Coulomb's law for electric charges, most closely resembles

Options

A. The law of conservation of momentum
B. The law of conservation of energy
C. The law of conversvation of charge
D. Newton's law of gravitation

Explanation

To solve the question regarding which law Coulomb's law for electric charges most closely resembles, we can follow these steps:

### Step-by-Step Solution:

1. **Understand Coulomb's Law**:
Coulomb's law states that the electric force \( F \) between two point charges \( Q_1 \) and \( Q_2 \) is given by the formula:
\[ F = k \frac{Q_1 Q_2}{r^2} \]
where \( k \) is Coulomb's constant and \( r \) is the distance between the charges.

2. **Understand Newton's Law of Gravitation**:
Newton's law of gravitation states that the gravitational force \( F \) between two masses \( M_1 \) and \( M_2 \) is given by:
\[ F = G \frac{M_1 M_2}{r^2} \]
where \( G \) is the gravitational constant and \( r \) is the distance between the masses.

3. **Compare the Two Laws**:
Both laws describe a force that is:
- Directly proportional to the product of two quantities (charges in Coulomb's law and masses in Newton's law).
- Inversely proportional to the square of the distance between them.

4. **Identify the Similarities**:
If we replace the charge \( Q \) with mass \( M \) and the constant \( k \) with \( G \), we can see that the structure of both equations is similar:
\[ F \propto \frac{Q_1 Q_2}{r^2} \quad \text{and} \quad F \propto \frac{M_1 M_2}{r^2} \]
This indicates that Coulomb's law and Newton's law of gravitation have a similar mathematical form.

5. **Conclusion**:
Therefore, we conclude that Coulomb's law for electric charges most closely resembles Newton's law of gravitation.

### Final Answer:
Coulomb's law for electric charges most closely resembles **Newton's law of gravitation**.