Two mutually perpendicular infinitely long straight conductors carrying uniformly distributed charges of linear densities λ 1 and λ 2 are positioned at a distance r from each other. Force between the conductors depends on r as

Step-by-step solution

Consider the arrangement given, Force on a differentiable length element d l of conductor 2 due to field of conductor 1 is d F = E 1 d q where, E 1 = field of wire 1 at location of d l This force can be resolved into components d F cos θ and d F sin θ net force is sum of all d F cos θ components, whereas Σ d F sin θ = 0 . So, net force on conductor 2 is F = ∫ d F = ∫ E 1 d q Here, E 1 = 2 k λ 1 R = 2 k λ 1 d q = λ 2 d l l r = tan θ and r R = cos θ ⇒ d l = r sec 2 θ d θ Also, θ varies from - π 2 to π 2 for conductor