Question

Two like charges are placed 1 m apart in air. If the force between them is 9 N, and one charge is 1 C, what is the other charge? (Use $ k = 9 \times 10^9 \, \text{Nm}^2/\text{C}^2 $)

• A. 1 C
• B. 0.1 C
• C. 0.01 C
• D. \( 10^{-9} \, \text{C} \)

Hint:

In Coulomb’s law, if you're given force, one charge, and distance, isolate the unknown charge using: \[ q = \frac{F r^2}{k q_{\text{known}}} \] Keep track of units and exponents carefully!

Answer 1

The Correct Option is D

To determine this, we apply Coulomb’s Law, which defines the electrostatic force between two point charges:
\[ F = k \cdot \frac{q_1 q_2}{r^2} \] Where:
\( F = 9 \, \text{N} \) (specified force)
\( k = 9 \times 10^9 \, \text{Nm}^2/\text{C}^2 \) (Coulomb’s constant)
\( r = 1 \, \text{m} \) (separation distance)
\( q_1 = 1 \, \text{C} \) (first charge)
\( q_2 = ? \) (the unknown second charge)
Procedure Step 1: Rearranging the formula to isolate \( q_2 \):
\[ q_2 = \frac{F \cdot r^2}{k \cdot q_1} \] Procedure Step 2: Inserting the known values
\[ q_2 = \frac{9 \cdot (1)^2}{9 \times 10^9 \cdot 1} = \frac{9}{9 \times 10^9} = \frac{1}{10^9} = 10^{-9} \, \text{C} \] Conclusion: \( q_2 = 10^{-9} \, \text{C} \)