Answered: A physicist builds an apparatus to…

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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A physicist builds an apparatus to measure the charge to mass ratio of ions. An ion is first accelerated to a speed of 6.50 ✕ 10⁷ m/s. It then passes through a region of magnetic field, with a magnitude of 4.09 ✕ 10⁻² T, perpendicular to the ion's velocity. Because the ion is moving so fast, it is only in the presence of the magnetic field for 2.00 ✕ 10⁻⁷ s. Upon exiting the magnetic field, the scientist measures that the ion was deflected a distance of 3.00 cm in a direction perpendicular to its initial velocity.

(a)

What is the ratio of the absolute value of the ion's charge to its mass (in C/kg)? Assume the velocity change is small, and that the component of the velocity along the ion's original direction does not change noticeably.

|q|

= C/kg

(b)

Suppose the physicist determines the ion is singly charged; that is, the magnitude of its charge is that of a proton. What is the mass of the ion (in kg)?

A physicist builds an apparatus to measure the charge to mass ratio of ions. An ion is first accelerated to a speed of \(6.50 \times 10^7 \, \text{m/s}\). It then passes through a region of a magnetic field, with a magnitude of \(4.09 \times 10^{-2} \, \text{T}\), perpendicular to the ion's velocity. Because the ion is moving so fast, it is only in the presence of the magnetic field for \(2.00 \times 10^{-7} \, \text{s}\). Upon exiting the magnetic field, the scientist measures that the ion was deflected a distance of \(3.00 \, \text{cm}\) in a direction perpendicular to its initial velocity.

(a) What is the ratio of the absolute value of the ion's charge to its mass (in C/kg)? Assume the velocity change is small, and that the component of the velocity along the ion's original direction does not change noticeably.

\[
\left| \frac{q}{m} \right| = \, \text{C/kg}
\]

(b) Suppose the physicist determines the ion is singly charged; that is, the magnitude of its charge is that of a proton. What is the mass of the ion (in kg)?

\[
\text{Mass of ion} = \, \text{kg}
\]

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