Calculating total Coulomb force vector ?

starstruck_

1. Homework Statement
Consider a configuration consisting one +q charge ( upper right) and three −q charges, arranged in a square.

Side lengths = d.

Calculate the total F force vector acting on charge +q.

2. Homework Equations
Vector form of culomb’s force
F=( kq1q2/r^2) rhat

(rhat for unit vector - I’m on my phone so I can’t really tyupe it out properly, sorry)

3. The Attempt at a Solution
Split into 3 Force vector (between +q and each charge ). F1 is horizontal, F2 is the diagonal force vector, F3 is the vertical force vector.

F1 = (-ke^2/r^2)rhat

r= d
rhat= (ihat)
Or is it rhat= d( ihat )?

Anyways,
F1= ((-ke^2)/d^2))(ihat)

F2 = (-ke^2/r^2)(rhat)
r = sqrt(d^2+d^2)
r= sqrt(2)d
rhat = r vector/|r vector|
Assuming tail at origin
r vector = <d,d>
rhat= d(ihat)+d(jhat)/(sqrt(2)d)

F2= (-ke^2/(2d^2))(d(ihat)/sqrt(2)d)+ (-ke^2/(2d^2))(d(jhat)/sqrt(2)d)

F2 =(-ke^2/(2sqrt(2)d^3))(d(ihat))+(-ke^2/(2sqrt(2)d^3))(d(jhat))

F3 = (-ke^2/r^2)(rhat)

r= d
rhat= jhat or is it rhat = d(jhat)?

F3= (-ke^2/d^2)(jhat)

And then I would just add all of the components together.

I’m just wondering if I did this rhat business correctly ?

It said to use the vector form of the Coulomb force, so I tried- I’m not used to working with forces in this manner.

((Also sorry if it’s really hard to understand what I did, I can try to write it down and post a picture of my work if possible)).

Related Introductory Physics Homework Help News on Phys.org

rude man

Homework Helper
Gold Member
Your basic approach is OK.

It's convenient in this forum to use bold letters to convey vectors.
So r_hat = r, i_hat = i, j_hat = j, r =r cosθ i + r sinθ j and F = Fx i + Fy j.

When you introduce r you are doing coordinate system switching between cartesian (x,y) and polar (r,θ) coordinates. But this is not necessary. You can just stick with cartesian. So for example F2 = kq/d2 i + kq/d2 j and so on for F1 and F3. Then just add all the x and y components separately to get the net force in the i and j directions. Note that you don't calculate r2 =2d2separately. At the end you can still compute r (and θ) if you want.

• starstruck_

"Calculating total Coulomb force vector ?"

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving