Two electric charges `q_(1) = q and q_(2) = -2q` are placed at a distance l = 6a apart. Find the locus of points in the plane of the charges where the field potential is zero

Explanation

Direct the coordinate axes as shown in Fig. 24.2. Let M be one of the points where the potential is zero:
`varphi=varphi_(1)=(q)/(4pi eposi_(0)r_(1))-(2q)/(4pi epsi_(0)r_(2))=0`
Hence `r_(2)=2r_(1)`
Substituting `r_(1)= sqrt((3a-x)^(2)+y^(2)) and r_(2)= sqrt((3a+x)^(2)+y^(2))`, we obtain after some manipulations
`(x-5a)^(2)+y^(2)=16a^(2)`
This is the equation of a circle of radius 4a, with centre at (5a, 0)