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## Homework Statement

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**= Ex

**i**+ Ey

**j**(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.**

## Homework Equations

E[/B] = Ex

**i**+ Ey

**j**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)

**= 2/sqrt(2)*(**

E

E

**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.

Thank you.