Two infinite conduting plates 1 and 2 are separated by a distance `l`. A point chagre `q` is located between the plates at a distance `x` from plate 1. Find the charges induced on each plate.

Explanation

The proton of point charge between two conducting planes is more easily trackled (if we want only the total charge induced on the plates) if we replace the point charge by a uniformly chagred plane sheet.
Then `E_(1) + E_(2) = (sigma)/(epsilon_(0))`
The conducting planes will be assumed to be grounded. Then `E_(1) x = E_(2) (l - x)`.
Hence, `E_(1) = (sigma)/(l epsilon_(0)) (l-x), E_(2) = (sigma)/(l epsilon_(0)) x`
This means that the induced charge density on the plane conductors are
`sigma_(1) = (sigma)/(l) (l-x), sigma_(2) = - (sigma)/(l) x`
Hence `q_(1) = -(q_(1))/(l) (l-x), q_(2)= - (q)/(l) x`