Since neutron stars contain only neutrons, which are electrically neutral, the large magnetic field strength cannot be due to moving electric charges. Instead, it must be caused by the large mass and large rotational velocity of the star.

If rotating gravitational fields cause magnetic fields, that would be the link between gravity and electromagnetism.

From B, m, and [math]\omega[/math], the magnetic field constant [math]k_B[/math] can be calculated.

Here are the calculations:

 

[math]\text{1 Tesla (SI unit T) = }10^4 \text{ Gauss (G)}[/math]

 

[math]Mass=1.4 M_{sun}, Radius=10 \text{ km}, \text{Spin rate: up to 38000 rpm}[/math]

[math]Density \sim 10^{14} g/cc, \text{Magnetic field} \sim 10^{12} \text{ Gauss (strongest magnetic field in known universe)}[/math]

[math]m=1.4 M_{sun}=1.4(1.99\times10^{30} kg)=2.786\times10^{30} kg[/math]

[math]f=1/T, T=1/f=1/38000 \text{ rpm} = 2.63\times10^{-5} min \times 60 s/min = 1.58\times10^{-3} s[/math]

[math]\omega=\frac{2\pi}{T}=\frac{2\pi \text{ rad}}{1.58\times10^{-3} s}=3979.35 \text{ rad/s}[/math]

[math]B=k_Bm\omega[/math]

[math]k_B=\frac{B}{m\omega}=\frac{1\times10^{12} \text{ G}}{(2.786\times10^{30} \text{ kg})(3979.35 \text{ rad/s)}}=9.02\times10^{-23}

\frac{G \cdot s}{rad \cdot kg}[/math]

While neutrons as a whole are electrically neutral, they still have a magnetic moment and interact with magnetic fields. This is because neutrons are themselves made up of electrically charged particles (quarks). In addtion, neutron stars are not made up entirely of neutrons, but consist of layers of different types of matter. The extremely strong magnetic fields of Magnatars for example are considered as generated by an dynamo effect in one of those layers.