A horizontal circular groove is made in a wooden board. Two positive charges (q each) are placed in the groove at a separation of `90^(@)` (see figure). Where shall we place (in the groove) a third charge and what shall be its magnitude such that all three of them remain at rest after they are released. Answer for two cases: (a) When the third charge is positive. (b) When the third charge is negative. Neglect friction and assume that the groove is very thin just wide enough to accommodate the particles. [Take `sin22.5^(@)=0.38,cos22.5^(@)=0.92]`

Answer

(a). `Q=+3.14q`
(b). `Q=-0.22q`