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 solve this, we use Coulomb’s Law, which gives the force between two point charges:
\[ F = k \cdot \frac{q_1 q_2}{r^2} \] Where:
\( F = 9 \, \text{N} \) (given force)
\( k = 9 \times 10^9 \, \text{Nm}^2/\text{C}^2 \) (Coulomb’s constant)
\( r = 1 \, \text{m} \) (distance between charges)
\( q_1 = 1 \, \text{C} \) (one of the charges)
\( q_2 = ? \) (the other charge we need to find)
Step 1: Rearranging the formula to solve for \( q_2 \):
\[ q_2 = \frac{F \cdot r^2}{k \cdot q_1} \] Step 2: Substituting the known values
\[ q_2 = \frac{9 \cdot (1)^2}{9 \times 10^9 \cdot 1} = \frac{9}{9 \times 10^9} = \frac{1}{10^9} = 10^{-9} \, \text{C} \] Final Answer: \( q_2 = 10^{-9} \, \text{C} \)