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.
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)
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
Or is it rhat= d( ihat )?
F2 = (-ke^2/r^2)(rhat)
r = sqrt(d^2+d^2)
rhat = r vector/|r vector|
Assuming tail at origin
r vector = <d,d>
F2= (-ke^2/(2d^2))(d(ihat)/sqrt(2)d)+ (-ke^2/(2d^2))(d(jhat)/sqrt(2)d)
F3 = (-ke^2/r^2)(rhat)
rhat= jhat or is it rhat = d(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)).