State Coulomb's law of electric force between two charged bodies.

Options

A. proportional to the sum of the charges
B. inversely proportional to the distance between charges
C. proportional to the product of the charges and inversely proportional to the distance
D. proportional to the product of the charges and inversely proportional to the square of distance.

Answer

**Step-by-Step Solution:**

1. **Understanding Coulomb's Law**: Coulomb's law describes the electrostatic force between two charged bodies. It states that the force between two point charges is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them.

2. **Mathematical Expression**: The mathematical expression for Coulomb's law is given by:
\[ F = k \frac{q_1 q_2}{r^2} \]
where:
- \( F \) is the magnitude of the electrostatic force between the charges,
- \( k \) is Coulomb's constant (approximately \( 8.99 \times 10^9 \, \text{N m}^2/\text{C}^2 \)),
- \( q_1 \) and \( q_2 \) are the magnitudes of the two charges,
- \( r \) is the distance between the centers of the two charges.

3. **Proportional Relationships**: From the equation, we can derive the following relationships:
- The force \( F \) is proportional to the product of the charges \( q_1 \) and \( q_2 \): \( F \propto q_1 q_2 \).
- The force \( F \) is inversely proportional to the square of the distance \( r \): \( F \propto \frac{1}{r^2} \).

4. **Conclusion**: Therefore, we can state Coulomb's law as:
- The electrostatic force between two point charges is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them.

**Final Statement**:
Coulomb's law can be summarized as:
"The electrostatic force \( F \) between two point charges \( q_1 \) and \( q_2 \) is given by \( F = k \frac{q_1 q_2}{r^2} \), where \( F \) is directly proportional to the product of the charges and inversely proportional to the square of the distance between them."

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