How to Calculate the Magnetic Field Strength of a Pulsar?

[florian101]

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

 

[AndyW]

Based on your post, it seems like you are trying to calculate the magnetic field strength of a pulsar using its magnetic moment and volume. However, there are a few things to consider before using this expression.

Firstly, the magnetic field of a pulsar is not a simple dipole field. Pulsars have much more complex magnetic field structures, including multiple poles and strong currents. Therefore, using the dipole expression for B(r) may not accurately reflect the true magnetic field strength of a pulsar.

Secondly, the magnetic moment of a pulsar is not a well-defined quantity. It is constantly changing due to the pulsar's rotation and emission of electromagnetic radiation. Therefore, calculating the magnetic moment using a single value of B_max may not be accurate.

Finally, integrating B^2 over the volume assumes that the magnetic field is constant throughout the volume, which may not be the case for a pulsar.

To accurately calculate the magnetic field strength of a pulsar, a more complex and detailed model is needed, taking into account the pulsar's unique magnetic field structure and changing properties.