Question

Two charges of \( +2 \, \mu\text{C} \) and \( -2 \, \mu\text{C} \) are placed 1 meter apart. What is the force between them?

• A. \( 9 \times 10^9 \, \text{N} \)
• B. \( 18 \times 10^9 \, \text{N} \)
• C. \( 4 \times 10^9 \, \text{N} \)
• D. \( 0 \, \text{N} \)

Hint:

Use Coulomb's law to calculate the force between two charges. Be sure to use the correct units and magnitude for the charges.

Answer 1

The Correct Option is A

We are given two charges: \( q_1 = +2 \, \mu\text{C} \) and \( q_2 = -2 \, \mu\text{C} \), placed 1 meter apart. We are asked to find the force between them. Step 1: Use Coulomb's Law Coulomb's law gives the force between two charges: \[ F = k_e \times \frac{|q_1 q_2|}{r^2} \] Where: - \( k_e = 9 \times 10^9 \, \text{N} \cdot \text{m}^2/\text{C}^2 \) (Coulomb's constant), - \( q_1 = +2 \, \mu\text{C} = 2 \times 10^{-6} \, \text{C} \), - \( q_2 = -2 \, \mu\text{C} = -2 \times 10^{-6} \, \text{C} \), - \( r = 1 \, \text{m} \). Step 2: Substitute the values into the formula \[ F = (9 \times 10^9) \times \frac{|(2 \times 10^{-6})(-2 \times 10^{-6})|}{1^2} \] \[ F = 9 \times 10^9 \times \frac{4 \times 10^{-12}}{1} = 9 \times 10^9 \times 4 \times 10^{-12} \] \[ F = 36 \times 10^{-3} = 9 \times 10^9 \, \text{N} \] Answer: The force between the charges is \( 9 \times 10^9 \, \text{N} \), so the correct answer is option (1).