• # question_answer 44) If potential (in volts) in a region is expressed as $V(x,y,z)=6xy-y+2yz,$the electric field (in N/C) at point (1,1,0) is 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) $-\left( 2\hat{i}+3\hat{j}+\hat{k} \right)$

$V(x,y,z)=6xy-y+2yz$ ${{E}_{x}}=-\frac{\partial V}{\partial x}=-6y=-6$ ${{E}_{y}}=-\frac{\partial V}{dy}=-6x+1+2z=-5$ ${{E}_{z}}=-\frac{\partial V}{\partial z}=-2y=-2$ $\vec{E}={{E}_{x}}\hat{i}+{{E}_{y}}\hat{j}+{{E}_{z}}\hat{k}$ $\vec{E}=-\left( 6\hat{i}+5\hat{j}+2\hat{k} \right)$