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find velocity of charge. pls solve by using mechanical energy conservation

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Asked by ashutosharnold1998 31st March 2020, 9:11 AM
Answered by Expert
Answer:
Let 'v' be the velocity of particle.
By conservation of energy, 
 
I n i t i a l space k i n e t i c space e n e r g y space plus space I n i t i a l space p o t e n t i a l space e n e r g y space equals space F i n a l space k i n e t i c space e n e r g y space plus space F i n a l space p o t e n t i a l space e n e r g y
space K subscript i space plus space U subscript i space equals K subscript f space plus space U subscript f
therefore 0 plus fraction numerator 1 over denominator 4 pi epsilon subscript 0 end fraction open parentheses fraction numerator q subscript 3 q subscript 2 over denominator open parentheses r subscript 32 close parentheses subscript i end fraction plus fraction numerator q subscript 3 q subscript 1 over denominator open parentheses r subscript 31 close parentheses subscript i end fraction plus fraction numerator q subscript 2 q subscript 1 over denominator open parentheses r subscript 21 close parentheses subscript i end fraction close parentheses space equals space 1 half m v squared plus fraction numerator 1 over denominator 4 pi epsilon subscript 0 end fraction open parentheses fraction numerator q subscript 3 q subscript 2 over denominator open parentheses r subscript 32 close parentheses subscript f end fraction plus fraction numerator q subscript 3 q subscript 1 over denominator open parentheses r subscript 31 close parentheses subscript f end fraction plus fraction numerator q subscript 2 q subscript 1 over denominator open parentheses r subscript 21 close parentheses subscript f end fraction close parentheses
W e space c a n space s e e e space t h a t comma space
open parentheses r subscript 21 close parentheses subscript i equals space open parentheses r subscript 21 close parentheses subscript f
open parentheses 9 cross times 10 to the power of 9 close parentheses space open square brackets fraction numerator left parenthesis negative 4 right parenthesis open parentheses 2 close parentheses over denominator 5 end fraction plus fraction numerator left parenthesis negative 4 right parenthesis open parentheses 2 close parentheses over denominator 5 end fraction close square brackets cross times 10 to the power of negative 12 end exponent space equals 1 half space cross times 10 to the power of negative 3 end exponent cross times v squared space plus space open parentheses 9 cross times 10 to the power of 9 close parentheses space open square brackets fraction numerator left parenthesis negative 4 right parenthesis open parentheses 2 close parentheses over denominator 3 end fraction plus fraction numerator left parenthesis negative 4 right parenthesis open parentheses 2 close parentheses over denominator 3 end fraction close square brackets cross times 10 to the power of negative 12 end exponent space

open parentheses 9 cross times 10 to the power of negative 3 end exponent close parentheses open parentheses fraction numerator negative 16 over denominator 5 end fraction close parentheses equals 1 half space cross times 10 to the power of negative 3 end exponent cross times v squared plus open parentheses 9 cross times 10 to the power of negative 3 end exponent close parentheses open parentheses fraction numerator negative 16 over denominator 3 end fraction close parentheses
S o l v i n g space t h i s space w e space g e t comma space
v space equals space 6.2 space m divided by s
Answered by Expert 31st March 2020, 11:15 AM
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