Electric potential in a region is varying according to relation V=frac{3 x^2}{2}-frac{y^2}{4} , wher

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2. Electric Potential and Capacitance

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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

$-6 \hat{i}+2 \hat{j}$

Solution

(b)

$V=\frac{3 x^2}{2}-\frac{y^2}{4}$

$E_x=\frac{-d V}{d x}=-3 x=-3$

$E_y=\frac{-d V}{d y}=+\frac{y}{2}=1$

$\vec{E}=-3 \hat{i}+\hat{j}$

Standard 12

Physics

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