A) \[V=-xy+\] constant
B) \[V=-(x+y)+\] constant
C) \[V=-({{x}^{2}}+{{y}^{2}})+\] constant
D) \[V=\] constant
Correct Answer: A
Solution :
\[dV=\overrightarrow{E}.\overrightarrow{dr}\] \[=-(y\widehat{i}+x\widehat{j}).(dx\widehat{i}+dy\widehat{j}+dz\widehat{k})\] \[=-ydx-xdy=-d(xy)\] [because using product rule of differential operator\[d(xy)=dx\times y+x\times dy]\] on integration we get \[V=-xy+\]constant.
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