Question

An electron and a proton are moving in circular orbits in the earth’s magnetic field directly above the earth’s geographic north pole, high above atmosphere, where the field’s magnitude is 40 µT.

a) Looking down on the orbits from above, what is the sense of the orbit for each of the particles—clockwise or counterclockwise?

b) What is the period of the orbit for the proton?

c) What is the frequency of the orbit for the electron

Answer 1

The force due to the magnetic field is calcullated from the Lorentz force

a)
So, in the north pole as the force is away from the pole, i.e., " perpendicular to the pole ", so, if we look down on the orbit below from above, the sense of rotation for proton (positively charged) is clockwise.
And for electron (negatively charged) the sense of rotation is the opposite, i.e., anti-clockwise.
b)
We have from the force balance

So, the time period is
  
So, for proton, putting the values, we get
  
c)
For electron , the frequency is