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

If `P (x , y,z)` is any point on the sphere,
`x^2 + y^2 + z^2 = (4)^2 = 16`
Also
`PA = sqrt ((x - 2)^2 + y^2 + z^2)`
=`sqrt((x^2 + y^2 + z^2) + 4 - 4 x ) = sqrt(20 - 4 x)`
And
`PB = sqrt ((x - 8)^2 + y^2 + z^2)`
=`sqrt((x ^2 + y^2 + z^2)+ 64 - 16 x)`
=`sqrt(80 - 16 x) = 2 sqrt(20 - 4 x)`
Thus
`V_P = k_e[q/(PA) - (2 q)/(PB)]= k_e [q/(sqrt (20 - 4 x))- (2 q)/(2 sqrt (20 - 4 x))] = 0`.