Question

The electric potential at a space point $P \, \left(x , \, y , \, z\right)$ is given as $V=x^{2}+y^{2}+z^{2}$ . The modulus of the electric field at that point is proportional to

• A. $V^{\frac{1}{2}}$
• B. $V$
• C. $V^{\frac{3}{2}}$
• D. $V^{2}$

Answer 1

Answer: (A)

$E_{x}=-2x, \, E_{y}=-2$ and $E_{z}=-2z$
$\left|E\right|=\sqrt{E_{x}^{2} + E_{y}^{2} + E_{z}^{2}}$
$=\sqrt{4 x^{2} + 4 y^{2} + 4 z^{2}}$
$=2\sqrt{x^{2} + y^{2} + z^{2}}=2\sqrt{V}$