Coulomb's law is analogous to

Options

A. Charge conservation law
B. Newton's second law of mation
C. Law of conservation of energy
D. Newton's law of gravitation

Answer

To determine what Coulomb's law is analogous to, we need to analyze the law itself and compare it with the given options.

### Step-by-Step Solution:

1. **Understanding Coulomb's Law**:
Coulomb's law states that the force \( F \) between two point charges \( q_1 \) and \( q_2 \) is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance \( r \) between them. Mathematically, it can be expressed as:
\[ F = k \frac{q_1 q_2}{r^2} \]
where \( k \) is Coulomb's constant.

2. **Identifying the Options**:
We need to compare Coulomb's law with the four options provided:
- A) Conservation of Charge
- B) Newton's Laws of Motion
- C) Law of Conservation of Energy
- D) Newton's Law of Gravitation

3. **Analyzing Each Option**:
- **Option A: Conservation of Charge**: This law states that the total charge in an isolated system remains constant. It does not have a similar mathematical form to Coulomb's law.
- **Option B: Newton's Laws of Motion**: Particularly the second law, which states \( F = ma \) (force equals mass times acceleration), does not resemble Coulomb's law in structure or form.
- **Option C: Law of Conservation of Energy**: This law states that energy cannot be created or destroyed, only transformed. It does not have a direct analogy to Coulomb's law.
- **Option D: Newton's Law of Gravitation**: This law 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. This is structurally similar to Coulomb's law, where the force is proportional to the product of two quantities (charges or masses) and inversely proportional to the square of the distance between them.

4. **Conclusion**:
Since both Coulomb's law and Newton's law of gravitation share a similar mathematical form, we conclude that Coulomb's law is analogous to Newton's law of gravitation.

### Final Answer:
Coulomb's law is analogous to **Newton's Law of Gravitation** (Option D).