Question

In a uniform electric field, the potential is $10\text{V}$ at the origin of coordinate system, and $8\text{V}$ at each of the points $(1,0,0),(0,1,0)$ and $(0,0,1)$.The potential at the point $(1,1,1)$ will be (in Volt)

Answer 1

$E_x=-\frac{\partial V}{\partial x}=-\frac{8-10}{1}=2\Rightarrow V_O-V_A=\mathrm{2.....}\left(1\right)$

$E_y=-\frac{\partial V}{\partial y}=-\frac{8-10}{1}=2\Rightarrow V_A-V_B=\mathrm{2.....}\left(2\right)$

$E_z=-\frac{\partial V}{\partial z}=-\frac{8-10}{1}=2\Rightarrow V_B-V_C=\mathrm{2.....}\left(3\right)$

Adding $\left(1\right),\left(2\right),\left(3\right)$
$V_O-V_C=6$
$10-V_C=6$
$V_C=4\text{Volt}$