# Measuring the Earth's Magnetic Field

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### The Idea

The Earth has a magnetic field that goes from the South Pole to the North Pole. The magnetic South Pole is actually close to the geographic North Pole. We can measure how strong the horizontal component of the Earth's magnetic field is by comparing its effect to that of a magnetic field produced by the current flowing in a coil of wire.

### What You Need

• insulated wire several meters in length
• compass, preferably one mounted on a low-friction pivot
• ruler
• protractor
• cylindrical shape to wrap the coil (The diameter of the shape depends on the length of the compass needle. The diameter of the coil needs to be larger than the length of the compass needle.)
• ring stand or other support to hold the coil of wire
• DC power supply capable of current in the range of 1.0 amp or higher
• DC-ammeter or a multimeter configured as an ammeter in the 0–10 A range
• room with nonferrous tables and free of stray magnetic fields

### Method

The Earth's magnetic field is:

(1.26 x 10–6 is the same as 0.0000126 and you can multiply inches by 0.00254 to get meters.)

1. Set up the compass. Make sure it is freespinning and pointing to the north. Metal desks containing iron or steel may interfere with this. Also, motors or loudspeakers may have significant magnetic fields that could affect the outcome of this measurement.
2. Form a coil of 15 turns using the cylindrical shape to form the coil. (For a small hand-held compass, a 1½ inch diameter pipe is a good form. For the pivot type compass, a soup can or coffee can is more appropriate.) After the coil is formed, withdraw the object used to wind the coil. Leave some wire at the start and end of the coil to allow it to be connected into a circuit.
3. Support the coil using a ring stand or other support. The coil is oriented vertically with the plane of the coil facing east and west. The compass should be contained inside the plane of the coil, as shown in Figure 117-1. A top view of this is shown in Figure 117-2 for clarity. Notice the ends of the compass points to the turns of the coil.
4. Make sure the DC power supply is turned off and the ammeter is set to read currents in the range of 1–10 amps.
5. After stripping the insulation from the ends of the coil, attach one end to the positive terminal of the ammeter and the other end to the negative terminal of the DC power supply. You can use jumper wires or attach the coil directly. Refer to Figures 117-1 and 117-2 for the appropriate connections.
6. Complete the electrical circuit by connecting the negative terminal of the ammeter to the positive terminal of the DC power supply.
7. Place the protractor so the zero degree line ins aligned with the direction the compass exposed only to the Earth's magnetic field.
8. Slowly and carefully turn on the DC power supply. Increase the current reading on the ammeter until the compass needle deflects 45 degrees from its starting position.
9. At this point, the horizontal component of the Earth's magnetic field is balanced by and equal to the magnetic field of the coil.

### Expected Results

The Earth's magnetic field varies with location, but it is in the ballpark of about 5 micro Teslas or 5 μT or 5 x 10–7 T. The following table summarizes the results for different latitudes, and it includes the scientific notation and decimal forms that are equivalent.

### Why It Works

The magnetic field of the coil is perpendicular to the plane of the coil. In this experiment, the magnetic field of the coil is perpendicular to the horizontal component of the magnetic field of the Earth. When the coil's magnetic field just equals the horizontal component of the Earth's magnetic field, the resultant points at a 45-degree angle between the two. When this occurs, the magnetic field of the Earth is given by that of the coil according to the equation:

where B is the coil's magnetic field in Teslas

N is the number of turns in the coil

μo is a measure of how strong a magnetic field is produced by a given current, called the permeability of free space, and equals 1.26 x 10–6 Teslas

I is the current in amps

R is the radius of the coil in meters.

As an example: A 15-turn coil that is 2 inches in diameter (or 0.051 meters) requires a current of 0.28 amps to turn the compass 45 degrees.

The magnetic field is:

B = (15 turns x 1.26 x 10–6 T-m/A x 0.28A) / (2 x 0.051m)

• = 0.00000052 T or 5.2 × 10–5 T

This is in the ballpark of the expected range for the Earth's magnetic field for middle latitudes.

### Other Things to Try

The previously measured value is the horizontal component of the Earth's magnetic field. Near the equator, the Earth's magnetic field is all horizontal. As you approach the poles, the direction of the magnetic field with respect to the Earth's surface increases. The angle the field makes with the Earth's surface can be measured using a compass that is free to rotate in the vertical plane. The total field (or the overall field strength vector) at that location can be determined from:

total field (Teslas) = horizontal component (Teslas) / cosine (angle to horizontal)

As with many experiments, it is comforting to know that the effect we intend to measure is, in fact, what our experimental results are giving us. One way to increase confidence in our results is to repeat it under different condition and verify we have the same outcome. According to our model, it should not matter how many coils we have. Repeating the measurement to see how much current is needed to turn the compass 45 degrees using 5, 10, or 20 coils should give a consistent result as the measurement described about using 15 coils.

### The Point

The magnetic field of the Earth can be measured by balancing it with a known magnetic field. If that magnetic field is at right angles to the horizontal component of the Earth's magnetic field, the compass will point in a new direction that is 45 degrees from the original position. Away from the equator, the Earth's magnetic field is at an angle to the horizontal, which can be measured. The overall magnetic field will be slightly higher than the horizontal component.