30 A particle has a charge q, a mass m, a linear momentum30of magnitude p, and a kinetic energy K. The particle moves in a cir-cular orbit of radius R perpendicular to a uniform magnetic field B.Show that (a) p = BqR and (b) K = }B²q²R?/m.

Answered: A particle has a charge q, a mass m, a…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

A particle has a charge q, a mass m, a linear momentum
30
of magnitude p, and a kinetic energy K. The particle moves in a cir-
cular orbit of radius R perpendicular to a uniform magnetic field B.
Show that (a) p = BqR and (b) K = }B²q²R?/m.

Expert Solution

Step 1

In a circular path, the magnetic field provides the centripetal acceleration to the particle.

Thus, the centripetal force is equal to the magnetic force.

$F_{C} = F$

$\frac{m v^{2}}{R} = v q B$ … $(1)$

Here, $F_{C}$ is the centripetal force, $F$ is the magnetic force, $m$ is the mass of the charge particle, $v$ is the velocity of the particle, $R$ is the radius of the orbital circuit, $q$ is the charge, and $B$ is the magnetic field.

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