Question

Two protons placed near one another with no other objects close by would a) accelerate away from each other. b) remain motionless. c) accelerate toward each other. d) be pulled together at constant speed. e) move away from each other at constant speed.

Short answer

Answer: a) accelerate away from each other

Step-by-step solution

Identify the force acting on the protons

In this situation, the only significant force acting on the protons is the electrostatic force. According to Coulomb's Law, this force can be calculated using the formula: F = k * (q1 * q2) / r^2 where F is the force, k is the electrostatic constant, q1 and q2 are the charges of the protons, and r is the distance between them. Since both protons have the same positive charge, this force will be repulsive.

Determine the motion of protons under the influence of the electrostatic force

Since the electrostatic force is repulsive and is the only force acting on the protons, they will experience an acceleration away from each other due to this force. Newton's second law states that: F = m * a where F is the force, m is the mass of the particle, and a is its acceleration. In this case, the repulsive force between the protons will cause them to accelerate away from each other. Now, let's analyze each option given in the exercise: a) accelerate away from each other: This is the correct answer based on our understanding of Coulomb's Law and Newton's second law. b) remain motionless: This is incorrect because the repulsive force between the protons will cause them to accelerate away from each other. c) accelerate toward each other: This is incorrect because the electrostatic force between the protons is repulsive, not attractive. d) be pulled together at constant speed: This is incorrect because the force between the protons is repulsive, not attractive. e) move away from each other at constant speed: This is incorrect because the protons will experience acceleration due to the repulsive electrostatic force and will not move at a constant speed. Therefore, the correct answer is option a) accelerate away from each other.

Key concepts

Coulomb's Law

Coulomb's Law describes the force between two charged particles, such as protons. It states that the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. This can be expressed with the formula: \( F = k \frac{q_1 q_2}{r^2} \).

• \( F \): The magnitude of the force between two charges.
• \( k \): The electrostatic constant, approximately \( 8.99 \times 10^9 \, \text{N m}^2/\text{C}^2 \).
• \( q_1 \), \( q_2 \): The charges of the particles.
• \( r \): The distance between the charges.

In our problem, both protons have the same positive charge, so the force between them is repulsive. This means that rather than attracting each other, they push away from one another. Understanding this foundational concept helps us predict the behavior of these particles when placed near each other.

Newton's Second Law

Newton's Second Law of motion states that the force acting on an object is equal to the mass of the object multiplied by its acceleration: \( F = m \cdot a \).

• \( F \): Force applied on the object.
• \( m \): Mass of the object.
• \( a \): Acceleration of the object.

In the context of our exercise, this law explains that the electrostatic force (derived from Coulomb's Law) on the protons will result in their acceleration. Because the force is repulsive, the protons will accelerate away from each other. The law provides a way to quantify how much they will accelerate, considering the electrostatic force and the mass of the protons.

Electrostatic Force

Electrostatic Force is the force exerted between electrically charged particles. It can be either attractive or repulsive. The nature of the force depends on the types of charges involved:

• Like charges (e.g., two protons) will repel each other.
• Opposite charges (e.g., a proton and an electron) will attract each other.

In our scenario, we consider the repulsive force between two protons. Since both have positive charges, they push away from one another. This force is powerful and decreases with distance, as described by Coulomb's Law. Understanding this concept allows us to predict how charged objects will move in space.

Repulsive Force between Protons

The repulsive force between protons is a direct application of Coulomb's Law. Since protons have the same positive charge, they naturally repel each other. This is an important concept in physics because it explains why protons require a strong nuclear force to be held together in an atomic nucleus despite their natural repulsion. When isolated, as in the exercise, the repulsive electrostatic force causes the protons to accelerate away from each other. This highlights the dynamic interactions among charged particles and is a fundamental principle governing the structure of matter and the behavior of atomic particles. By understanding the repulsive force, students can better grasp how protons and other charged particles interact in different scenarios.