Physics
Magnetic-Effects-Of-Current-And-Magnetism
Easy

Question

OABC is a current carrying square loop an electron is projected from the centre of loop along its diagonal AC as shown. Unit vector in the direction of initial acceleration will be

  1. stack k with hat on top
  2. negative open parentheses fraction numerator stack i with hat on top plus stack j with hat on top over denominator square root of 2 end fraction close parentheses
  3. negative stack k with hat on top
  4. fraction numerator stack i with hat on top plus stack j with hat on top over denominator square root of 2 end fraction

The correct answer is: negative open parentheses fraction numerator stack i with hat on top plus stack j with hat on top over denominator square root of 2 end fraction close parentheses


    q = e; Let 'x' be the side length of square loop. B equals 4 fraction numerator mu subscript 0 i over denominator 2 pi left parenthesis x divided by 2 right parenthesis end fraction left square bracket 2 Sin invisible function application 45 right square bracket semicolon fraction numerator 8 square root of 2 mu subscript 0 i over denominator 4 pi x end fraction left parenthesis negative k with not stretchy hat on top right parenthesis
    Current direction will be in the opposite direction of e- motion.
    table attributes columnalign left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell not stretchy rightwards double arrow v with not stretchy rightwards arrow on top equals v cos invisible function application 45 i with not stretchy hat on top minus v cos invisible function application 45 j with not stretchy hat on top not stretchy rightwards double arrow v with rightwards arrow on top equals fraction numerator 1 over denominator square root of 2 end fraction open parentheses v subscript x i with not stretchy hat on top cross times v subscript y j with not stretchy hat on top close parentheses end cell row cell F with not stretchy rightwards arrow on top equals q left parenthesis v with not stretchy rightwards arrow on top cross times B with not stretchy rightwards arrow on top right parenthesis not stretchy rightwards double arrow a with not stretchy rightwards arrow on top equals fraction numerator negative e over denominator m end fraction left parenthesis v cross times B with not stretchy rightwards arrow on top right parenthesis equals fraction numerator negative e over denominator m end fraction open parentheses fraction numerator 1 over denominator square root of 2 end fraction left parenthesis v i with not stretchy hat on top minus v j with not stretchy hat on top right parenthesis cross times 8 square root of 2 fraction numerator mu subscript 0 i over denominator 4 pi a end fraction left parenthesis negative k with not stretchy hat on top right parenthesis close parentheses end cell end table
    table attributes columnalign left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell equals fraction numerator plus e over denominator m end fraction open parentheses fraction numerator 8 mu subscript 0 i over denominator 4 pi a end fraction close parentheses left parenthesis v left parenthesis negative j with not stretchy hat on top right parenthesis minus v i with not stretchy hat on top right parenthesis end cell row cell equals fraction numerator negative e over denominator m end fraction open parentheses fraction numerator 8 mu subscript 0 i over denominator 4 pi a end fraction close parentheses left parenthesis j with not stretchy hat on top plus i with not stretchy hat on top right parenthesis v equals e over m fraction numerator 8 mu subscript 0 i v over denominator 4 pi a end fraction left square bracket negative left parenthesis j with not stretchy hat on top plus i with not stretchy hat on top right parenthesis right square bracket end cell row cell therefore a with not stretchy hat on top equals fraction numerator a over denominator vertical line a vertical line end fraction equals fraction numerator negative left parenthesis i with not stretchy hat on top plus j with not stretchy hat on top right parenthesis over denominator square root of 2 end fraction end cell end table

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