# Passing through the earth's magnetic field

When a projectile such as a jet plane passed through the earth's magnetic field, does an electric current get generated in the projectile? I don't sense it when I fly commercially. Why not?

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Faraday cage enclosure – Michael Luciuk Jan 12 at 16:47
You mean an induced current due to the inhomogeneity of Earth's magnetic field? How do you suppose you would "sense" that when you fly? Anyway, it will probably be extremely small since the magnetic field variations are on very large scales. – jkej Jan 12 at 17:09
Thank you. I forgot about Faraday's cage. – Tony Vignone Jan 12 at 17:09

## 1 Answer

Yes indeed. We do have observe an induced emf when moving perpendicular to the magnetic field. Let's assume that our plane travels at some $50\ ms^{-1}$ and the length of its wings to be $30\ m$. The vertical component of Earth's magnetic field is around some $4\times 10^{-5}\ T$

Roughly, the induced emf is given by $$e=-B\ l\ v =-50\times 30\times 4\times 10^{-5}$$ $$\implies e=-0.06\ V$$

You must be an amazingly sensitive bot in order to detect that very small voltage. If you cling to the wings somehow and wanna feel the current, we could make use of Ohm's law. But, the amperes would be further worse. Our body resistance is about $10^5\ \Omega$ $$I=\frac{0.06}{10^5}=0.6\ \mu A$$

What do ya think of this current?

As Michael says, Faraday's cage is a great example...

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