Consider a spherical surface of radius 4 m cenred at the origin. Point charges +q and - 2q are fixed at points A( 2 m, 0,0) and B( 8 m, 0, 0), respectively. Show that every point on the shperical surface is at zero potential.

Explanation

let `P(x,y,z)` be any pont on the sphere. From the property of theh sphere,
`x^2+y^2+z^2-(4)^2=16`………….i
Further `PA=sqrt((x-2)^2+y^2+z^2)`………..ii
and `PB=sqrt((x-8)^2+y^2+z^2)`……….iii
`V_P=1/(4piepsilon_0)[q/(PA)-(2q)/(PB)]`
`=1/(4piepsilon_0)[q/sqrt((x-2)^2+y^2+z^2)-(2q)/sqrt((x-8)^2-y^2=z^2)]`
`=1/(4piepsilon_0)[q/sqrt(x^2+y^2=z^2+4-4x)-(2q)/sqrt((x^2+y^2+z^2+64-16x))]`
`=1/(4piepsilon_0)[q/sqrt((16+4-4x))-(2q)/sqrt((16+64-16x))]`
`=0`