Question

The magnetic field in the interstellar space of our galaxy has a magnitude of about 2.53 × 10^-10 T. How much energy is stored in this field in a cube 12.3 light‐years on edge? (For scale, note that the nearest star is 4.3 light‐years distant and the radius of the galaxy is about 8 × 10⁴ light‐years.)

Answer 1

For the magnetic field the energy density (Energy/Volumen) is:

$\eta =\frac{B^{2}}{2\mu }$

If we multiply by a volume of a uniform sphere of 12.3 light years (1,1637e+18 m) we obtaing the energy stored

$E =\frac{B^{2}}{2\mu }\cdot \frac{4\pi (1.1637\cdot 10^{18})}{3}$

$E =\frac{(2.53\cdot 10^{-10}\, T)^{2}}{2\cdot 4\pi \cdot 10^{-7} \, N/A^{2}}\cdot \frac{4\pi (1.1637\cdot 10^{18}\, m)}{3}$