A system consists of a thin charged wire ring of radius r and a very long uniformly charged wire oriented along the axis of the ring, with one of its ends coinciding with the center of the ring. The total charge on the ring is q. and he linear charge density on the straight wire is `lambda`, The interaction force between the ring and the wire is

Explanation

The force of interaction due to ring on the element `dx` is
`dF=(GM(dm))/((r^(2)+x^(2)))cosalpha` where, `cosalpha=(x)/(sqrt(x^(2)+r^(2)))`
`impliesdF=(Gmxlambdadx)/((r^(2)+x^(2))^(3//2))`
`impliesF=Gmlambda int_(0)^(oo)(x dx)/((r^(2)+x^(2))^(3//2))=GMlambda int_(0)^(pi//2)(r^(2)tan theta sec^(2) theta d theta)/(r^(3) sec^(3) theta)`
`=(GMlambda)/(r )int_(0)^(pi//2)sin thetad theta=(GMlambda)/(r )|-costheta|_(0)^(pi//2)=(GMlambda)/(r )`