Coulomb's law for the force between electric charges most closely resembles with

Options

A. Law of conservation of energy
B. Newton's law of gravitation
C. Newton's second law of motion
D. The law of conservation of charge.

Answer

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

### Step-by-Step Solution:

1. **Understanding Coulomb's Law**:
Coulomb's law states that the force \( F \) between two point charges \( q_1 \) and \( q_2 \) separated by a distance \( r \) is given by:
\[ F = k \frac{|q_1 q_2|}{r^2} \]
where \( k \) is Coulomb's constant.

2. **Understanding Newton's Law of Gravitation**:
Newton's law of gravitation states that the force \( F \) between two masses \( m_1 \) and \( m_2 \) separated by a distance \( r \) is given by:
\[ F = G \frac{m_1 m_2}{r^2} \]
where \( G \) is the gravitational constant.

3. **Comparing the Two Laws**:
- Both laws describe a force that is inversely proportional to the square of the distance between the two entities (charges or masses).
- Both laws have a constant that relates to the strength of the interaction (Coulomb's constant \( k \) for electric charges and gravitational constant \( G \) for masses).

4. **Conclusion**:
Since both Coulomb's law and Newton's law of gravitation have a similar mathematical form, where the force is inversely proportional to the square of the distance, we can conclude that Coulomb's law most closely resembles Newton's law of gravitation.

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

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