Two point charges of magnitude `+q and -q` are placed at `(-d//2,0,0) and (d//2,0,0)` are respectively. Find the equation of the euipotential surface where the potential is zero.

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.