A thin wire ring of radius `R` carries a charge `q`. The ring si oriented parallel to an infinite conducting plane and is spearated by a distance `l` from it. Find :
(a) the surface chagre density at that point fo the plane symmetrical with respect to the ring,
(b) the strength and the potential of the electric field at the centre of the ring.

Explanation

It can be easil seen that in accourdance with the image method, `a` charge `-q` must be located on a similar ring but on the other side of the conducting plane. (Fig) at the same perpendiucular distance. From the solution of `3.9` net electric field at `O`,
`vec(E) = 2 (ql)/(4pi epsilon_(0) (R^(2) + l^(2))^(3//2)) (-vec(n))` where `vec(n)` is
outward normal with respect to the conducting plane.
Now `E_(n) = (sigma)/(epsilon_(0))`
Hence `sigma = (-ql)/(2pi (R^(2) + l^(2))^(3//2))`
where minus sign indicates that teh induced carge si opposite in sign to that of charge `q gt 0`.