JEE Main & Advanced JEE Main Paper (Held On 25 April 2013)

  • question_answer
                    A metal sample carrying a current along X-axis with density \[{{J}_{x}}\]is subjected to a magnetic filed\[{{\operatorname{B}}_{z}}\](along-z axis). The electric field \[{{\operatorname{E}}_{y}}\]developed along Y-axis is directly proportional to \[{{\operatorname{J}}_{x}}\]as well as \[{{B}_{z}}\]. The constant of proportionality as has SI unit.     JEE Main Online Paper ( Held On 25  April 2013 )

    A)                 \[\frac{{{m}^{2}}}{A}\]                                 

    B)                                        \[\frac{{{m}^{3}}}{A\operatorname{s}}\]

    C)                                        \[\frac{{{m}^{2}}}{A\operatorname{s}}\]                                            

    D)                                        \[\frac{{{\operatorname{A}}_{\operatorname{S}}}}{{{\operatorname{m}}^{3}}}\]

    Correct Answer: B

    Solution :

                     According to question \[{{E}_{y}}\propto {{J}_{x}}{{B}_{z}}\] \[\therefore \]Constant of proportionality \[K=\frac{{{E}_{y}}}{{{B}_{z}}{{J}_{x}}}=\frac{C}{{{J}_{x}}}=\frac{{{m}^{3}}}{As}\] [As\[\frac{E}{B}=C\](speed of light) and \[J=\frac{I}{Area}\]]


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