<p>Inclination is given by</p>

<p>$$I=\arctan(2\cot\theta)$$
where theta is equal to 90° minus the observer's latitude (in the Northern Hemisphere), therefore</p>

<p>$$I=\arctan(2\cot(90-40))=59,21^\circ$$</p>

<p>To get declination the following figure helps:</p>

<p><a href="https://i.sstatic.net/F119x.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/F119x.png" alt="enter image description here"></a></p>

<p>Declination is the angle between geographic north and magnetic north. (I suppose 80°N, 72°W are the coordinates of the North Geomagnetic Pole.) Let's do the math!</p>

<p>$$D=\arctan\left({{{33}\over{40}}}\right)=39,52^\circ $$</p>

CC BY-SA 3.0
2016-01-05T00:02:52.470Z
2016-01-05T22:38:37.920Z
2016-01-05T22:38:37.920Z
Bálint
<p>I'm trying to answer the following question:</p>

<blockquote>
  <p>Compute the inclination and declination of the magnetic field that would be observed in Boulder, Colorado (40°N, 105°W) if the Earth’s field corresponded to a perfect geocentric dipole whose axis penetrates the Earth’s surface at 80°N, 72°W.</p>
</blockquote>

<p>Source: question 4, exercise set 5.10, on p. 360 of Lowrie (2007).</p>

<p>I found the inclination using $\arctan(2\tan(40))$, but am unsure of how to get the declination.</p>

<hr>

<p>Reference:</p>

<p>Lowrie, W. (2007). <em>Fundamentals of Geophysics</em>, 2nd ed. Cambridge University Press.</p>

<geophysics><homework><geomagnetism>
Calculating magnetic declination for a non-axial dipole field
GeoSuper
# Calculating magnetic declination for a non-axial dipole field

(Asked by: username_0 on 2015-11-02)

I'm trying to answer the following question:

> Compute the inclination and declination of the magnetic field that would be observed in Boulder, Colorado (40°N, 105°W) if the Earth’s field corresponded to a perfect geocentric dipole whose axis penetrates the Earth’s surface at 80°N, 72°W.

Source: question 4, exercise set 5.10, on p. 360 of Lowrie (2007).

I found the inclination using $\arctan(2\tan(40))$, but am unsure of how to get the declination.

---

Reference:

Lowrie, W. (2007). *Fundamentals of Geophysics*, 2nd ed. Cambridge University Press.

**Tags:** geophysics, homework, geomagnetism


---

## 1 answers

### Answer by username_1 on 2016-01-05. Score: 4

Inclination is given by

$$I=\arctan(2\cot\theta)$$
where theta is equal to 90° minus the observer's latitude (in the Northern Hemisphere), therefore

$$I=\arctan(2\cot(90-40))=59,21^\circ$$

To get declination the following figure helps:

[![enter image description here](https://i.sstatic.net/F119x.png)](https://i.sstatic.net/F119x.png)

Declination is the angle between geographic north and magnetic north. (I suppose 80°N, 72°W are the coordinates of the North Geomagnetic Pole.) Let's do the math!

$$D=\arctan\left({{{33}\over{40}}}\right)=39,52^\circ $$


---

