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.

Consider a spherical surface of radius 4 m cenred at the origin. Point

1.	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.
Answer» 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`.

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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.

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