## Surface Integral Considered as a Potential Function 2

To find\[\int_s \frac{\alpha}{\sqrt{(x-x_0)^2 +(Y-Y_0)^2 +(Z-Z_0)^2}}dS\]

, the surface being a sphere not containing the point \[(x_0 , y_0 , z_0)\]

we can consider the integral as a potential function. As long as the distribution of charge over the surface is spherically symmetrical, we can treat the charge distribution over the surface as a point charge at the center of the sphere.Continuing the potential analygy, take the charge per unit area as 1. If the radius of the sphere is

\[r\]

then the charge equals the surface area equals \[4 \pi r^2\]

.\[\int_s \frac{\alpha}{\sqrt{(x-x_0)^2 +(Y-Y_0)^2 +(Z-Z_0)^2)}}dS = \frac{4 \pi r^2}{\sqrt{x_0^2 +y_0^2+z_0^2}} \]