 Solution

The force on the real line charge is due to the induced conductor field, represented by the image charge; its own singular field must be omitted. The opposite image at distance $2d$ produces at the origin a field toward the conductor,Multiplying by the charge per unit length gives the attractive force per unit length:The attraction holds for either sign of $\mu$. The geometry assumes $d>0$, so the real line lies outside the conductor.