A charge q1=6
𝜇
C is at position (x1,y1), another charge q2=9
𝜇
C is at position (x2,y2) and a third charge q3=2
𝜇
C is at position (x3,y3). Find the x component of the total force exerted by q1 and q2 on q3. The unit of your answer is N. (
𝑘
=
1
(
4
𝜋
𝜖
𝑜
)
=8.99x109Nm2/C2)

Assume

x1=6cm, y1=6cm

x2=4cm, y2=7cm

x3=4cm,y3=8cm

Question

A charge q1=6
𝜇
C is at position (x1,y1), another charge q2=9
𝜇
C is at position (x2,y2) and a third charge q3=2
𝜇
C is at position (x3,y3). Find the x component of the total force exerted by q1 and q2 on q3. The unit of your answer is N. (
𝑘
=
1
(
4
𝜋
𝜖
𝑜
)
=8.99x109Nm2/C2)

Assume

x1=6cm, y1=6cm

x2=4cm, y2=7cm

x3=4cm,y3=8cm

BlackTom AI · Accepted Answer

We start by listing the given quantities and converting units to be consistent. The charges are q1 = 6 μC, q2 = 9 μC, q3 = 2 μC. In coulombs: q1 = 6e-6 C, q2 = 9e-6 C, q3 = 2e-6 C. The positions in meters are: r1 = (0.06, 0.06), r2 = (0.04, 0.07), r3 = (0.04, 0.08).

For each charge qi, the force on q3 due to qi is given by F_i = k * q3 * qi * (r3 − ri) / |r3 − ri|^3, where k = 8.99e9 N·m^2/C^2.

1) Force from q1:
- Vector from q1 to q3: r31 = r3 − r1 = (0.04 − 0.06, 0.08 − 0.06) = (−0.02, 0.02).
- Distance |r31| = sqrt((−0.02)^2 + (0.02)^2) = sqrt(0.0004 + 0.0004) = sqrt(0.0008) ≈ 0.028284 m.
- Cubed distance: |r31|^3 ≈ (0.028284)^3 ≈ 2.2627e−5 m^3.
- Product q3 * q1 = (2e−6)(6e−6) = 12e−12 = 1.2e−11 C^2.
- Constant factor for this interaction: C1 = k * (q3 * q1) / |r31|^3 ≈ (8.99e9 * 1.2e−11) / 2.2627e−5 ≈ 0.10788 / 2.2627e−5 ≈ 4.77e3 N/m.
- Components of F1: F1 = C1 * r31 ≈ 4.77e3 * (−0.02, 0.02) ≈ (−95.3, +95.3) N.

2) Force from q2:
- Vector from q2 to q3: r32 = r3 − r2 = (0.04 − 0.04, 0.08 − 0.07) = (0, 0.01).
- Distance |r32| = sqrt(0^2 + 0.01^2) = 0.01 m. |r32|^3 = (0.01)^3 = 1e−6 m^3.
- Product q3 * q2 = (2e−6)(9e−6) = 18e−12 = 1.8e−11 C^2.
- Constant factor: C2 = k * (q3 * q2) / |r32|^3 = (8.99e9 * 1.8e−11) / 1e−6 = 0.16182 / 1e−6 ≈ 1.6182e5 N/m.
- Components of F2: F2 = C2 * r32 = 1.6182e5 * (0, 0.01) = (0, 1618.2) N.

Now sum the x-components to get the total x-component of the force on q3 due to q1 and q2:
- F_x,total = F1_x + F2_x = (−95.3) + 0 ≈ −95.3 N.

The computed total x-component is approximately −95.3 N. Depending on rounding at intermediate steps, this value may appear as about −95.5 N in a rounded result. The key idea is that the x-contribution comes from the x-component of the force from q1 (which has an equal negative x and positive y component due to the geometry) plus the x-component from q2 (which lies directly above q3, contributing no x-component).

Similar Questions

Coulomb's Law states that the magnitude of the electrostatic force between two point charges is:

A charge of 2 X 10-7 C is acted upon by a force of 0.1 N. Determine the distance to the other charge of 4.5 X 10-7 C with both the charges in vacuum.

In a Coulomb’s Law experiment, if the charge of one object is doubled, what would happen to the force on the other charged object?

The law that states that "the force is directly proportional to the product of charges and inversely proportional to the square of separation between them" is called

A charge of 2 X 10-7 C is acted upon by a force of 0.1N. Determine the distance to the other charge of 4.5 X 10-7 C with both the charges in vacuum.

If you are give the relationship 𝐹 = 𝑘 𝑞 2 𝑟 2 + 𝐶 and you plotted 𝐹 vs 1 𝑟 2 which of the following would be true about your graph?

More Practical Tools for Students Powered by AI Study Helper

Homework AI Solver

Stylized AI Paper Writer

Plagiarism Checker Assistant

Citation AI Academic Writing Tool

In-Class Translation Assistant

AI Note Generator

AI Quiz Answers

Past Exam Questions from University Test Bank

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler