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the figure is given and at the bottom is its question.

Asked by Arushi Juyal 12th December 2017, 8:34 PM
Answered by Expert
Answer:
Refer the figure for the following calculation.
 
we should find angle α to get the deflected path length in field region
 
begin mathsize 12px style open parentheses R minus h close parentheses squared space plus space fraction numerator m squared v squared over denominator 2 q B space end fraction space equals space R squared space................... left parenthesis 1 right parenthesis  R a d i u s space R space i s space o b t a i n e d space f r o m space B q v space equals space fraction numerator m v squared over denominator R end fraction R space equals space fraction numerator m v over denominator B q end fraction B y space s u b s t i t u t i n g space f o r space R space i n space left parenthesis 1 right parenthesis comma space w e space g e t space left parenthesis R minus h right parenthesis space equals fraction numerator m v over denominator square root of 2 q B end fraction end style
Hence α = 45º and deflected path length begin mathsize 12px style equals fraction numerator pi R over denominator 4 end fraction equals space fraction numerator pi m v over denominator 4 q B end fraction end style
It can be seen from figure angle β = α = 45º. Hence begin mathsize 12px style d space equals space fraction numerator m v over denominator q B end fraction end style
Total path length just before collision is begin mathsize 12px style fraction numerator pi m v over denominator 4 q B end fraction plus fraction numerator m v over denominator q B end fraction space equals space fraction numerator m v over denominator 4 q B end fraction open parentheses pi plus 4 close parentheses end style
since the collision is elastic, we will get same path length after collision
 
Hence overall path length is begin mathsize 12px style fraction numerator m v over denominator 2 q B end fraction open parentheses pi plus 4 close parentheses end style
to get time t we divide pathlength by velocity v, then begin mathsize 12px style t space equals space fraction numerator m over denominator 2 q B end fraction open parentheses pi plus 4 close parentheses end style 
Answered by Expert 12th December 2017, 11:08 PM
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