Find the equation that would solve this problem r1 Z L2 r2

Find the equation that would solve this problem r_1 = Z - L/2 r_2 = Z + L/2

Solution

Electric filed at point P due to charge q₁,E₁=kq₁/(Z-L/2)²

Electric filed at point P due to charge -q₂,E₂=k(-q₂₎/(Z+L/2)²

if electric filed is zero at point p then E_1⁺E₂=0

kq₁/(Z-L/2)²-kq₂₎/(Z+L/2)²=0