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how can we do it by vector method
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Asked by aaryamanmodern | 15 Jul, 2023, 01:02: PM
answered-by-expert Expert Answer
Force begin mathsize 14px style F with rightwards arrow on top end styleon current carrying conductor is begin mathsize 14px style F with rightwards arrow on top space equals space i l with rightwards arrow on top cross times B with rightwards arrow on top end style .
Force begin mathsize 14px style F with rightwards arrow on top subscript C A end subscript end style is calculated as 
begin mathsize 14px style F with rightwards arrow on top subscript C A end subscript space equals left parenthesis 2 space cross times 4 right parenthesis space open vertical bar table row cell i with hat on top end cell cell j with hat on top end cell k row cell cos 60 end cell cell sin 60 end cell 0 row 0 0 cell negative 1 end cell end table close vertical bar space equals space 8 left parenthesis negative sin 60 space i with hat on top plus space cos 60 space j with hat on top right parenthesis space N end style
 
Force begin mathsize 14px style F with rightwards arrow on top subscript A D end subscript end style is calculated as 
begin mathsize 14px style F with rightwards arrow on top subscript A D end subscript space equals left parenthesis 2 space cross times 4 right parenthesis space open vertical bar table row cell i with hat on top end cell cell j with hat on top end cell k row cell cos 60 end cell cell negative sin 60 end cell 0 row 0 0 cell negative 1 end cell end table close vertical bar space equals space 8 left parenthesis sin 60 space i with hat on top plus space cos 60 space j with hat on top right parenthesis space N end style
 
Force begin mathsize 14px style F with rightwards arrow on top subscript C D end subscript end style is calculated as 
begin mathsize 14px style F with rightwards arrow on top subscript C D end subscript space equals left parenthesis 2 space cross times 4 right parenthesis space open vertical bar table row cell i with hat on top end cell cell j with hat on top end cell k row 1 0 0 row 0 0 cell negative 1 end cell end table close vertical bar space equals space 8 space j with hat on top space space N end style
 
Force begin mathsize 14px style F with rightwards arrow on top subscript C E end subscript end style is calculated as 
begin mathsize 14px style F with rightwards arrow on top subscript C E end subscript space equals left parenthesis 2 space cross times 4 right parenthesis space open vertical bar table row cell i with hat on top end cell cell j with hat on top end cell k row cell cos 60 end cell cell negative sin 60 end cell 0 row 0 0 cell negative 1 end cell end table close vertical bar space equals space 8 left parenthesis sin 60 space i with hat on top plus space cos 60 space j with hat on top right parenthesis space N end style
 
Force begin mathsize 14px style F with rightwards arrow on top subscript E D end subscript end style is calculated as 
begin mathsize 14px style F with rightwards arrow on top subscript E D end subscript space equals left parenthesis 2 space cross times 4 right parenthesis space open vertical bar table row cell i with hat on top end cell cell j with hat on top end cell k row cell cos 60 end cell cell sin 60 end cell 0 row 0 0 cell negative 1 end cell end table close vertical bar space equals space 8 left parenthesis negative sin 60 space i with hat on top plus space cos 60 space j with hat on top right parenthesis space N end style

If we add all forces , then we get
 
begin mathsize 14px style F with rightwards arrow on top subscript C A end subscript space plus space F with rightwards arrow on top subscript A D end subscript space plus space F with rightwards arrow on top subscript C D end subscript space plus space F with rightwards arrow on top subscript C E end subscript space plus space F with rightwards arrow on top subscript E D space space end subscript equals space left parenthesis space 24 space N space right parenthesis space j with hat on top space end style


Answered by Thiyagarajan K | 15 Jul, 2023, 08:44: PM
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