A positive point charge q1 at the origin and a negative charge q2 at x=2m. The resultant electric field is 10.8 i N/C at x=1m and -8 i N/C at x=3m. Find q1 and q2.

Question

A positive point charge q1 at the origin and a negative charge q2 at x=2m. The resultant electric field is 10.8 i N/C at x=1m and -8 i N/C at x=3m. Find q1 and q2.

Answer 1

Distance between Q1 and point 1m, is 1m and for q2 also 1m; for point at 3m: q1  3m, q2 1m;Use superposition for electric field and that test chrge will be attracted by negative (q2) and revealed by positive charge (q1)

E=kQ/r² then E_1m= kq₁/1 –kq₂/1  E_3m= kq₁/9 –kq₂/1

Or

E_1m= kq₁ –kq₂     E_3m= kq1/9 –kq2 and after subtraction (8/9)kq₁= E_1m – E_3m  and q₁=9(E_1m – E_3m)/(8k) ; now q₂= (kq₁ - E_1m)/k