Sphere A, with a charge of +64 C, is positioned at the origin. A second sphere, B, with a charge of -16 C, is placed at +1.00 on the x-axis. Where must a third sphere, C, of charge +12 C, be placed so that there is no net force on it?

Question

Sphere A, with a charge of +64 C, is positioned at the origin. A second sphere, B, with a charge of     -16 C, is placed at +1.00 on the x-axis. Where must a third sphere, C, of charge +12 C, be placed so that there is no net force on it?

Elena · Answer

F=0 if E = 0
The point is located to the right from the second charge at the distance ‘x’ =>
kq₁/(X+x)² =kq₂/x²
X=1
64/(1+x)² = 16/ x²,
3x²-2x-1 =0 ,
x={2±sqrt(4+12)}/6.
x₁=1, x₂=-1/3 (※)
Ans: Coordinate of the point is X+x =1+1 =2