The aurora is caused when electrons and protons moving in th

The aurora is caused when electrons and protons, moving in the earth’s magnetic field of \\(\\approx 5.0\\times10^{-5} {\ m T}\\), collide with molecules of the atmosphere and cause them to glow.

What is the frequency of the circular orbit for an electron with speed \\(1.0 \\times 10^6 \\; \ m m/s\\)?

Express your answer with the appropriate units.

What is the frequency of the circular orbit for a proton with speed \\(5.0 \\times 10^4 \\; \ m m/s\\)?

Express your answer with the appropriate units.

Solution

Mass of electron m=9.11*10^-31 kg

Mass of proton m=1.67*10^-27 kg

charge of proton and electron is same

q=1.6*10^-19C

a)

Given B=5*10^-5T

Centripetal force =magnetic force

mv²/r =qvB

=>r=mv/qB

r=(9.11*10^-31)(10⁶)(1.6*10^-19)(5*10^-5)

r=0.114 m

Time Period to complete one revolution

T=2pir/V =2pi*0.114/10⁶

T=7.155*10^-7 s

frequency of circular orbit

f=1/T =1.4*10⁶ Hz

b)

For proton

r=(1.67*10^-27)(5*10⁴)/(1.6*10^-19)(5*10^-5)=10.44 m

TIme period

T=2pi*10.44/(5*10⁴) =1.31*10^-3 s

frequency

f=1/T =762.4 Hz