Two particles of charges +e and +2 e are at 16 cm away from each other. Where should another charge q be placed between them, so that the system remains in equilibrium?

Step-by-step solution

For the system to be in equilibrium, we have force on charge q due to +e= force on charge q due to +2 e i.e. 1 4 ₀ e . q x^2 = 1 4 ₀ 2 e q (16-x)^2 2 x^2=(16-x)^2 aligned & 2 x^2=256+x^2-32 x & [ (a-b)^2=a^2+b^2-2 a b ] aligned x^2+32 x-256=0 (i) On solving Eq. (i), we get x=6.63 ~cm