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NEET Sample Paper NEET Sample Test Paper-78

  • question_answer
    Figure shows three spherical and equipotential surfaces A, B and C round a point charge q. The potential difference\[{{V}_{A}}-{{V}_{B}}={{V}_{B}}-{{V}_{C}}\]. If \[{{t}_{1}}\,\,and\,\,{{t}_{2}}\] be the distances between them then

    A)  \[{{t}_{1}}\,\,=\,\,{{t}_{2}}\]             

    B)  \[{{t}_{1}}\,\,>\,\,{{t}_{2}}\]

    C)  \[{{t}_{1}}\,\,<\,\,{{t}_{2}}\]             

    D)  \[{{t}_{1}}\,\,\le \,\,{{t}_{2}}\]

    Correct Answer: C

    Solution :

    \[{{V}_{A}} -{{V}_{B}} = potential difference between\] \[=\,\,\,kq\left( \frac{1}{{{r}_{A}}}-\frac{1}{{{r}_{B}}} \right)\,\,=\,\,kq\left( \frac{{{r}_{B}}-{{r}_{A}}}{{{r}_{A}}{{r}_{B}}} \right)\] \[=\,\,\,\frac{kq{{t}_{1}}}{{{r}_{A}}{{r}_{B}}}\] \[\Rightarrow \,\,\,\,\,\,\,{{t}_{1}}=\frac{({{V}_{A}}-{{V}_{B}}){{r}_{A}}{{r}_{B}}}{kq}\] \[\Rightarrow \,\,\,\,\,\,\,\,\,\,{{t}_{1}}\propto {{r}_{A}}{{r}_{B}}\] Similarly \[{{t}_{2}}\propto {{r}_{B}}{{r}_{C}}\] Since \[{{r}_{A}}<{{r}_{B}}<{{r}_{C}}\,\,\,\Rightarrow \,\,\,{{r}_{A}}{{r}_{B}}<{{r}_{B}}{{r}_{C}}\] \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{{t}_{1}}<{{t}_{2}}\]


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