Why Is My Calculation of the Net Force on q1 Incorrect?

[thatonenozz]

Homework Statement

q1= 6.7 μC
q2= -4.5 μC
q3= 2.2 μC
q4= 2.2 μC
d= 7.7 cmWhat is the x-component of the net force on q1?

Homework Equations

The Attempt at a Solution

This is part of an online problem set, and is currently the only question I have not answered correctly. I find it strange because I have approached it the same way as similar problems in the problem set (ex. What is the x-component of the net force on q2?) so I have a hard time understanding where I am going wrong. Perhaps someone can help, so here goes my thought process.

So the obvious one to start with is the force exerted on q1 by q2 since the x-component is the entire force. Plugging in values of q1= 6.7 μC, q2= -4.5 μC and d= 0.077m to the above equation gives a force of -45.258 N. Moving on to the force on q1 by q4. By plugging in q1= 6.7 μC and q2= 2.2 μC with d= 0.077m we get 22.126 N for the entire force. To get the x-component of this force, I then multiplied by cos(60) because it is an equilateral triangle and got an answer of 11.063 N. Since q3=q4 and they are at the same distance from q1 with the same angle, I assumed the x-components of their forces would be the same, so i multiplied by 2 and got back to 22.126 N once again. When adding them all up, I get 22.126 - 45.258 = -23.132 N. SmartPhysics says this is wrong. I disagree! What do you guys think? Have I made a very obvious mistake somewhere along the way?

 

[SammyS]

Homework Statement

https://www.smartphysics.com/Content/Media/Images/EM/01/h1_twoD2a.png

q1= 6.7 μC
q2= -4.5 μC
q3= 2.2 μC
q4= 2.2 μC
d= 7.7 cm

What is the x-component of the net force on q1?

Homework Equations

The Attempt at a Solution

This is part of an online problem set, and is currently the only question I have not answered correctly. I find it strange because I have approached it the same way as similar problems in the problem set (ex. What is the x-component of the net force on q2?) so I have a hard time understanding where I am going wrong. Perhaps someone can help, so here goes my thought process.

So the obvious one to start with is the force exerted on q1 by q2 since the x-component is the entire force. Plugging in values of q1= 6.7 μC, q2= -4.5 μC and d= 0.077m to the above equation gives a force of -45.258 N. Moving on to the force on q1 by q4. By plugging in q1= 6.7 μC and q2= 2.2 μC with d= 0.077m we get 22.126 N for the entire force. To get the x-component of this force, I then multiplied by cos(60) because it is an equilateral triangle and got an answer of 11.063 N. Since q3=q4 and they are at the same distance from q1 with the same angle, I assumed the x-components of their forces would be the same, so i multiplied by 2 and got back to 22.126 N once again. When adding them all up, I get 22.126 - 45.258 = -23.132 N. SmartPhysics says this is wrong. I disagree! What do you guys think? Have I made a very obvious mistake somewhere along the way?

Use symmetry to compare the vertical component of force exerted by q₃ to that exerted by q₄ .