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$\begingroup$ You're simply calculating $\frac{1}{2\,\mu_0}\,|\vec{B}|^2$ and multiplying by a suitable volume to get your $10^{19}{\rm J}$, right? I'm not sure that this works though: wouldn't the liquid core flow keep replenishing the field, in which case you would be sapping the Earth's rotational kinetic energy (which would keep us powered for a great deal of time)? Might be a good idea to add to your last line the fact that our magnetic field shields our atmosphere from the Solar wind, and thus is essential to keeping the Earth livable. $\endgroup$
– Selene Routley
Commented Nov 19, 2014 at 9:14

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