An electron and a proton enter a magnetic field...

Name: Problem 33, Chapter 19: Master Resource Book in JEE Main Physics
Uploaded: 2022-01-15T15:45:00-08:00
Duration: 1 min 26 s
Channel: Hunza Gilgit
Description: An electron and a proton enter a magnetic field perpendicularly. Both have same kinetic energy. Which of the following is true ? (a) Trajectory of electron is less curved (b) Trajectory of proton is less curved (c) Both trajectories are equally curved (d) Both more on straight line path

An electron and a proton enter a magnetic field perpendicularly. Both have same kinetic energy. Which of the following is true ? (a) Trajectory of electron is less curved (b) Trajectory of proton is less curved (c) Both trajectories are equally curved (d) Both more on straight line path

An electron and a proton enter a magnetic field perpendicularly. Both have same kinetic energy. Which of the following is true ?
(a) Trajectory of electron is less curved
(b) Trajectory of proton is less curved
(c) Both trajectories are equally curved
(d) Both more on straight line path

Key Concepts

Lorentz Force

The Lorentz force is the force experienced by a charged particle when it moves through a magnetic field, expressed as F = qvB (for perpendicular entry). This force is always perpendicular to the velocity of the particle, causing the particle to move in a circular (or helical) path, with the radius of the path determined by the balance between the magnetic force and the centripetal force required for circular motion.

Circular Motion of Charged Particles

When a charged particle enters a magnetic field perpendicularly, it undergoes uniform circular motion because the magnetic force acts as the centripetal force. The radius of this motion is given by r = mv/(qB), where m is the mass of the particle, v is its speed, q is its charge, and B is the magnetic field strength. This relation is key to understanding differences in trajectory curvature for particles with varying properties.

Kinetic Energy and Momentum Relations

Kinetic energy (K = ½mv²) and momentum (p = mv) are fundamental quantities in mechanics. For particles with the same kinetic energy, their momenta depend inversely on the square root of their masses. This relationship is crucial when comparing how electrons and protons, which have vastly different masses, behave under the same kinetic energy conditions in a magnetic field.

Mass-to-Charge Ratio

The mass-to-charge ratio (m/q) is critical in determining the curvature of a charged particle's trajectory in a magnetic field. Since the radius of curvature is directly proportional to m/(qB), particles with a lower mass-to-charge ratio will have more tightly curved (smaller radius) paths compared to those with a higher ratio when subject to the same conditions.

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