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 most closely resembles, we can follow these steps:

### Step 1: Understand 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 the formula:
\[ F = k \frac{Q_1 Q_2}{r^2} \]
where \( k \) is Coulomb's constant. This law indicates that the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.

### Step 2: Analyze the Options
We have four options to consider:
1. Law of Conservation of Energy
2. Newton's Law of Gravitation
3. Newton's Laws of Motion
4. Law of Conservation of Charge

### Step 3: Evaluate Each Option
- **Law of Conservation of Energy**: This law states that energy cannot be created or destroyed, only transformed. It does not involve forces, so it is not relevant to our comparison.

- **Newton's Law of Gravitation**: This law states that the force \( F \) between two masses \( m_1 \) and \( m_2 \) separated by a distance \( r \) is given by:
\[ F = G \frac{m_1 m_2}{r^2} \]
This law is similar to Coulomb's law in that it describes a force that is directly proportional to the product of two quantities (masses or charges) and inversely proportional to the square of the distance between them.

- **Newton's Laws of Motion**: These laws describe the relationship between the motion of an object and the forces acting on it. They do not specifically relate to the forces between two charges, so they are not relevant here.

- **Law of Conservation of Charge**: This law states that the total electric charge in an isolated system remains constant. Like the conservation of energy, it does not involve forces, making it irrelevant for our comparison.

### Step 4: Conclusion
The law that most closely resembles Coulomb's law is **Newton's Law of Gravitation** because both laws describe a force that depends on the product of two quantities (charges or masses) and inversely on the square of the distance between them.

### Final Answer
The correct option is **Newton's Law of Gravitation**.

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