What is the Net Force on q1 in a Rectangle of Charges?

[Cimino54]

Homework Statement

Four charges,
q1 = +145 µC, q2 = +55 µC, q3 = −150 µC, and q4 = +27 µC,
are fixed at the corners of a 4 m by 5 m rectangle, as illustrated in the figure below. What are the magnitude (in N) and the direction (in degrees counterclockwise from the +x-axis) of the net force acting on q1? (Assume the x-axis extends from q1 to the right.)

Homework Equations

1. F_e = (kq₁q₂)/(r²)
2. a² + b² = c²
3. F_x = Fsinθ
4. F_y = Fcosθ

The Attempt at a Solution

1. I determined the distance between charges 1/3 & 2/4 using Pythagorean theorem.
2. I solved for the forces between all charges using equation 1. I solved for the forces between 1/2, 3/4, 1/4, 2/3, 1/3, and 2/4.
3. I resolved forces 1/3 and 2/4 into x and y components using equations 3 & 4.
4. I add all x components together and all y components together.
5. I used equation 2 to get the overall magnitude of the x+y components.

 

[kuruman]

Hi Cimino54 and welcome to PF.

You describe what you did, but you do not show what you got and how that relates to what the problem is asking. For example, what is the relevance of solving for all the possible pairs of forces (step 2 in your attempt at solution)? Before you start calculating stuff, you need to have a strategy. What is your strategy here?

 

[Cimino54]

 

[kuruman]

OK, there are a lot of numbers in your post that are difficult to interpret. For example, at the very bottom I see two sets of x and y components of forces. Both sets are labeled F_x and F_y. Which forces are these? You need to use subscripts to distinguish where they come from. Start from the equation that you have written as $\vec{F}_{q1}=\vec{F}_{q2}+\vec{F}_{q3}+\vec{F}_{q4}$. That's a good starting point. Now you need to write the 6 components on the right, namely F_q2x, F_q2y, F_q3x, F_q3y, F_q4x, F_q4y. Can you do that? Also, I see triangles in your solution that have a 45^o angle. What angle is that? How is it formed?

 

[haruspex]

OK, there are a lot of numbers in your post that are difficult to interpret. For example, at the very bottom I see two sets of x and y components of forces. Both sets are labeled F_x and F_y. Which forces are these? You need to use subscripts to distinguish where they come from. Start from the equation that you have written as $\vec{F}_{q1}=\vec{F}_{q2}+\vec{F}_{q3}+\vec{F}_{q4}$. That's a good starting point. Now you need to write the 6 components on the right, namely F_q2x, F_q2y, F_q3x, F_q3y, F_q4x, F_q4y. Can you do that? Also, I see triangles in your solution that have a 45^o angle. What angle is that? How is it formed?

Might I suggest starting with something simpler?
Cimino, can you calculate the X and Y components of the force q₃ exerts on q₁? Please show all your working.