The correct option is **C. Both electrostatic and gravitational forces follow an inverse-square law.** ### Detailed Explanation: 1. **Understanding the Forces**: - **Electrostatic Force**: This is the force between charged particles. It can be either attractive or repulsive depending on the nature of the charges involved (like charges repel, unlike charges attract). - **Gravitational Force**: This is the force of attraction between two masses. It is always attractive, as mass does not have a negative counterpart. 2. **Inverse-Square Law**: - Both forces follow the inverse-square law, which states that the force between two objects is inversely proportional to the square of the distance between them. This can be mathematically expressed as: - For electrostatic force (Coulomb's Law): \[ F_e = k \frac{|q_1 q_2|}{r^2} \] where \( F_e \) is the electrostatic force, \( k \) is Coulomb's constant, \( q_1 \) and \( q_2 \) are the magnitudes of the charges, and \( r \) is the distance between the charges. - For gravitational force (Newton's Law of Gravitation): \[ F_g = G \frac{m_1 m_2}{r^2} \] where \( F_g \) is the gravitational force, \( G \) is the gravitational constant, \( m_1 \) and \( m_2 \) are the masses, and \( r \) is the distance between the masses. 3. **Why Option C is Correct**: - Since both forces decrease in strength with the square of the distance, they share this fundamental characteristic, making option C accurate. ### Analysis of Other Options: - **Option A**: "Electrostatic forces are always attractive, while gravitational forces can be both attractive and repulsive." - **Why it's wrong**: This statement is incorrect because while electrostatic forces can be both attractive and repulsive, gravitational forces are always attractive. Therefore, this option misrepresents the nature of gravitational forces. - **Option B**: "Gravitational forces are significantly stronger than electrostatic forces at the atomic scale." - **Why it's wrong**: This statement is misleading. At the atomic scale, electrostatic forces are actually much stronger than gravitational forces. For example, the electrostatic force between electrons and protons in an atom is vastly greater than the gravitational force acting on them. In fact, the ratio of the strength of the electrostatic force to the gravitational force is approximately \( 10^{36} \). - **Option D**: "Electrostatic forces act over much larger distances compared to gravitational forces." - **Why it's wrong**: This statement is also incorrect. Both forces can act over large distances, but the effective range of electrostatic forces is limited by the presence of other charges and the medium in which they exist. Gravitational forces, while they can act over vast distances (like between planets), are generally weaker than electrostatic forces at smaller scales. ### Summary: - Both electrostatic and gravitational forces follow an inverse-square law. - Electrostatic forces can be attractive or repulsive, while gravitational forces are always attractive. - At the atomic scale, electrostatic forces are much stronger than gravitational forces. - The effective range of both forces can vary, but they do not inherently act over larger distances in a comparative sense. This understanding of the relationship between electrostatic and gravitational forces is crucial for grasping fundamental concepts in physics, especially in fields like electromagnetism and gravitation.