A system consits fo a thin charged wire ring of radius `R` and a very long uniformly charged thread oriented along the axis of the ring, with one of its ends coinciding with the centre of the ring. The total charge of the ring, with one of the ring so equal to `q`. The charge of the thread (per unit length) is equal to `lambda`. Find the interaction froce between the ring and the thread.

Explanation

Force df on the wire `=dqvec(E)`
`(Kqx)/((x^(2)+R^(2))^(3//2)).lamdadx`
`F=Kqlamdaint_(0)^(oo)(xdx)/((R^(2)+x^(2))^(3//2))`
`F=(lamdaq)/(4piin_0R)`

Alternate :
Due to wire electric field on the points of ring in y-direction is
`E_(y)=(Klamda)/(R)`
Thus force on ring due to wire is
`q(Klamda)/(R)=(Kqlamda)/(R)=(lamdaq)/(4piin_0R)`
and `E_x = 0` [As cancelled out]
(Here x components of forces on small elements of rings are cancelled by the x component of diametrically opposite elements.)