Question

The potential of the electric field produced by point charge at any point $(x,y,z)$ is given by $V=3x^2+5$, where $x$, $y$ are in metres and $V$ is in volts. The intensity of the electric field at $(-2,1,0)$ is:

• A. $+17V{m}^{-1}$
• B. $-17V{m}^{-1}$
• C. $+12V{m}^{-1}$
• D. $-12V{m}^{-1}$

Answer 1

The correct option is C $+12V{m}^{-1}$

Potential $\left(V\right)=3x^2+5$

Intensity of the electric field, $E=\frac{-dV}{dx}$

$\therefore$ $E=-\frac{d(3x^2+5)}{dx}=-6x$
$\therefore E{|}_{x=-2}$ $=-6(-2)=12V/m$