Two charges Q and -2Q are placed at (3a,0) and (-3a,0). Find the locus of the points where the potential due these two is charges same.

Electric potential due to a point charge = 

The electrical potential due to point charges

so let (x,y) be th e locus of point net potential at point is zero

V(x,y,z)= 0

[Q / k.((x-3a)² + y² )^1/2 ] + [ -2Q / k.((x+3a)² + y² )^1/2 ] = 0

4*((x-3a)² + y² )^1/2 - ((x+3a)² + y² )^1/2 = 0

The locus is a circle : x² + y² +9a² -10.a.x = 0

it's got to be an equipotential surface.

1. for pt charges the equipotential surfaces are concentric circles.

consider a unit charge q at a distance x from one of the charges ,now use potential formula KQq/r2 solve