Question

The point charges in the figure below have the following values: q₁ = +2.8

Answer 1

Assuming q1 is free to move:

find the magnitude and direction of the net electrostatic
force exerted on the point charge q1,

q1=2.8 uc
q2=5.3 uc
q3=-0.89 uc
let k=9*10^-3
F=k*q^2/r^2

vector Force on q1 from q2: "third quadrant"
F=9*10^-3*(2.8)*(5.3)/
(4.35/100)^2 = 70.58 N

Componets of F: acts @ 240 degrees from x-axis
Fi=70.58* Cos(240)=-35.29i N <---
Fj= 70.58* Sin(240)=-61.12j N

Force on q1 from q3
Fi=9*10^-3*(2.8)*(0.89)/
(4.35/100)^2 = 11.85 N --->

Sum x=
-35.29i+11.85i = -23.44 N
Sum y=-61.12j N

x= -23.44
y= -61.12
*************************************
The resultant Force on q1
= sqr(x^2+y^2) = 65.461 N

angle with positive x-axis is:
atan (y/x) =249.02 degrees

b) d =2*4.35 = 8.7cm

vector Force on q1 from q2: "third quadrant"
F=9*10^-3*(2.8)*(5.3)/
(8.7/100)^2 = 17.645 N

Componets of F: acts @ 240 degrees from x-axis
Fi=17.645* Cos(240)=-8.822i N <---
Fj= 17.645* Sin(240)=-45.28j N

Force on q1 from q3
Fi=9*10^-3*(2.8)*(0.89)/
(8.7/100)^2 = 2.9625 N --->

Sum x=
-8.822i+2.9625i = -5.8595 N
Sum y=-45.28j N

*************************************
The resultant Force on q1
= sqr(x^2+y^2) = 45.657 N

angle with positive x-axis is:
atan (y/x) =82.626 degrees