JEE Class main Answered
how can we do it by vector method
![question image](https://images.topperlearning.com/topper/new-ate/topr_385519924931114Screenshot20230715130126.jpeg)
Asked by aaryamanmodern | 15 Jul, 2023, 13:02: PM
Force
on current carrying conductor is
.
![begin mathsize 14px style F with rightwards arrow on top end style](https://images.topperlearning.com/topper/tinymce/cache/65dc93af5d8bab1de7b0096c22f518cb.png)
![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](https://images.topperlearning.com/topper/tinymce/cache/df1e894bf043978cc91a03ef6f2cb0a5.png)
Force
is calculated as
![begin mathsize 14px style F with rightwards arrow on top subscript C A end subscript end style](https://images.topperlearning.com/topper/tinymce/cache/dc6707d1ca03ac5943bced0f197a06bf.png)
![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](https://images.topperlearning.com/topper/tinymce/cache/6db0c290ec45a98e5dc6d562c74dd4d0.png)
Force
is calculated as
![begin mathsize 14px style F with rightwards arrow on top subscript A D end subscript end style](https://images.topperlearning.com/topper/tinymce/cache/efbda5ab054243f7639db44ae331ea58.png)
![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](https://images.topperlearning.com/topper/tinymce/cache/5361f09ddd1d21184d715a3088c319b7.png)
Force
is calculated as
![begin mathsize 14px style F with rightwards arrow on top subscript C D end subscript end style](https://images.topperlearning.com/topper/tinymce/cache/34497396c23255c865905a86a5bc0cd8.png)
![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](https://images.topperlearning.com/topper/tinymce/cache/f2e55bbf2be14a12b25a802d8a15ce29.png)
Force
is calculated as
![begin mathsize 14px style F with rightwards arrow on top subscript C E end subscript end style](https://images.topperlearning.com/topper/tinymce/cache/6d542cb4f039ad67c327ed68ad7dc097.png)
![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](https://images.topperlearning.com/topper/tinymce/cache/1715e9ec5719a86e2f2a42302aa2717b.png)
Force
is calculated as
![begin mathsize 14px style F with rightwards arrow on top subscript E D end subscript end style](https://images.topperlearning.com/topper/tinymce/cache/9c8a4771cd7baa007ef5173de46966c9.png)
![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](https://images.topperlearning.com/topper/tinymce/cache/711a4a83a479fb18e150b0bd56941b8d.png)
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](https://images.topperlearning.com/topper/tinymce/cache/5686f228a1b4ab6162bfea49f9d15e4d.png)
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