Question

The electric potential $V$ at any point $(x,y,z)$, all in meters in space is given by $V=4x^2\text{volt}$. The electric field at the point $(1,0,2)$ in volt/meter is :
[NEET- 2011 (Mains)]

• A. $16$ along negative x-axis.
• B. $16$ along positive x-axis.
• C. $8$ along positive x-axis.
• D. $8$ along negative x-axis.

Answer 1

The correct option is D $8$ along negative x-axis.

The electric field along x-axis is given by,

$\overrightarrow{E}=-\frac{dV}{dx}\hat{i}$

$=-\frac{d\left(4x^2\right)}{dx}$

$=-8x\hat{i}\text{volt/meter}$
${\overrightarrow{E}}_{(1,0,2)}=-8\hat{i}\text{V/m}$

Hence, $\left(D\right)$ is the correct answer.