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Q no 5
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Asked by manasvijha | 25 Mar, 2019, 07:41: AM
answered-by-expert Expert Answer
cyclotron frequency ν which is same as frequency of electircal field is given by,   
 
begin mathsize 12px style nu space equals space fraction numerator B space e over denominator 2 πm end fraction space space space space space o r space space space space B space equals fraction numerator 2 πm space straight nu over denominator e end fraction space end style  .........................(1)
Kinetic energy = (1/2)mv2................................(2)
 
in cyclotron,  v/R = Be/m    ..........................(3)
 
where v is  linear speed  and R is radius of circular path.
 
if we substitute v from (3) in eqn.(2), we get kinetic energy = begin mathsize 12px style 1 half m fraction numerator B squared e squared over denominator m squared end fraction R squared end style  ......................(4)
by substituting Be/m from eqn.(1) in eqn.(4), we get kinetic energy = begin mathsize 12px style 1 half m space 4 straight pi squared space straight nu squared space straight R squared space equals space 2 space straight m space straight pi squared space straight nu squared space straight R squared end style
Answered by Thiyagarajan K | 25 Mar, 2019, 14:57: PM

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