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

Asked by ashutosharnold1998 | 31 Mar, 2020, 09:11: AM

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 Shiwani Sawant | 31 Mar, 2020, 11:15: AM

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