# Electric force problem

1. Feb 12, 2010

### kontejnjer

1. The problem statement, all variables and given/known data
Hello forums! I'd like to ask you for your assistance on this particular problem:

Three charges are placed at the edges of a triangle (Q1=+2 C, Q2=-4 C, Q3=+3 C) as shown on the picture (b=10 cm). What is the resultant force on charge Q2 (neglecting gravity and assuming the charges are in a vacuum)?

2. Relevant equations

F=k*Q1*Q2/r^2

k=9*10^9 N m^2 C^-2

3. The attempt at a solution
The distance "a" is given by:
tan 30°=a/b
Which gives: a=5.7735 cm.

Using the Pythagorean theorem I got: c=11.547 cm.

Then I calculated the force between Q1 and Q2 to be: F1=-2.16*10^13 N
Then I calculated the force between Q3 and Q2 and got: F2=-8.1*10^12 N

The problem I'm having is calculating the resultant force (Fr) on Q2. Which sort of formula should I use to calculate it?
I made a force diagram as well:

2. Feb 12, 2010

### Jebus_Chris

Force is a vector so you need to add the components. Find F2y and add it to F1 and then find F2x.

3. Feb 12, 2010

### kontejnjer

I think I got it. So, what I did was this:
sin 30°=Fy1/F2
From this, I got: Fy1=-4.05*10^12 N
then I added this to F1 and got: Fy2=Fy1+F1 => Fy2=-2.565*10^13 N
I got the x component from:
cos 30°=Fx/F2
And got: Fx=-7.0148*10^12 N
Then I used the Pythagorean theorem to find the resultant and got: Fr=$$\sqrt{(Fy2)^2+(Fx)^2}$$
Fr=-2.65919*10^13 N

Does this look correct?