In this section, we’re going to talk about measuring the magnetic field. A simple and familiar type of magnetic field sensor is the magnetic compass. The compass was discovered by the Chinese over 2,000 years ago. It contains a magnetized needle that aligns with the Earth’s magnetic field. The Earth rotates about an axis that passes through the North and South geographic poles. The Earth itself is a gigantic magnet and the North and South poles of the magnet do not correspond to the North and South geographic poles of the Earth. We can imagine the magnetic field lines from this giant internal magnet passing out of the surface of the planet, arcing through space, and then diving back in to the ground at the North magnetic pole.
The red arrow that I’m holding represents approximately one of the Earth’s magnetic field lines. We can think of these as imaginary lines which come out of the Earth, arc through the sky and land again at the North Pole of the planet. Now, I have aligned this arrow by measuring the three components of the Earth’s magnetic field using my phone. And, at the moment, the way I have this arrow and the phone oriented, the only component of magnetic field that’s non zero is in the Y direction, that’s the, this direction on my, on my phone.
The magnetic poles of the Earth are constantly moving and that’s a bit problematic for a sensor like a compass which points at the magnetic poles. We need to understand something about where the magnetic poles are with respect to the geographic poles and how they are moving. The needle of a compass points towards the Magnetic North Pole of the planet. But, true North or geographic North is in a different direction. Here, we have a right-handed coordinate frame where the axes are pointing to geographic North, geographic East and vertically down toward the center of the planet. Imagine now a plane that contains the magnetic field vector which is denoted by a red arrow and the symbol B. Angle between this plane and the geographic North direction is the magnetic declination angle D.
This diagram shows magnetic declination for the year 2010 and we can see that it varies quite significantly across the planet. Magnetic North can be up to plus or minus 20 degrees away from true North. These values become quite extreme in the vicinity of the South Magnetic Pole which we can see very clearly here. If you’re sailing a boat and you’re using a nautical chart, the appropriate magnetic declination is typically marked somewhere on that chart. Magnetic declination varies over time and this fascinating video shows the contour lines of magnetic declination varying over periods of hundreds of years.
The magnetic field lines are generally not parallel to the surface of the Earth. In the Southern Hemisphere, the magnetic field lines come out of the ground. And, in the Northern Hemisphere, the magnetic field lines disappear into the ground. So, we can introduce another angle which is referred to as magnetic inclination denoted typically by the symbol I and that represents the angle of the magnetic field line with respect to the surface of the Earth. And, this is a map of magnetic inclination over the surface of the planet. The sign convention used is Northern Hemisphere centric. So, if the magnetic field line is descending in to the ground, the inclination angle is considered to be positive. Here is another chart and this one shows the strength of the magnetic field, the magnitude of the magnetic field vector and this is units of nano teslas. That’s 10 to the minus 9 Tesla. For comparison, a modern MRI machine has a magnetic field strength of around 4 to 8 Tesla. That’s a hundred thousand times stronger than the magnetic field strength of the Earth.
We learn the principles behind magnetometers, sensors that measure the Earth’s magnetic field.