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NEET Sample Paper NEET Sample Test Paper-8

  • question_answer
    The electric potential at a point (x, y) is given by \[V=Kxy\]. The electric field intensity at a distance r from the origin varies as:

    A)  \[{{r}^{2}}\]                                              

    B)  \[r\]

    C)  2r                               

    D)  \[2{{r}^{2}}\]

    Correct Answer: B

    Solution :

    As, \[V'=-KXY\]represents the case of dependence of three variables simultaneously. \[\Rightarrow \]               \[\varepsilon =\left[ \frac{\partial V}{\partial X}1+\frac{\partial V}{\partial X}j \right]=K(Yi+Xj)\] \[\Rightarrow \]               \[\varepsilon =\sqrt{\varepsilon _{X}^{2}+\varepsilon _{Y}^{2}}\]                 \[\sqrt{{{({{K}_{Y}})}^{2}}+{{({{K}_{X}})}^{2}}}=Kr\] i.e, \[\varepsilon \propto r\]  (as,  \[r=Xi+Yj\])


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