What is the force F (a vector) on the -10 nC charge in the figure? Give your answer as a magnitude and an angle measured cw or ccw (specify which) from the +x-axis.
The figure shown is in the shape of a rectangle. On the top left is a +15 nC charge; on the top right is a -5.0 nC charge; on the bottom right is a -10 nC charge. There is no charge on the bottom left. The distance between the top charges is 3.0 cm. The distance between the top and bottom right charges is 1.0 cm.
Fnet = F1on3 + F2on3 = K|q1||q2|/r2
K ≅ 9.0*10^9 N*m^2/C^2
The Attempt at a Solution
The first thing I did was write out the first equation and plug in the given values as (9*10^9)(15*10^-9)(10*1-^-9)/(.0316)2 for F1on3. I found .0316 by using Pythagorus' equation to find the distance between the first and third charges. Then I plugged in (9*10^9)(5*10^-9)(10*10^-9)/(.01)2 for F2on3. Typing these values into my calculator, I got 1.35*10^-3 N and 4.5*10^-3 N. This is where I first got stuck, because I am figuring that one value is supposed to be subtracted from the other, because they would be of differently directed charges. 1on3 would be directed southeast and 2on3 would be directed straight down.
I tried to get closer to the correct answer by using the Law of Sines to find the angle between the first charge and the 3 cm distance. I wrote out 3.16/sin(90) = 1/sin(x). For x, I got 18.4°. I plugged this into the vertical component of F1on3 to get 4.26*10^-4 N. 2on3 points straight down, so I opted to subtract 4.26*10^-4 N from that. I ended up with 4.07*10^-3 N, which is close to the correct magnitude, but not quite.
The correct answer provided in the back of my textbook is 4.3*10^-3 N, at 253° ccw. As far as correctly reaching the magnitude, I'm confused, and as far as how to obtain the right direction, I am stumped. Any and all hints, tips and suggestions would be greatly appreciated.
Additionally, this is my first post, so please forgive me if my formatting is less than ideal.