Find the Magnetic Latitude of your Location Using the Magnetometer

Concepts Covered:

✔ Earth’s Magnetic Field: Understanding its orientation and geographic variations.

✔ Magnetic Inclination: Measuring the angle of the magnetic field relative to the horizontal plane.

✔ Magnetic vs. Geographic Latitude: Exploring why these two measurements differ.

✔ Magnetic Field Modeling: Connecting observations to the dipole magnetic field model.

Experimental Procedure:

In this activity, we will use a magnetometer and an inclinometer to measure the magnetic inclination at our location. This measurement will help estimate the magnetic latitude using the mathematical relationship:

tan⁡(L)=2tan⁡(i)tan(L)=2tan(i)

where i is the magnetic inclination and L is the magnetic latitude.

Step-by-Step Instructions:

1️⃣ Measure Magnetic Inclination:

• Open FizziQ and activate the Magnetometer instrument.

• Identify the axis displaying the magnetic field along Y.

• Rotate the smartphone to find the direction where Y is maximized.

• Using the Duo recording mode, simultaneously measure the magnetic field in Y and the angle between the smartphone and the horizontal plane.

2️⃣ Calculate Magnetic Latitude:

• Apply the formula tan(L) = 2tan(i) to compute L.

• Compare the result with the geographic latitude of the location.

• Observe differences and discuss their possible causes.

Key Scientific Concepts:

Magnetic Inclination

Magnetic inclination is the angle between Earth’s magnetic field lines and the horizontal plane. It indicates whether the field is more horizontal (near the magnetic equator) or vertical (near the magnetic poles):

• At the magnetic equator, the inclination is 0° (the field is parallel to the ground).

• At the magnetic poles, the inclination is 90° (the field is perpendicular to the ground).

• At intermediate latitudes, the inclination gradually changes.

Dipole Magnetic Field Model

Earth’s magnetic field can be modeled as a dipole magnetic field, similar to a giant bar magnet inside the Earth. The field lines emerge from the magnetic south pole and enter through the magnetic north pole, forming a shape similar to a classic bar magnet.

Geographic vs. Magnetic Latitude

• Geographic Latitude: Defined relative to Earth’s rotational axis.

• Magnetic Latitude: Based on the magnetic equator, which is perpendicular to Earth’s magnetic field, not its rotational axis.

Since Earth’s magnetic dipole axis is tilted by approximately 11° from its rotational axis, a location’s magnetic latitude differs from its geographic latitude.