Question

Electric potential in a region is varying according to the relation $V=\frac{3 x^{2}}{2}-\frac{y^{2}}{4}$, where $x$ and $y$ are in metre and $V$ is in volt. Electric field intensity (in $N / C )$ at a point $(1 \,m , 2\, m )$ is

• A. $3 \hat{i}-\hat{j}$
• B. $-3 \hat{i}+\hat{j}$
• C. $6 \hat{i}-2 \hat{j}$
• D. $-6 \hat{i}+2 \hat{j}$

Answer 1

Answer: (B)

$V=\frac{3 x^{2}}{2}-\frac{y^{2}}{4}$
$E_{x}=\frac{-d V}{d x}=-3 x=-3$
$E_{y}=\frac{-d V}{d y}=+\frac{y}{2}=1$
$\vec{E}=-3 \hat{i}+\hat{j}$