The aurora is caused when electrons and protons, moving in the earth's magnetic field of ≈5×10−5 t, collide with molecules of the atmosphere and cause them to glow. what is the radius of the circular orbit for (a) an electron with speed 1.0×106m/s and (b) a proton with speed 7.0×104m/s. what is re in meters and what is rp in meters?

a) 0.114 meters is the radius of the circular orbit for an electron with given speed.

b) 14.6 meters is the radius of the circular orbit for a proton with given speed.

Explanation:

Force on the charge particle :

Since, the particle is revolving around in a circular path ;

particle in constantly moving in circular path under action of magnetic field:

F = F'

Where :

r = radius of the circular path

m = mass of the particle

v = velocity of the particle

B = magnetic field

q = magnitude of  charge on the particle

a)  Velocity of the electron =  

Mass of electron = m =

Charge on an electron , q=

B =

Radius of the circular orbit for an electron with given speed =

0.114 meters is the radius of the circular orbit for an electron with given speed.

b)  Velocity of the proton =  

Mass of electron = m =

Charge on an electron , q=

B =

Radius of the circular orbit for a proton with given speed =

14.6 meters is the radius of the circular orbit for a proton with given speed.