Why is the angle of declination greater at higher latitudes and lower near equator?

Question

Why is the magnetic angle of declination greater at higher latitudes?

If I take a point 'Q' on the Earth's surface as in this figure: (I edited this picture off the internet, so the plane isn't very accurate. I just want to show how the geographical and magnetic axis would lie in the same plane.)

Won't the angle of declination be zero here? The geographic and magnetic meridian are the same, hence we could conclude there is no declination. This is at a 'higher' (at least more than the equator) latitude but this implication would make the above statement incorrect.

Answer 1

The definition of angle of declination is the angle between the geometric meridian and the magnetic meridian. You can look up the exact definition in words on wikipedia, but there is a easier way to visualise it. Firstly, we should know that the magnetic poles are a bit tilted to the actual geometric north and south poles.

Imagine you are a sailor. You are in the nothern hemisphere and want to go to the geometric North pole. If you use a compass, it will take you to the magnetic North pole instead of the geometric pole. The angle of declination is nothing but the angle between these two paths.

Image for reference:

These paths are curved due to the Earth's curvature. Therefore, these paths will not be 1 dimensional, but 2-dimensional. There are two points on the earth, A and B which are your positions(as a sailor). Here's the fun part: $\alpha$ and $\beta$ are angle of declinations! Why? Because if you are are position A, then the 2-D paths show us the planes. Path A to Geometric North is geometric meridian, while Path A to Magnetic North is magnetic meridian.

Now, it is easier to say that as you move away from the poles, the angle of declination decreases, because angle subtended by two far away points is less than two closer points. Therefore $\beta$ is less than $\alpha$.

Hence, then declination angle increases as we move closer to the poles.

IMPORTANT: However, this was a general case explanation. The angle of declination not only depends on the lattitude, but also the longitude. If the paths to geometric north and magnetic north coincide, then the angle of declination will be 0 irrespective of the lattitude.

It is just generally said that at higher lattitude, the angle of declination is higher, but obviously, yes it will depend on the longitude as well.

Conclusion: You cannot be sure whether the angle of declination will increase or decrease just by knowing the lattitudes. You should also have some information about the longitudees too, to know for sure

Answer 2

The picture is a little misleading in that the magnetic poles are not that far from the geographic poles, things should be a bit more symmetrical .

Regardless, this may not completely answer your question but do this thought experiment.

As you state, there is some line (not necessarily straight in reality) where the magnetic and geographic poles are in line. But consider what happens as you approach one of the poles on this line and then PASS it. Your compass will be reading 180 deg in the wrong direction, the worst error possible. This bad error only happens in the areas closer to the poles.

Now consider being on the equator so that you, the geographic pole, and the magnetic pole all form an isosceles triangle. The legs of the triangle are much longer than the distance between the two poles. Thus the angle is relatively small and the error is not so bad.

Answer 3

Magnetic declination is the angle between magnetic north and geo north. It depends where you are. If you are somewhere in between magn. and geo pole it will be 180 degrees. If you are on a line between magnetic north and geo south it will be 0.