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Q1XQ2 Given the Coulomb's formula F = ke r2 where ke = (9.0 × 109 Nm/), F is the force between charges in Newton, Q1 and Q2 are the respective two charges in Coulombs, and r is the distance in meters. Calculate the distance between two charges of 20 uC and 18 µC if the force between the two charges is 2.8x104 N

Q1XQ2 Given the Coulomb's formula F = ke r2 where ke = (9.0 × 109 Nm/), F is the force between charges in Newton, Q1 and Q2 are the respective two charges in Coulombs, and r is the distance in meters. Calculate the distance between two charges of 20 uC and 18 µC if the force between the two charges is 2.8x104 N

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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**Coulomb's Law Formula and Example Problem** **Coulomb's Law Formula:** \[ F = k_e \frac{Q_1 \times Q_2}{r^2} \] where: \[ k_e = (9.0 \times 10^9 \, \text{Nm}^2/\text{C}^2) \] **Explanation:** - \( F \) is the force between charges measured in Newtons. - \( Q_1 \) and \( Q_2 \) are the respective two charges measured in Coulombs. - \( r \) is the distance between the two charges measured in meters. - \( k_e \) is Coulomb's constant, \( 9.0 \times 10^9 \, \text{Nm}^2/\text{C}^2 \). **Example Problem:** **Calculate the distance between two charges of 20 µC (microcoulombs) and 18 µC if the force between the two charges is \( 2.8 \times 10^4 \) N.** Given: - \( Q_1 = 20 \, \mu\text{C} = 20 \times 10^{-6} \, \text{C} \) - \( Q_2 = 18 \, \mu\text{C} = 18 \times 10^{-6} \, \text{C} \) - \( F = 2.8 \times 10^4 \, \text{N} \) 1. Substitute the known values into the Coulomb's law formula: \[ 2.8 \times 10^4 = (9.0 \times 10^9) \frac{(20 \times 10^{-6}) \times (18 \times 10^{-6})}{r^2} \] 2. Simplify the equation to solve for \( r \): \[ 2.8 \times 10^4 = 9.0 \times 10^9 \frac{360 \times 10^{-12}}{r^2} \] \[ 2.8 \times 10^4 = 3.24 \times 10^{-2} (r^2) \] \[ r^2 = \frac{3.24 \times 10^{-2}}{2.8 \
Transcribed Image Text:**Coulomb's Law Formula and Example Problem** **Coulomb's Law Formula:** \[ F = k_e \frac{Q_1 \times Q_2}{r^2} \] where: \[ k_e = (9.0 \times 10^9 \, \text{Nm}^2/\text{C}^2) \] **Explanation:** - \( F \) is the force between charges measured in Newtons. - \( Q_1 \) and \( Q_2 \) are the respective two charges measured in Coulombs. - \( r \) is the distance between the two charges measured in meters. - \( k_e \) is Coulomb's constant, \( 9.0 \times 10^9 \, \text{Nm}^2/\text{C}^2 \). **Example Problem:** **Calculate the distance between two charges of 20 µC (microcoulombs) and 18 µC if the force between the two charges is \( 2.8 \times 10^4 \) N.** Given: - \( Q_1 = 20 \, \mu\text{C} = 20 \times 10^{-6} \, \text{C} \) - \( Q_2 = 18 \, \mu\text{C} = 18 \times 10^{-6} \, \text{C} \) - \( F = 2.8 \times 10^4 \, \text{N} \) 1. Substitute the known values into the Coulomb's law formula: \[ 2.8 \times 10^4 = (9.0 \times 10^9) \frac{(20 \times 10^{-6}) \times (18 \times 10^{-6})}{r^2} \] 2. Simplify the equation to solve for \( r \): \[ 2.8 \times 10^4 = 9.0 \times 10^9 \frac{360 \times 10^{-12}}{r^2} \] \[ 2.8 \times 10^4 = 3.24 \times 10^{-2} (r^2) \] \[ r^2 = \frac{3.24 \times 10^{-2}}{2.8 \
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