Suppose that q1 = 3 µC (3.0×106 on the figure in cm. Find the angle in degrees that the net force on 93 makes 6 C), 92 = -2 µC, and q3 = 1 µC. Coordinates are shown counterclockwise from the +x axis. (1,4) 92 Fnet = F13 + F23 F23 4+) + F13 93 (5,0) (0,0)

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Chapter1: Units, Trigonometry. And Vectors
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### Problem Statement

Suppose that \( q_1 = 3\, \mu C \) \((3.0 \times 10^{-6}\, C)\), \( q_2 = -2\, \mu C \), and \( q_3 = 1\, \mu C \). Coordinates are shown on the figure in cm. Find the angle in degrees that the net force on \( q_3 \) makes counterclockwise from the +x axis.

### Diagram Description

The diagram displays three point charges positioned on a coordinate system:

1. **Charge \( q_1 \)**
   - Charge: \( +3\, \mu C \)
   - Position: Origin \((0,0)\)

2. **Charge \( q_2 \)**
   - Charge: \( -2\, \mu C \)
   - Position: Coordinates \((1,4)\) cm

3. **Charge \( q_3 \)**
   - Charge: \( +1\, \mu C \)
   - Position: Coordinates \((5,0)\) cm

### Vector Forces

1. **Force \( \vec{F}_{13} \)**
   - Origin: \( q_1 \)
   - Destination: \( q_3 \)
   - Direction: Along the positive x-axis from \( q_1 \) to \( q_3 \)

2. **Force \( \vec{F}_{23} \)**
   - Origin: \( q_2 \)
   - Destination: \( q_3 \)
   - Direction: At an angle from \( q_2 \) to \( q_3 \)
   
3. **Net Force \( \vec{F}_{\text{net}} \)**
   - The vector sum of \( \vec{F}_{13} \) and \( \vec{F}_{23} \)

### Objective

Calculate the net angle (in degrees) that the net force \( \vec{F}_{\text{net}} \) on \( q_3 \) forms with the positive x-axis in a counterclockwise direction.

### Approach

To solve the problem, the following steps should be carried out:

1. **Calculate individual forces** (\( \vec{F}_{13} \) and \( \vec{F}_{23} \)) using Coulomb's law.
2. **Determine the components** of these forces
Transcribed Image Text:### Problem Statement Suppose that \( q_1 = 3\, \mu C \) \((3.0 \times 10^{-6}\, C)\), \( q_2 = -2\, \mu C \), and \( q_3 = 1\, \mu C \). Coordinates are shown on the figure in cm. Find the angle in degrees that the net force on \( q_3 \) makes counterclockwise from the +x axis. ### Diagram Description The diagram displays three point charges positioned on a coordinate system: 1. **Charge \( q_1 \)** - Charge: \( +3\, \mu C \) - Position: Origin \((0,0)\) 2. **Charge \( q_2 \)** - Charge: \( -2\, \mu C \) - Position: Coordinates \((1,4)\) cm 3. **Charge \( q_3 \)** - Charge: \( +1\, \mu C \) - Position: Coordinates \((5,0)\) cm ### Vector Forces 1. **Force \( \vec{F}_{13} \)** - Origin: \( q_1 \) - Destination: \( q_3 \) - Direction: Along the positive x-axis from \( q_1 \) to \( q_3 \) 2. **Force \( \vec{F}_{23} \)** - Origin: \( q_2 \) - Destination: \( q_3 \) - Direction: At an angle from \( q_2 \) to \( q_3 \) 3. **Net Force \( \vec{F}_{\text{net}} \)** - The vector sum of \( \vec{F}_{13} \) and \( \vec{F}_{23} \) ### Objective Calculate the net angle (in degrees) that the net force \( \vec{F}_{\text{net}} \) on \( q_3 \) forms with the positive x-axis in a counterclockwise direction. ### Approach To solve the problem, the following steps should be carried out: 1. **Calculate individual forces** (\( \vec{F}_{13} \) and \( \vec{F}_{23} \)) using Coulomb's law. 2. **Determine the components** of these forces
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