A) \[-\left( 6\hat{i}+9\hat{j}+\hat{k} \right)\]
B) \[-\left( 3\hat{i}+5\hat{j}+3\hat{k} \right)\]
C) \[-\left( 6\hat{i}+5\hat{j}+2\hat{k} \right)\]
D) \[-\left( 2\hat{i}+3\hat{j}+\hat{k} \right)\]
Correct Answer: C
Solution :
\[V(x,y,z)=6xy-y+2yz\] \[{{E}_{x}}=-\frac{\partial V}{\partial x}=-6y=-6\] \[{{E}_{y}}=-\frac{\partial V}{dy}=-6x+1+2z=-5\] \[{{E}_{z}}=-\frac{\partial V}{\partial z}=-2y=-2\] \[\vec{E}={{E}_{x}}\hat{i}+{{E}_{y}}\hat{j}+{{E}_{z}}\hat{k}\] \[\vec{E}=-\left( 6\hat{i}+5\hat{j}+2\hat{k} \right)\]
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