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JEE Main & Advanced Physics Electrostatics & Capacitance Question Bank Self Evaluation Test - Electrostatic Potential and Capacitance

  • question_answer
    The electric potential at a point (x, y) in the \[x\text{ }\text{ }y\] plane is given by \[V=-kxy.\] The field intensity at a distance r from the origin varies as

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

    B) \[r\]

    C) \[\frac{1}{r}\]

    D) \[\frac{1}{{{r}^{2}}}\]

    Correct Answer: B

    Solution :

    [b] \[\vec{E}=\frac{\partial v}{\partial x}\hat{i}+\frac{\partial v}{\partial y}\hat{j}\] \[\therefore |\vec{E}|=k\left( \sqrt{{{x}^{2}}+{{y}^{2}}} \right)=kr\] Given \[v=-kxy\text{        }E\propto r\] \[\therefore \vec{E}=ky\hat{i}+ky\hat{j}\]


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