The point charges in the figure below have the following values: q 1 = +2.7 µC,

Question

The point charges in the figure below have the following values: q1 = +2.7 µC, q2 = +5.5 µC, q3 = -0.89 µC. (Let the +x-axis point to the right.)

(a) Given that the distance d in the figure is 4.35 cm, find the magnitude and direction of the net electrostatic force exerted on the point charge q1.

(b) Find the magnitude and direction of the force in part (a) if the distance d is doubled.

? ° (counterclockwise from the +x-axis)

Explanation / Answer

a) Assuming q1 is free to move:
q1=2.7 uc
q2=5.5 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*(2.7)*(5.5)/(4.35/100)^2 = 70.63 N

Componets of F: acts @ 240 degrees from x-axis
Fi=70.63* Cos(240)=-35.32 i N
Fj= 70.63* Sin(240)=-61.17 j N

Force on q1 from q3
Fi=9*10^-3*(2.7)*(0.89)/(4.35/100)^2 = 11.43 N

Sum x= -35.32i+11.43i = -23.89 N
Sum y=-61.17j N

x= -23.89
y= -61.17
The resultant Force on q1 = sqr(x^2+y^2) = 65.67 N

angle with positive x-axis is:
atan (y/x) =248.67 degrees

b) If d will be doubled then force will reduce by 4

F = 16.42 N

Direction will remain same.

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