Question

The aurora is caused when electrons and protons, moving in the earth's magnetic field of ≈5.0×10−5T, collide with molecules of the atmosphere and cause them to glow. Part A What is the radius of the circular orbit for an electron with speed 3.0×106 m/s ? Assume that the electron moves in a plane perpendicular to the magnetic field.

Answer 1

Answer:

$r=0.341m$

Explanation:

The circular movement is produced by the magnetic field:

$F=q*v*B$

This force is a centripetal force because the electron moves in a plane perpendicular to the magnetic field. For a centripetal Force, that produces a circular orbit with a radius r:

$F=m*a=m*v^{2}/r$

If we solve these two equations in order to find r, with the mass and charge of a electron:

$qvB=mv^{2}/r\\r=mv/(qB)=9,1*10^{-31}*3*10^{6}/(1.6*10^{-19}*5*10^{-5})=0.341m$