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two protons enter a region of transverse magnetic field.what will be ratio of time period of revolution if the ratio of energyy is 2.

Asked by pawar.kuldip1712000 5th January 2018, 7:21 PM
Answered by Expert
Time period of revolution is derived as follows.
begin mathsize 12px style q B V space equals space m omega squared r omega space equals space fraction numerator 2 pi over denominator T space end fraction space equals space square root of fraction numerator q B v over denominator m r end fraction end root T space equals space 2 pi square root of fraction numerator m r over denominator q B v end fraction end root end style
q is proton's charge, B is magnetic field, v is speed of proton, ω is angular speed , r is radius of circular path and T is time period.
Hence  begin mathsize 12px style T space proportional to space fraction numerator 1 over denominator square root of v end fraction end style
if the initial energies are in the ratio 1 : 2 then their velocity ratio is 1 : √2.
then ratio of time period is 21/4 : 1
Answered by Expert 7th January 2018, 4:47 PM
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