# Magnetic field of a pulsar

## Main Question or Discussion Point

hay
I need the following expression

B^2V

of a pulsar. B is the magnetic field and V is the volume. I can do this in a strong approximation with B = 10^8T and v = 10km but I would like to do it properly. Therefore I choose the magnetic field of a dipol

B(r) = mu_0/(4*pi*r^3) (3*r(r*m) - m)

where m is the vector magnetic moment and r is the unit vector in r-direction. mu_0 is the permeability of free space = 1.2566 10^-6 H/m.
Now I have several problems... first of all the magnetic moment m what is the magnetic moment of a pulsar? I did the following:

mu_0*m/(4pi*r^3) = B_max/2

(the equation is a self made approximation and comes with no warranty) with B_max approximately 10^8T I get 10^19 m^2A. Is this correct???

To calculate the term B^2V I suppose I have to integrate B^2 over the Volume in spherical coordinates.

B^2V = int^r_0 int^2pi_0 int^pi_0 r^2 sin(theta) B(r)^2 dr d phi d theta
= int^r_0 int^2pi_0 r^2 4pi B(r)^2 dr d theta

with B(r) from above... is this correct?
thank you very much for any comments or corrections
florian