In the figure four particles are fixed along an x axis, separated by distances d = 3.00 cm.

Question

In the figure four particles are fixed along an x axis, separated by distances d = 3.00 cm. The charges are q₁ = +3e, q₂ = -e, q₃ = +e, and q₄ = +8e, with e = 1.60 × 10^-19 C. What is the value of the net electrostatic force on (a) particle 1 and (b) particle 2 due to the other particles?

Answer 1

Given: distances between charges d = 3.00 cm = 0.03 m.

The charges are q₁ = +3e, q₂ = -e, q₃ = +e, and q₄ = +8e, with e = 1.60 × 10^-19 C.

Asked: What is the value of the net electrostatic force on (a) particle 1 and

(b) particle 2 due to the other particles?

Electrostatic force between two charges determined from Coulomb’s Law

F = ke qQ/d^2, q, Q charges, d- distance between them and

ke Coulomb constant = 8.988 x 10^9 kg m^2 s^-2C^-2

Net Electric force Q1 = Fq1q2 (right, attraction) + Fq1q3 (left, repulsion) + Fq1q4(left)

                                   = (8.988 x 10^9 x 3 x 1.60 × 10^-19 x 1 x 1.60 × 10^-19)/ (.03)^2 –

                                      (8.988 x 10^9 x 3 x 1.60 × 10^-19 x 1 x 1.60 × 10^-19)/ (.06)^2 –

                                      (8.988 x 10^9 x 3 x 1.60 × 10^-19 x 8 x 1.60 × 10^-19)/ (.09)^2

                                = 7.67 x 10^-25 – 1.92 x 10^-25 – 6.82- x 10^-25 = -1.07 x 10^-25 N

Answer: Net force on particle 1: 1.07 x 10^-25 N left

Net Electric force Q2 = Fq2q1 (left, attraction) + Fq2q3 (right, attraction) + Fq2q4(right)

                                  = -(8.988 x 10^9 x 3 x 1.60 × 10^-19 x 1 x 1.60 × 10^-19)/ (.03)^2 +

                                      (8.988 x 10^9 x 1 x 1.60 × 10^-19 x 1 x 1.60 × 10^-19)/ (.03)^2 +

                                      (8.988 x 10^9 x 1 x 1.60 × 10^-19 x 8 x 1.60 × 10^-19)/ (.06)^2

                                  = -7.67 x 10^-25 + 2.56 x 10^-25 + 5.11 x 10^-25 = 0 N

Answer: Net force on particle 2: 0 N

I hope this helps.

Sincerely,

Shailesh (Sky) Kadakia, Expert Tutor WYZANT

Former Professor, University of Pittsburgh, Pittsburgh PA

Electrical Engineering Technology Department