In the figure, charge q 1 = 3 × 10-6 C is placed at the origin and charge q 2 =
ID: 1661144 • Letter: I
Question
In the figure, charge q 1 = 3 × 10-6 C is placed at the origin and charge q 2 = -5.1 × 10-6 C is placed on the x-axis, at x = -0.20 m. Where along the positive x-axis can a third charge Q = -8.3 µC be placed such that the resultant force on this third charge is zero?Verizon LTE 6:53 PM session.masteringphysics.co HW01: Charge & Coulomb's Law tem Part A n the figure, charge q1 3 x 106 C is placed at the origin and charge q2-5.1 x 10c is placed on the x-axis, at x =-0.20 m. Where along the positive x-axis can a third charge Q =-8.3 C be placed such that the resultant force on this third charge is zero? 020m Express your answer using two significant figures. 796 X Incomect, Try Again;4 attempts remalining Provide Feedback
Explanation / Answer
Given,
q1 = 3 x 10^-6 C ; q2 = -5.1 x 10^-6 C ; x = -0.2 m ; Q = -8.3 uC
For the net force on the third charge to be zero
F13 = F23
Kq1Q/r13^2 = Kq2Q/r23^2
3 x 10^-6/(0.2 + x)^2 = 5.1 x 10^-6/x^2
3 x^2 = 5.1 (0.04 + x^2 + 0.4 x)
3 x^2 = 0.204 + 5.1 x^2 + 2.04 x
2.1 x^2 + 2.04 x + 0.204 = 0
The abve quadratic eqn gives us:
x = -0.113 ; -0.85 m
x = -0.85 satisfies the condition,
Hence, x = -0.85 m
[check
3 x 10^-6/(0.2 - 0.85)^2 = 5.1/-0.85^2
7.1 = 7.1]