Question

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. $-\left(2\hat{i}+3\hat{j}+\hat{k}\right)$

Answer 1

The correct option is C $-\left(6\hat{i}+5\hat{j}+2\hat{k}\right)$

$\overrightarrow{E}=-(\frac{\partial V}{\partial x}\hat{i}+\frac{\partial V}{\partial y}\hat{j}+\frac{\partial V}{\partial z}\hat{k})$
$=-(6y\hat{i}+(6x-1+z)\hat{j}+2y\hat{k})$

At point (1,1,0) $\therefore \overrightarrow{E}=-(6\times 1\hat{i}+(6\times 1-1+0)\hat{j}+2\times 1\hat{k})$
$=-(6\hat{i}+5\hat{j}+2\hat{k})$