# All Questions

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### What conditions are necessary for Birkeland currents to form?

If charged particles flow through non-magnetised space will they form Birkeland current? Or can such currents only form along existing magnetic field lines? Part of the reason I ask is this: http://...
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### Proof of minimum distance between object and image of a convex lens image being 4*focal length

I can prove that the minimum distance between an object and its image, through a convex lens is 4*focal length, if I assume that the distance between the object and the lens is the same as the ...
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### Why are topological phases described by modular tensor categories?

After some reading, I have an inuitive idea what topological phases of matter are. But where is the connection to modular tensor categories? Is there fundamental literature where this is covered? ...
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### What is the gravitational field inside a hollow spherical cavity embedded in a solid sphere? [duplicate]

Imagine a solid sphere of radius $R$. From the inside of this sphere we remove a smaller sphere of radius $r$. The sphere can be situated anywhere inside the massive sphere. How does the gravitational ...
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### What are the odds of finding an electron a long way from an atom? As in metres away?

Pretty self-explanatory, heard that there is a chance that you might find an electron on the other side of the universe, just wanted to know.
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### Why is it misty at such high temperatures as per weather reports?

I am residing in New Delhi (pardon me for any irrelevant data I might include), and I noticed a really interesting thing. It's an average 30 degrees Celsius out here, and yet, most/some weather ...
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### Exact expression for the ground state energy in the 1D Bose-Hubbard model

I heard that Bose-Hubbard model is exactly solvable in 1D. What is then expression for the ground state energy $E_{0}(N, M, ...)$ as a function of total number of particles $N$, number of lattice ...