Three equal charges are placed on the three corners of a square as shown below. If the magnitude of force between ' q ₁ ' and ' q ₂ ' is ' F ₁₂ ' and that between ' q ₁ ^ and ' q ₃ ^ is F ₁₃ , then the ratio of F ₁₃ to F ₁₂ is

Step-by-step solution

The ratio of the electrostatic forces between charges is determined using Coulomb’s Law, F = k |q₁ q₂| r^2 , with all charges equal to q . Force between adjacent charges: For q₁ and q₂ on adjacent corners of the square, the separation is r₁₂ = a , giving F₁₂ = kq^2 a^2 . Force between opposite charges: For q₁ and q₃ on opposite corners, the diagonal distance is r₁₃ = a 2 , yielding F₁₃ = kq^2 (a 2 )^2 = kq^2 2a^2 . The ratio is thus F₁₃ F₁₂ = kq^2 2a^2 kq^2 a^2 = 1 2 , corresponding to option C .