Question

The electric potential $V$ at any point (x,y,z) all in meters in space is given by $V=4x^2$ volt. The electric field at the point (1,0,2) in volt/meter is:

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

Answer 1

The correct option is A 8 along negative X-axis

$E_x=-\frac{dV}{dx}=-\frac{d\left(4x^2\right)}{dx}=-8x$
${\left(E\right)}_{1,0,2}=-8\times 1=-8\frac{V}{m}$
$\overrightarrow{E}=E_x\hat{i}$
$\overrightarrow{E}=-8\hat{i}\frac{V}{m}$