You are working for the summer at a research laboratory. Your research director has devised a scheme for holding small charged particles at fixed positions. The scheme is shown in the figure below.

 

An insulating cylinder of radius a and length L » a is positively charged and carries a uniform volume charge density p. A very thin tunnel is drilled through a diameter of the cylinder and two small spheres

with charge q are placed in the tunnel. These spheres are represented by the blue dots in the figure. They find equilibrium positions at a distance of r on opposite sides of the axis of the cylinder. Your

research director has had great success with this scheme.

(a) Determine the specific value of r at which equilibrium exists. 

   

Sp x