Two small identical conducting balls each of radius r and mass m are placed on a frictionless horizontal table, connected by a light conducting spring of force constant K and un-deformed length L (L gtgt r). A uniform electric field of strength E is switched on in horizontal direction parallel to the spring. (a) How much charge will appear on the two balls when they are at separation L. (b) The system fails to oscillate if K lt `K_0`. Find `K_0`. (c) Assuming `K = 2K_0`, find the time period of oscillation after the electric field is switched on.

Answer

(a). `+-2pi in_(0)ErL`
(b). `k_(0)=2pi in_(0)rE^(2)`
(c) `(1)/(E)=sqrt((pim)/(in_(0)r))`