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If the electric potential is given by \(\chi=cxy\), calculate the electric field.

Discussion:

$$ E_x=-\frac{\partial\chi}{\partial x}=-cy$$ $$ E_y=\frac{\partial \chi}{\partial y}=-cx$$ Hence electric field $$ \vec{E}=-c(y\hat{i}+x\hat{j})$$

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This really is incredible as well as what I’d been searching for. Thank you for this.