Problem 4 - Master Resource Book in JEE Main Physics

Question

An electron and a proton are moving under the influence of mutual forces. In calculating the change in the kinetic energy of the system during motion, one ignores the magnetic force of one on another. This is because, \(\quad\) [NCERT Exemplar] (a) the two magnetic forces are equal and opposite, so they produce no net effect (b) the magnetic forces do no work on each particle (c) the magnetic forces do equal and opposite (but non-zero) work on each particle (d) the magnetic forces are necessarily negligible

Step-by-Step Solution

Answer

(b) the magnetic forces do no work on each particle.

Step 1: Understanding Magnetic Forces

When charged particles such as an electron and a proton are in motion, they experience magnetic forces due to their velocities and the magnetic fields they generate. However, the magnetic force is always perpendicular to the direction of motion of the charge.

Step 2: Evaluating Work Done by Magnetic Forces

Work done is defined as the force applied on an object times the displacement in the direction of the force. For magnetic forces, since they are perpendicular to the velocity of the particles, the displacement in the direction of the force is zero.

Step 3: Conclusion on Magnetic Force Work

Since there is no displacement in the direction of a magnetic force, the work done by a magnetic force is zero. Therefore, the magnetic forces do no work on either particle.

Step 4: Answer to the Given Options

Based on the analysis, the correct reason to ignore magnetic forces is because they do not perform work on the particles, aligning with option (b): the magnetic forces do no work on each particle.

Key Concepts

Kinetic Energy

Kinetic energy is the energy that a particle possesses due to its motion. It is directly related to the velocity of the particle. The formula used to calculate kinetic energy is \[ KE = \frac{1}{2} mv^2 \]where \( m \) is the mass and \( v \) is the velocity of the particle.
Unlike potential energy, kinetic energy is not confined to a specific position; instead, it is associated with the movement of the object itself.

• Kinetic energy increases with an increase in speed.
• Even particles at rest have potential to acquire kinetic energy if they start moving.
• Units of kinetic energy are the same as any form of work – Joules in the SI unit system.

When analyzing charged particles like an electron and a proton, their change in kinetic energy during interactions depends on the forces acting on them. Understanding kinetic energy helps in predicting how these particles will move when subjected to various forces.

Charged Particles Motion

When you think of charged particles such as electrons or protons, it's essential to acknowledge how they move under the influence of forces. These particles not only have electric charges but also create electric and magnetic fields when moving.

• As charged particles move, they generate a magnetic field, which affects other surrounding charged particles.
• Interactions between particles are highly dependent on their relative velocities and distances.
• The motion of charged particles can be characterized using concepts from both electric forces and magnetic forces.

When such particles move, they're influenced by the Lorentz force, which is a combination of electric and magnetic forces. This force determines the path and acceleration of charged particles. The motion under mutual forces of charged particles can result in changes to their energy and velocity.

Magnetic Forces in Physics

Magnetic forces are a fundamental aspect of physics, particularly in the study of electromagnetism. They occur when moving charges interact with magnetic fields, leading to a force perpendicular to their motion, commonly known as the Lorentz force.
For two charged particles, such as an electron and a proton, the mutual magnetic forces they exert on each other are vital. However, these forces do not contribute to the work done during their interaction.
This is because:

• Magnetic forces are always perpendicular to the direction of motion.
• The work done by a force is the force multiplied by the displacement in the force’s direction.
• Since the direction of magnetic force and displacement are perpendicular, no work is done.

Hence, while magnetic forces are crucial in determining trajectories, they do not directly change the kinetic energy or speed of the particles. Understanding this concept is key to solving problems where magnetic forces are involved.