### Example of Calculating the Net Force on a ChargeThe following figure shows three electric charges. All three charges (Q1, Q2, and Q3) are placed in a plane. Charge Q1 is 1 meter to the right of charge Q2, and 2 meters below Q3. The net force on the charge Q1 due to other two charges can be calculated using the principle of superposition.#### Step-by-Step Solution:1. Identify the charges and their positions: - Charge $ Q_1 = 4.0 \times 10^{-6} \, \text{C} $ - Charge $ Q_2 = -6.0 \times 10^{-6} \, \text{C} $ - Charge $ Q_3 = 12.0 \times 10^{-6} \, \text{C} $2. Distance between charges: - Distance between $ Q_1 $ and $ Q_2 $: 1 m - Distance between $ Q_1 $ and $ Q_3 $: 2 m3. Calculate the force vectors exerted by Q2 and Q3 on Q1. Then we will add these to find the net force on Q1. - The force $ F $ between two charges is given by Coulomb's law $ F = k \frac{|Q_1 Q_2|}{r^2} $, where $ k $ is Coulomb's constant $ (8.99 \times 10^9 \, \text{N m}^2/\text{C}^2) $.4. Force $ F_{21} $ between $ Q_2 $ and $ Q_1 $: \[ F_{21} = k \frac{|Q_1 Q_2|}{d_{21}^2} \] Substitute values: \[ F_{21} = 8.99 \times 10^9 \, \left( \frac{(4.0 \times 10^{-6})(-6.0 \times 10^{-6})}{1^2} \right) \, \text{N} \]5. Force $ F_{31} $ between $ Q_3 $ and $ Q_1 $: \[

Given Charge on Q1=12.0×10-6C,Q2=-6.0×10-6C, Q3=4.0×10-6C Distance, d3→1=2m, d2→1=1m Coulomb's law…

Q3 4.0 x 10-6 C m2Q1 = 12.0 x 10-6 C 2 m 1 m Q2-6.0 x 10-6 C Two charges, Q₁ = 12.0 x 10-6 C and Q₂ = 16.0 x 10-6 C, are placed to the right and below a third charge, Q3 = 4.0 x 10-6 C. First let's calculate the forces that Q, and Q₂ exert on Q3. Then we will add these two force vectors to determine the net force on Q:

Q3 4.0 x 10-6 C m2Q1 = 12.0 x 10-6 C 2 m 1 m Q2-6.0 x 10-6 C Two charges, Q₁ = 12.0 x 10-6 C and Q₂ = 16.0 x 10-6 C, are placed to the right and below a third charge, Q3 = 4.0 x 10-6 C. First let's calculate the forces that Q, and Q₂ exert on Q3. Then we will add these two force vectors to determine the net force on Q:

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ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

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Concept explainers

Electric Charges and Fields

One of the fundamental properties is the electromagnetic property. Charge cannot be destroyed by any process and this contributes formally to the law of charge conservation.

Question

### Example of Calculating the Net Force on a Charge

The following figure shows three electric charges. All three charges (Q1, Q2, and Q3) are placed in a plane. Charge Q1 is 1 meter to the right of charge Q2, and 2 meters below Q3. The net force on the charge Q1 due to other two charges can be calculated using the principle of superposition.

#### Step-by-Step Solution:

1. Identify the charges and their positions:
- Charge $ Q_1 = 4.0 \times 10^{-6} \, \text{C} $
- Charge $ Q_2 = -6.0 \times 10^{-6} \, \text{C} $
- Charge $ Q_3 = 12.0 \times 10^{-6} \, \text{C} $

2. Distance between charges:
- Distance between $ Q_1 $ and $ Q_2 $: 1 m
- Distance between $ Q_1 $ and $ Q_3 $: 2 m

3. Calculate the force vectors exerted by Q2 and Q3 on Q1. Then we will add these to find the net force on Q1.
- The force $ F $ between two charges is given by Coulomb's law $ F = k \frac{|Q_1 Q_2|}{r^2} $, where $ k $ is Coulomb's constant $ (8.99 \times 10^9 \, \text{N m}^2/\text{C}^2) $.

4. Force $ F_{21} $ between $ Q_2 $ and $ Q_1 $:
\[
F_{21} = k \frac{|Q_1 Q_2|}{d_{21}^2}
\]
Substitute values:
\[
F_{21} = 8.99 \times 10^9 \, \left( \frac{(4.0 \times 10^{-6})(-6.0 \times 10^{-6})}{1^2} \right) \, \text{N}
\]

5. Force $ F_{31} $ between $ Q_3 $ and $ Q_1 $:
\[

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