Question

STATEMENT-1 : Two uniform proton beams going in the same direction repel each other. STATEMENT-2 : Magnitude of electric force between two protons is always higher than magnetic force between them. (1) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement- 1 (2) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement- 1 (3) Statement-1 is True, Statement-2 is False (4) Statement- 1 is False, Statement- 2 is True.

Short answer

Option (2): Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.

Step-by-step solution

Analyze Statement-1

Two uniform proton beams going in the same direction will repel each other due to the electrostatic repulsion between the positively charged protons. Thus, Statement-1 is true.

Analyze Statement-2

The electric force between two protons is given by Coulomb's law and is generally much stronger than the magnetic force between the same two protons, which is due to their movement. Hence, Statement-2 is true.

Evaluate the explanation

While both statements are true, the primary reason that the proton beams repel each other is the electrostatic force, not because the electric force between two protons is always higher than the magnetic force. Therefore, Statement-2 does not correctly explain Statement-1.

Key concepts

Proton Beams

Proton beams are streams of protons that move together in the same direction. Protons are subatomic particles with a positive charge. When these charged particles are in motion, they create both electric and magnetic fields due to their charge and motion.

However, because protons have the same type of charge, they naturally repel each other according to Coulomb's law. This is why two proton beams, even when moving parallel to each other, will repel. This repulsion is due to the electrostatic force between the positively charged particles. It's crucial to understand that this force is independent of their motion direction; it solely depends on their charge.

Thus, even though proton beams might be directed in the same or different directions, the fundamental repulsive force remains the same due to their uniform positive charge.

Electromagnetic Forces

Electromagnetic forces are the combination of electricity and magnetism. When dealing with charged particles like protons, we look at both electric and magnetic forces.

The electric force between two charged objects is described by Coulomb's law. This force is relatively strong and depends on the amount of charge and the distance between the charges. In contrast, the magnetic force on a moving charge is a result of its velocity and the magnetic field it produces or interacts with.

In the context of proton beams, the electric repulsion is typically much stronger than the magnetic attraction. The electric force can be directly calculated using Coulomb's law, whereas the magnetic force involves velocity factors and is often much weaker due to the small speeds involved relative to the speed of light. This explains why, in most practical scenarios, the electric force dominates over the magnetic force between two protons.

Coulomb's Law

Coulomb's law describes the electric force between two point charges. It states that the force between the charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them:

\[ F = k_e \frac{q_1 q_2}{r^2} \]
where \( F \) is the force, \( k_e \) is Coulomb's constant, \( q_1 \) and \( q_2 \) are the charges, and \( r \) is the distance between the charges.

For two protons, \( q_1 \) and \( q_2 \) are both the charge of a proton, and the force is repulsive because both charges are the same and positive.
This repulsive force is quite substantial compared to other forces on the atomic scale.

Therefore, Coulomb's law helps us understand why proton beams repel each other strongly. Even if the protons are in motion, the dominant force between them is due to their charge, not their motion, aligning with the principles described in the exercise solution.