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

`r=0.341m`

Step-by-step 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`