Two charges `-2Q` abd `Q` are located at the points with coordinates `(-3a, 0)` and `(+3a, 0)` respectively in the x-y plane. (i) Show that all points in the x-y plane where the electric potential due to the charges is zero, on a circle. Find its radius and the location of its centre (ii) Give the expression V(x) at a general point on the x-axis and sketch the function V(x) on the whole x-axis. (iii) If a particle of charge +q starts from rest at the centre of the circle, shown by a short quantitative argument that the particle eventually crosses the circule. Find its speed when it does so.

Answer

(a) Radius 4a, cantre at `(5a,0)`
(b). `V=(Q)/(4piepsilon_(0))[(1)/(|(x-3a)|)-(2)/(|(x+3a)|)]`
(c). At `x=9a` where `V=0`, the charged particle eventually crosses the circle
`v=sqrt((Qq)/(8piepsilon_(0)ma))`