Question

The charge $Q$ and $-2Q$ are placed at some distance. What is the locus of point in the plane of the charges where the potential is zero?

1. Parabola

2. Circle

3. Ellipse

Write your answer in terms 1,2 and 3 only.

Answer 1

Let (h,k) be the point where potential is zero.

$V=\frac{K(-2Q)}{\sqrt{R^2+(h-d{)}^2}}+\frac{K\left(Q\right)}{\sqrt{h^2+R^2}}$

As it is given that potential is zero so,

=> $\frac{2}{\sqrt{R^2+(h-d{)}^2}}=\frac{1}{\sqrt{R^2+h^2}}$

=> $4(R^2+h^2)=R^2+h^2+d^2-2hd$

=> $3R^2+3h^2-d^2+2hd=0$

=> $R^2+h^2-\frac{d^2}{3}+\frac{2}{3}hd=0$

This is the equation of circle.