a point charge `q` is situated at a distance `r` from one end of a thin conduction rod of length `L` having a charge `Q` (uniformly distributed a long its length).find the magnitudes of electric force between the two.

Explanation

Consider a small element of the rod of length dx, at a distance x from the poin charge q. Trating the element as a point charge, the force between q, and charge element will be `dF=1/( 4pi epsilon_(0)) (dqQ)/(x^(2))`
But `dQ=Q/L dx`
So `dF=1/( 4 pi epsilon_(0)) (qQdx)/(Lx^(2))`
`F=intdF=1/( 4 pi epsilon_(0)) (qQ)/L int_(r)^(r+L)(dx)/(x^(2))`
`=1/(4 pi epsilon_(0)) (qQ)/L[-1/x]_(r)^(r+L)=1/(4pi epsilon_(0)) [1/r=1/(r+L)]`
`F=1/(4pi epsilon_(0)) (qQ)/(r(r+L))`