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 can follow these steps:

### Step 1: Understand Coulomb's Law
Coulomb's law describes the electrostatic force between two point charges. It states that the force (F) between two charges (q1 and q2) 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 is expressed as:
\[ F = k \frac{q_1 q_2}{r^2} \]
where \( k \) is Coulomb's constant.

### Step 2: Identify the Components of Coulomb's Law
- **Directly Proportional**: The force is directly proportional to the product of the charges (\( q_1 \) and \( q_2 \)).
- **Inversely Proportional**: The force is inversely proportional to the square of the distance between the charges (\( r^2 \)).

### Step 3: Find an Analogous Law
To find an analogous law, we look for another fundamental force that has a similar relationship between its components. Newton's law of gravitation describes the force between two masses (m1 and m2) and is given by:
\[ F = G \frac{m_1 m_2}{r^2} \]
where \( G \) is the gravitational constant.

### Step 4: Compare the Two Laws
- **Directly Proportional**: Just like Coulomb's law, the gravitational force is directly proportional to the product of the two masses (\( m_1 \) and \( m_2 \)).
- **Inversely Proportional**: Both laws are inversely proportional to the square of the distance between the two objects.

### Conclusion
Since both Coulomb's law and Newton's law of gravitation share the same mathematical form and relationship between their respective quantities, 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.

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