# Deriving the magnetic field due to a dipole

I am trying to follow along with a derivation from Cullity, Introduction to magnetic materials 2011. I am getting stuck at a very early stage when computing the components of the magnetic field at a point P due to a magnetic dipole at the origin, where P is at an angle $$\theta$$ from the direction of the dipole's magnetic moment (in a 2D plane). See diagram:

I compute

$$H_r = \frac{m \rm{cos}(\theta)}{r^3}$$.

However, they compute

$$H_r = \frac{2m \rm{cos}(\theta)}{r^3}$$.

See bottom of diagram for the equations in the textbook. Or see the book chapter here

Why do the have $$2 \times$$ what I calculate for $$H_r$$? Are we not simply taking the cosine of the field, to find the field along from the line from the centre of the dipole to P?

the magnetic field on the axis of the dipole is $$2KM/r^3$$ here dipole is $$M$$ in the general case, which you are talking about, the axial dipole is $$Mcos(\theta)$$ so the magnetic field on the axis of $$Mcos(\theta)$$ dipole will be $$2KMcos[\theta]/r^3$$ just replaced $$M$$ with $$Mcos[\theta]$$.