A) \[10a\left( y\widehat{i}+x\widehat{j} \right)~\]
B) \[-10a\left( y\widehat{i}\text{ }+x\widehat{j} \right)\]
C) \[-a\left( y\widehat{i}+x\widehat{j} \right)\]
D) \[-10a\left( x\widehat{i}+y\widehat{k} \right)\]
Correct Answer: B
Solution :
\[{{E}_{x}}\,=\,-\frac{\partial V}{\partial x}\,\,\widehat{i}\,\,=\,\,-\frac{\partial }{\partial x}\,(10axy)\,\,\widehat{i}\,\,=\,\,-10ay\,\widehat{i}\] \[{{E}_{y}}\,=\,-\frac{-\partial V}{\partial y}\,\,\widehat{j}\,\,=\,\,-\frac{\partial }{\partial y}\,(10axy)\,\,\widehat{i}\,\,=\,\,-10ax\,\widehat{j}\] \[E=-10a\left( y\widehat{i}+x\widehat{j} \right)\]
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