A charge q is placed at the centre of the line joining two equal charges Q. If the system of the three charges is in equilibrium, then what will be the value of q?

Explanation

Suppose the three charges be placed as shown in the figure.
` (##ARH_CC_CHSE_ODI_PHY_XII_C01_E04_061_S01.png" width="80%">
As, the net force on q is zero , so it is already in equilibrium . For equilibrium of other two charges , the net force on each charge must be zero,
Total force on charge at B is
` (1)/(4piin_0) . (Qq)/(x^(2)) + (1)/(4piin_0) . (Q .Q)/((2x)^(2)) =0`
or ` " " (1)/(4piin_0) = (1)/(4 piin_0) . (Q^(2))/(4x^(2)) rArr q= - (Q)/(4)`