Solving for Charge Q at Corner C in Electric Field Problem

[Unkownentity]

Homework Statement

In the square ABCD every corner is marked (from the left top corner, moving to the right) D, C, B, A, we have places a positive charge Q = 2,5 * 10^-8. In the corner C a charge of q should be placed so the total of electricforces on A = 0. The distans between A and D is 1,0mm. Should the charge q places on corner C be positiv or negative and decide what charge of q that needs to be placed at corner C

Homework Equations

F= k*Q₁*Q₂/r²

The Attempt at a Solution

What i started to do was to write down the forces affecting the charge A. Which was a repelling force from B facing to the left at charge A and a repelling force from D facing down at charge A. What we now know is that charge C has to somehow "neutralize" these forces, thus the charge C has to be negative.

After have written down the forces affecting A we can se the that the total force affecting A is a diagonal facing "South west". By using F= k*Q₁*Q₂/r² we can decide the repelling forces affecting A (i got 5,6N) and then use these forces by the help of pythagoras theorem to decide the diagonal (i got 7,9N). We now know the total force and thus an attracting force of 7,9N should neutralize the forces and the total outcome should result into A=0. Using F= k*Q₁*Q₂/r² again although leaving one charge Q unknown and substituting F with 7,9N i got the the charge Q has to be 3,51*10^-8

I really hope this made sense for you guys, when i started with the quest i actually had no idea to do it so now I'm just curios to see if i have the right solution :P

Thanks for taking a look! =)

 

[willem2]

Your answer for the net force of B and D is correct. Your answer for Q is much too small. I think it's a factor 1000 too small, and on top of that I think you didn't use that the diagonal is longer, so will be bigger in the equation for the force between A and C

 

[Unkownentity]

Yeah sorry i just noticed my mistake it should be correct now i edited everything, does it seem correct now?

Thanks for answering