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JCECE Engineering JCECE Engineering Solved Paper-2011

  • question_answer
    The potential field of an electric field \[\mathbf{E}=(y\mathbf{i}+x\mathbf{j})\] is

    A) \[V=-(x+y)+\]constant

    B) \[V=\]constant

    C)  \[V=-({{x}^{2}}+{{y}^{2}})+\]constant

    D)  \[V=-xy+\]constant

    Correct Answer: D

    Solution :

    We know that                 \[dV=-\mathbf{E}\cdot \mathbf{dr}\]                 \[=-(y\mathbf{i}+x\mathbf{j})\cdot (\mathbf{i}dx+\mathbf{j}dy+\mathbf{k}dz)\]                 \[=-(ydx+nxdy)\]         \[dV=-d(xy)\] Integrating both sides, we get \[V=-xy+\]constant


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