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

To solve the problem of calculating the force between two charges, we use Coulomb's Law. Coulomb's Law states:

F = k |q₁q₂| / r²

Where: 

• F is the force between the charges (N).
• q₁ and q₂ are the magnitudes of the charges (C₁, C₂).
• r is the distance between the charges (m).
• k is Coulomb's constant, k = \(8.988 \times 10^9 \, \text{N} \cdot \text{m}^2/\text{C}^2\).

Given:

• q₁ = \( +2 \, \mu\text{C} \) = \( +2 \times 10^{-6} \, \text{C} \)
• q₂ = \( -2 \, \mu\text{C} \) = \( -2 \times 10^{-6} \, \text{C} \)
• r = 1 m

Substitute the values into Coulomb's Law:

F = \(\frac{8.988 \times 10^9 \times |2 \times 10^{-6} \times -2 \times 10^{-6}|}{1^2}\)

= \(8.988 \times 10^9 \times 4 \times 10^{-12}\)

= \(35.952 \times 10^{-3}\)

= \(9 \times 10^9 \, \text{N}\) (approx.)

Thus, the force between the two charges is \(9 \times 10^9 \, \text{N}\).