Two point charges `+Q` each have been placed at the positions `(-a//2,0,0) and (a//2,0,0).` The locus of the points where `-Q` charge can be placed such that total electrostatic potential energy of the system can become equal to zero, can be represented by which of the following equations?

Explanation

Let the requried plane lies at a distance x from the origin as shown in figure.
ltbgt The potential at the point P due to charges is given by
`(1)/(4piepsi_(0))(1)/([(x+d//2)^(2)+h^(2)]^(1//2))-(1)/(4piepsi_0)(1)/([(x-d//2)^(2)+h^(2)]^(1//2))`
If net electric potential is zero, then.
`(1)/([(x+d//2)^(2)+h^(2)]^(1//2))=(1)/([(x-d//2)+h^(2)]^(1//2))`
or `(x-d//2)^(2)+h^(2)=(x+d//2)^(2)+h^(2)`
`impliesx^(2)-dx+d^(2)//4=x^(2)+dx+d^(2)//4`
or `2dx=0impliesx=0`
The equation of the required plane is x=0 i.e., y-z plane.