What will be the answer for this question?

Asked by dineshchem108 | 29th May, 2019, 11:12: PM

Expert Answer:

begin mathsize 14px style L e t space m a g n e t i c space f i e l d space v e c t o r space B with rightwards arrow on top space equals space a space i with hat on top space plus space b space j with hat on top space plus space c space k with hat on top space
I f space v e l c o i t y space v e c t o r space v with rightwards arrow on top equals space 1 i with hat on top space comma space space t h e n space f o r c e space q open parentheses space v with rightwards arrow on top space cross times space B with rightwards arrow on top space close parentheses space space equals space q open vertical bar table row cell i with hat on top end cell cell j with hat on top end cell cell k with hat on top end cell row 1 0 0 row a b c end table close vertical bar space equals space q open parentheses negative c space j with hat on top space plus space b space k with hat on top space close parentheses space space.......... left parenthesis 1 right parenthesis end style 

But for thae above velocity vector, given force is  begin mathsize 14px style F with rightwards arrow on top space equals space q open parentheses negative 1 space j with hat on top space plus space 1 space k with hat on top space close parentheses end style ..................................(2)
Hence by comparing eqn.(1) and (2),   we get,   b = c = 1;
 
begin mathsize 14px style I f space v e l c o i t y space v e c t o r space v with rightwards arrow on top equals space 1 j with hat on top space comma space space t h e n space f o r c e space q open parentheses space v with rightwards arrow on top space cross times space B with rightwards arrow on top space close parentheses space space equals space q open vertical bar table row cell i with hat on top end cell cell j with hat on top end cell cell k with hat on top end cell row 0 1 0 row a b c end table close vertical bar space equals space q open parentheses c space i with hat on top space minus space a space k with hat on top space close parentheses space space.......... left parenthesis 3 right parenthesis end style
But for thae above velocity vector, given force is  begin mathsize 14px style F with rightwards arrow on top space equals space q open parentheses 1 space i with hat on top space minus space 1 space k with hat on top space close parentheses end style ..................................(4)
Hence by comparing eqn.(3) and (4), we get ,   c = a = 1 ;
 
Hence magnetic field vector is given by, begin mathsize 14px style B with rightwards arrow on top space equals space i with hat on top space plus space j with hat on top space plus space k with hat on top space end style

Answered by Thiyagarajan K | 30th May, 2019, 02:52: PM

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