The geometrical positions of point-like charges and point A situated in the xy-plane in terms of the length parameter a. The vector of electric field E at point A is shown schematically and measured as E = Exi + Eyj (that is, both Ex and Ey are given). If possible, find the unknown charges q1 and q2.
**E_2 is the electric field with respect to q2. Not shown in figure. **
**E_1 is the electric field with respect to q1. (Same direction as E) **
**k_e is Coulomb's constant.**
E[/B] = Exi + Eyj
Ex = E_1*cos(45°) - E_2*cos(45°)
Ey = E_1*sin(45°) + E_2*sin(45°)
E = F/q = (k_e*q)/r^2
The Attempt at a Solution
E_1 [/B]= (k_e*q1)/(2a)^2 = (k_e*q1)/(4a^2)
E_2 = (k_e*q2)/(2a)^2 = (k_e*q2)/(4a^2)
Ex = (E_1 - E_2)*2/sqrt(2)
Ey = (E_1 + E_2)*2/sqrt(2)
E = 2/sqrt(2)*(E_1 - E_2) i + 2/sqrt(2)*(E_1 + E_2) j = 2/sqrt(2)*(k_e/(4a^2))*(q1 - q2) i + 2/sqrt(2)*(k_e/(4a^2))*(q1 + q2)
I am stuck here; I'm not sure if I've been going about this correctly or what steps to take next.