The point charges in the figure below have the following values: = q_1 = + 1.8 m

Question

The point charges in the figure below have the following values: = q_1 = + 1.8 mu C, q_2 = + 6.5 mu C, q_3 = -0.89 mu C. (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 q_1. magnitude N direction degree (counterclockwise from the +x-axis) (b) Find the magnitude and direction of the force in part (a) if the distance d is doubled. magnitude N direction degree (counterclockwise from the +x-axis)

Explanation / Answer

  Assuming q1 is free to move:

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

q1=1.8 uc
q2=6.5 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*(1.8)*(6.5)/
(4.35/100)^2 = 55.648 N

Componets of F: acts @ 240 degrees from x-axis
Fi=55.648* Cos(240)=-27.824i N <---
Fj= 55.648* Sin(240)=-48.192j N

Force on q1 from q3
Fi=9*10^-3*(1.8)*(0.89)/
(4.35/100)^2 = 7.6195 N --->

Sum x=
-27.824i+7.6195i = -20.2045 N
Sum y=-48.192j N

x= -20.2045
y= -48.192
*************************************
The resultant Force on q1
= sqr(x^2+y^2) = 52.2560 N

angle with positive x-axis is:
atan (y/x) =67.254 degrees

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