The positive charge Q1 = Q0 is at location x = 0 and the positive charge

Q2 = 4Q0 at location x = d. A third charge Q3 is in the line connecting the two

Charges Q1 and Q2 are placed so that the entire system is in equilibrium

is located. Determine the location x of the charge Q3, its magnitude and sign.

My attempt at an solution.

The fact that the system is in equilibrium this should apply

F1 + F2 + F3 = 0

To get F1 I've done the following:

F1 =\( \frac{Q}{4*\pi * \epsilon0 * r^2} \)

Now since Q1 is the value of Q0 I've put that in and than fur r I've put 0 in meaning that the force F1 will be equall to 0.

Assuming this is correct this what we have now;

F2 + F3 = 0

I've used the same formula in F2 and F3, and than the problem starts. I don't know how to get the value of x out of F3. I've tried multiplying adding or simply trying to form it so i can get an equallity but cannot do it.I'm starting to think that my entire method is wrong? Can someone please confirm.And if my method is right, what is my next step from here? The solutions that are susposed to come out are x = d/3 and Q3 = -4/9Q0

Thank you!