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.

Options

A. `(2KQ)/(r(r+L))`
B. `(KQq)/r^2`
C. `(KQq)/(r(r-L))`
D. `(KQq)/(r(r+L))`

Answer

D

Explanation

Charge on element length dx -
`dq= (Q/L) dx`
Force due to element charge dq and q –
`dF=(Kqdq)/(x^2)`
`F=int_r^(r+L)(Kq(Q//L)dx)/x^`
`=(KqQ)/L [(x^(-2x+1))/(-2+1)]_r^(L+r)=(-KqQ)/L[1/x]_(r)^(L+r)`
`=(-KqQ)/L [1/(L+r)-1/r]implies F=(KQq)/(r(L+r))`