An infinitely long, uniformly charged straight line has linear charge density λ1 coul/m. A straight rod of length 'b' lies in the plane of the straight line and perpendicular to it, with its enared end at distance 'a' from the line. The charge density on the rod varies with distance 'y', measured from the lower end, according to λ(on rod) = (λ2*b)/(y+a), where λ2 is a constant. Find the electrical force exerted on the rod by the charge on the infinite straight line, in the λ1, λ2, a, and b, and constants like ε0.
The Attempt at a Solution
I first treated the problem as if there was only a point P above the infinite line and applied Gauss's Law using a cylinder as my Gaussian surface. My answer was
E = (λ2 * b) / [2pi*ε0*(a+b)^2]
From my understanding, I now have to relate my first answer to a change in distance of the point P along the rod. Any help would be appreciated.
Thank you in advance.