Electric potential in a region is varying according to the relation V=(3 x2/2)-(y2/4), 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

Question

Electric potential in a region is varying according to the relation V=(3 x2/2)-(y2/4), 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 hati- hatj (B) -3 hati+ hatj (C) 6 hati-2 hatj (D) -6 hati+2 hatj

Tardigrade Admin · Accepted Answer

V=(3 x2/2)-(y2/4) Ex=(-d V/d x)=-3 x=-3 Ey=(-d V/d y)=+(y/2)=1 vecE=-3 hati+ hatj

Q. 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

$3 \hat{i} - \hat{j}$

$- 3 \hat{i} + \hat{j}$

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

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

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

Q. Electric potential in a region is varying according to the relation V=23x2​−4y2​, where x and y are in metre and V is in volt. Electric field intensity (in N/C) at a point (1m,2m) is

3i^−j^​

−3i^+j^​

6i^−2j^​

−6i^+2j^​