A charge Q is divided into two parts and placed at a given distance so that the force between them is maximum. The value of each charge is:

Step-by-step solution

Let the two parts of the charge Q be q and Q - q . The electrostatic force between them when placed at a given distance r is given by Coulomb's law: F = 1 4 ₀ q(Q - q) r^2 For the force to be maximum, the first derivative of F with respect to q must be zero: dF dq = 0 1 4 ₀ r^2 d dq (qQ - q^2) = 0 Since 1 4 ₀ r^2 is a non-zero constant, we get: d dq (qQ - q^2) = 0 Q - 2q = 0 2q = Q q = Q 2 The other part of the charge is Q - q = Q - Q 2 = Q 2 . Thus, the value of each charge is Q 2 and Q 2 .