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Expert-verified Found in: Page 868 ### Physics For Scientists & Engineers

Book edition 9th Edition
Author(s) Raymond A. Serway, John W. Jewett
Pages 1624 pages
ISBN 9781133947271 # For your senior project, you would like to build a cyclotron that will accelerate protons to $10$% of the speed of light. The largest vacuum chamber you can find is $50$cm in diameter. What magnetic field strength will you need?

You will need the magnetic field strength is $1.25$T

See the step by step solution

## Introduction

The given is the speed of the particle is $10$$%$ of the speed of light and the diameter of the chamber is $50cm$. The objective is to find the magnetic field strength.

## Step 1

The cyclotron motion is defined as a particle traveling in a uniform circular motion perpendicular to the magnetic field at a constant speed. The radius of the circular motion produced by the magnetic field is related to it by an equation in the form

${r}_{cyc}=\frac{mv}{qB}$

Where $q$ denotes the particle's charge, $v$ denotes its speed, $B$ denotes the magnetic field, and $m$ denotes the particle's mass. Because the particle's speed is $10%$

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