Question

A charged particle can orbit the (magnetic) equator due to magnetism. There’s an orbit called geosynchronous orbit, where ω=2π/1 day; at this rate, it stays over the same location. It needs to be pretty far away to nail this, as we’ll see. Out that far, the Earth can be treated as a distant dipole, B(R)=B0r^3⊕/R^3, where r⊕≈6×10^3km is the radius of Earth and B0≈30μT is the magnetic field at the surface on the equator.(Ignore gravity.)

(a) In order to orbit geosynchronously, the particle must be moving east. (This is the way the world spins.) Which can do this, electrons (−) or protons (+)?

(b) Using the masses and charges in the notes, find the radius at which the particle you chose orbits geosynchronously.

Answer 1