped in position)
  • on a non-magnetic support (wood, cardboard, plastic) support, assemble the circuit according to the picture. Here a variable resistor of 100 ohm is used, as well as 2 reaodable Nimh AA cells (at the difference of alkaline battery, they have a voltage of 1.25V each thus a  2.5 V total). You may need to adapt to your local field (for instance, using the 4mm pitch to get a lager field).
  • mark the N-S direction with a felt tip on the compass housing, repeat for the 45 degrees direction; insert the compass in the solenoid, so that N-S  markings point perpendicular to the solenoid axis
  • go outdoors, and move away from buildings and possible distortions of the magnetic field
  • orient your device so that the needle (in absence of current) points perpendicular to the solenoid axis (this means that the axis will be along E-W magnetic direction) (see picture)
  • connect the circuit (power supply - variable resistor - coil - multimeter )
    and increase the current until the needle points at 45°. At this moment,
    the length of the magnetic field created is equal to the horizontal component of the Earth's field

  • For the calculation , see below, ...

    For the 8mm spacing solenoid, we get

    If we adjust I to get a 45° angle, we get
    In Brussels, we measured (on Sept 15th, 2017)  I = 132 mA, which yields
  • Alternate method.
    In case you can't find a suitable variable resistor, just use fixed resistors by trial and error until you reach an angle close to 45°, then use the measured value of the angle (see figure) to determine the Earth's field.
  • As a comparison, you could measure simultaneously the 3 components of the magnetic field using a "smartphone". Most have 3D magnetic captors (although the calibration seems to vary quite a bit ..). For instance, the  PhyPHOX suite of physics applications can be used.
Some hints
  • We tried to use a button-like (20mm) compass (typically sold as a gadget to attach to a key ring), with the goal to use a smaller section coil; however this failed since the needle got easily "stuck" in the very thin casing.
  • Avoid any ferromagnetic parts in the assembly (nails, .. ),
  • Battery power (AA cells) is used to perform the experiment far away from buildings and magnetic disturbances  - AVOID CAR BATTERIES, which can cause injuries in case of short-circuit. -- we moved 30 m from any building to perform our local measurement.
  • If using enameled wire, be careful to remove carefully the insulating material at the ends, as the colour of the enamel is close to the copper's one.
Calculation, Example
The field inside the solenoid is
where  N/L is the number of turns per unit lenght, I the current intensity,
and  1/K is a geometric factor parametrizing the departure from an ideal (infinite and thin) solenoid .  (1/K will be discussed in the "calibration" page)
For the 8mm spacing solenoid, we get

If we adjust I to get a 45° angle, we get
In Brussels, we measured (on Sept 15th, 2017)  I = 132 mA, which yields

The calibration shows that K is close to 1, and we can estimate a few %
error on the evaluation of the angle (initial and final position of the needle), so we are well in line with the values from the World Magnetic Field model.

Note that a very careful alignement of the compass needle on the 0 and 45° lines is essential (it should be repeated several times). For this reasons, we found it convenient to draw those lines on the compass with a felt tip pen.

Comparison to Standard Measurements
Worlwide data and models of the Earth magnetic field are available,
notably from the British Geological Survey.
In particular, a map of the Horizontal component of the magnetic field is found HERE (the values need to be adjusted for time)
(the picture is taken form the British Geological Survey site ,
click to see the full resolution on their site)

A calculator using the World Magnetic Model is found HERE

Motivation : The purpose here is not to reach an extreme precision (around 10% is sufficient),
but to promote international collaboration on a topic which

  • showcases a "one Earth" concept, where
  • collaboration between teams of (aspiring) scientists world-wide is essential.

  • the measurement illustrates important concepts in physics
  • the basic measurement is easy and could easily be done by "end of secondary school" students (in Belgium, secondary school addresses ages 12-18)
  • the project can easily be extended to include
    • calibration (bringing in the concepts of induction)
    • determination of the local declination (by establishing the local true South direction, or meridian, venturing into basic astronomy)
  •  the basic experiment is not expensive, (and really cheap if  basic equipment like a multimeter is accessible)
  • students can engage in a collaborative project, and establish contacts world-wide.
 we plan to use a common document to log the resutls ,
you can find a first attempt HERE