An electron and a proton with equal momentum enter...

Name: Problem 1914, Chapter 13: JEE Physics
Uploaded: 2021-10-02T09:30:49-08:00
Duration: 1 min 20 s
Channel: Narayan Hari
Description: An electron and a proton with equal momentum enter perpendicularly into a uniform magnetic then. (a) The path of proton shall be more curved than that of electron. (b) The path of proton shall be less curved turn that of electron. (c) Both are equally curved. (d) Path of both will be straight line.

An electron and a proton with equal momentum enter perpendicularly into a uniform magnetic then. (a) The path of proton shall be more curved than that of electron. (b) The path of proton shall be less curved turn that of electron. (c) Both are equally curved. (d) Path of both will be straight line.

An electron and a proton with equal momentum enter perpendicularly into a uniform magnetic then.
(a) The path of proton shall be more curved than that of electron.
(b) The path of proton shall be less curved turn that of electron.
(c) Both are equally curved.
(d) Path of both will be straight line.

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Key Concepts

Charged Particle Motion in Magnetic Fields

A charged particle moving in a uniform magnetic field experiences a force (the Lorentz force) that is perpendicular to both its velocity and the magnetic field. This causes the particle to follow a curved or circular path when its velocity is perpendicular to the field.

Lorentz Force

The Lorentz force, given by F = qvB for particles moving perpendicular to the field, is responsible for the circular motion. It provides the centripetal force that bends the trajectory of the particle in the magnetic field.

Radius of Curvature (Cyclotron Radius)

The radius of the circular path, found using the formula r = p/(qB) where p is the momentum and q is the charge, shows that for equal momentum and equal magnitude of charge, the curvature of the paths will be the same. This formula is crucial in understanding why particles with the same momentum and charge magnitude have equal bending in a magnetic field.

Magnetic Rigidity

Magnetic rigidity is defined as the product of the magnetic field strength and the radius of curvature (B?). It quantifies how resistant a charged particle's path is to being curved by a magnetic field, linking the particle's momentum and charge to its trajectory.

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