B How Much Energy is Stored in Earth's Magnetic Field?

[Mikael17]

TL;DR Summary

Earth's magnetic field

How much power (Megawatts) would it require if we were to create a magnetic field as large and strong as the Earth's magnetic field?. I haven't learned how to calculate this, but just curious.

 

[Vanadium 50]

These aren't even the right units. A watt is a unit of power. That's like asking how many megawatts it takes to get from New York to Las Vegas.

 

[Ibix]

That's the wrong question to ask. It takes zero power to maintain a magnetic field, although if you are using an electromagnet and aren't using superconductors it takes power to maintain the current. So the answer to the power requirement is between zero and absolutely enormous, depending on how you build your solenoid.

The question you probably want to ask is about energy. How much energy is stored in the Earth's magnetic field? Unfortunately, I don't know the answer. The energy density of a magnetic field of strength $B$ in a volume with magnetic permeability $\mu\mu_0$ is $B^2/2\mu\mu_0$, but to get the total energy you need to integrate that over the whole volume of the field, and I don't know how $B$ varies. It's about 50 micro Tesla at Earth's surface and the magnetosphere extends to about 100,000km on the day side. It's much longer on the night side, but much weaker too. And I've no idea how it varies inside the Earth.

Finger in the wind, try a sphere of radius 100,000km and a B field of 50 micro Tesla with $\mu=1$. $\mu_0\approx 10^{-6}\mathrm{H/m}$. That'll come out on the order $10^{21}\mathrm{J}$.

There are so many approximations there that I wouldn't really trust the number. However, note that the total power generation capacity of the world is on the order of a terrawatt. You'd need all of that for a few centuries to generate $10^{21}\mathrm{J}$. So even if my estimate is off by a few orders of magnitude, it's more energy than is readily available. And we haven't even discussed the infrastructure needed to generate a field like that - the cooling capacity for superconductors the size of the Earth would increase the energy budget many, many times.