Three charges ' +3 q ' , ' Q ' and ' +q ' are placed in a straight line of length ' ' at points at distances 0, 2 and respectively. The value of Q in order to have the net force on +q to be zero, Q=x q . The value of x is

Step-by-step solution

Key Concept: Coulomb's Law and Principle of Superposition. The electrostatic force between two point charges is governed by Coulomb's Law: F = k |q₁ q₂| r^2 , where k = 1 4 ₀ and r is the separation distance. The net force on a charge is the vector sum of the individual forces from all other charges. Let q₁ = +3q at x = 0 , q₂ = Q at x = 2 , and q₃ = +q at x = . The net force on q₃ must be zero, requiring the forces from q₁ and q₂ to balance. The repulsive force from q₁ on q₃ is F₁ = k (3q)(q) ^2 = 3kq^2 ^2 , direc