Question

Electric field vector in a region is given by $E =(3 \hat{ i }+4 y \hat{ j }) V - m ^{-1}$. The potential at the origin is zero. Then, the potential at a point $(2,1) m$ is

• A. 7 V
• B. 8 V
• C. -8 V
• D. -7 V

Answer 1

Answer: (C)

As, $E=\frac{-\partial V_{x}}{\partial x} \hat{ i }+\frac{-\partial V_{y}}{\partial y} \hat{ j }$
$\frac{-\partial V_{x}}{\partial x} =3$ and $\frac{-\partial V_{y}}{\partial y}=4 y$
$\Rightarrow V_{x} =-3 x $ and $V_{y}=-2 y^{2}$
So, $V=$ potential function
$=\left(3 x+2 y^{2}\right)$
Potential at point $(2,1)$ is
$V=-\left(3 \times 2+2 \times 1^{2}\right)=-8\, V$