In the figure, the particles have charges q1 = -q2 = 310 nC and q3 = -q4 = 96 nC, and distance a = 3.8 cm. What are the (a) x and (b) y components of the net electrostatic force on particle 3? The figure shows four particles labeled 1, 2, 3, and 4 plotted in Quadrant 1 on an x y coordinate system. The particles are the vertices of a square with sides of length a. Particle 1 is on the positive y axis, particle 2 is in Quadrant 1, particle 3 is at the origin, and particle 4 is on the positive x axis.
Given:
q1=-q2=310nC=310*10^-9 C
q3=-q4=96nC=96*10^-9 C
a=3.8 cm=0.038 m
Let force on q3 due to q1 is F1
F1=kq1q3/a^2
F1=(8.99*10^9*310*10^-9*96*10^-9)/(0.038)^2
F1=0.186 N
Let force on q3 due to q2 is F2
F2=kq2q3/2a^2
F2==(8.99*10^9*310*10^-9*96*10^-9)/2(0.038)^2
F2=0.093N
Let force on q3 due to q4 is F4
F4= kq3q4/a^2
F4=(8.99*10^9*96*10^-9*96*10^-9)/(0.038)^2
F4=0.0576 N
So from diagram
X component of force is Fx
Fx=F4+F2cos45
Fx=0.0567+0.093*cos 45
Fx=0.123 N
And
Y component of force is Fy
Fy=F2sin45-F1
Fy=0.093 sin45-0.186
Fy=-0.120N
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