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Chapter 29: Q. 63 (page 833)

An antiproton is identical to a proton except it has the opposite charge, -e. To study antiprotons, they must be confined in an ultrahigh vacuum because they will annihilate—producing gamma rays—if they come into contact with the protons of ordinary matter. One way of confining antiprotons is to keep them in a magnetic field. Suppose that antiprotons are created with a speed of 1.5×104m/s and then trapped in a 2.0mT magnetic field. What minimum diameter must the vacuum chamber have to allow these antiprotons to circulate without touching the walls?

Short Answer

Expert verified

The minimal diameter needed for antiprotons to circulate without colliding with the walls is 0.1565m

Step by step solution

01

 Step :1 Introduction

The given is the velocity 1.5*104m/s, 2.0mT Magnetic field, Mass is 1.67*10-27kg(based on the formula used), q is 1.6*10-19C(based on the formula used). The objective is to find the The minimal diameter needed for antiprotons to circulate without colliding with the walls. the problem is solved using the equation of circular motion of magnetic field

02

Step :2 Velocity 

F=qvB

F=mar

F=mv2r

Fr=mv2

r=mv2F

r=mv2qvB

r=mvqB

d=2mvqB [diameter(d)=2*radius(r)]

d=2*(1.67*10-27kg)*(1.5*104m/s)(1.6*10-19C)*(2*10-3T)

d=0.1565m

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