JEE Main & Advanced Physics Mathematical Tools, Units & Dimensions Question Bank Self Evaluation Test - Physical World, Units and Measurements

  • question_answer
    The electric field is given by \[\overset{\to }{\mathop{E}}\,=\frac{A}{{{x}^{3}}}\hat{i}+By\hat{j}+C{{z}^{2}}\hat{k}\].The SI units of A, B and C are respectively: [where x, y and z are in m]

    A) \[\frac{N-{{m}^{3}}}{{{x}^{3}}},V/{{m}^{2}},\,N/{{m}^{2}}-C\]

    B)  \[V-{{m}^{2}},V/m,\,N/{{m}^{2}}-C\]

    C)  \[V/{{m}^{2}},V/m,\,N-C/{{m}^{2}}\]

    D)  \[V/m,\,N-{{m}^{3}}/C,\,N-C/m\]

    Correct Answer: A

    Solution :

    [a] Unit of Electric field \[(E)=(N/C)=(V/m)\] So, unit of \[A=E\times {{x}^{3}}=\frac{N-{{m}^{3}}}{C}=(V-{{m}^{2}})\] Unit of \[B=E/y=\frac{N}{mc}=\left( \frac{V}{{{m}^{2}}} \right)\] Unit of \[C=E/{{z}^{2}}=\frac{N}{{{m}^{2}}c}=\left( \frac{V}{{{m}^{3}}} \right)\]


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