BuyFindarrow_forward

College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300

Solutions

Chapter
Section
BuyFindarrow_forward

College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300
Textbook Problem

A proton (charge +e, mass mp), a deuteron (charge +e, mass 2mp), and an alpha particle (charge +2e, mass 4mp) are accelerated from rest through a common potential difference ΔV. Each of the particles enters a uniform magnetic field B , with its velocity in a direction perpendicular to B . The proton moves in a circular path of radius τp. In terms of τp, determine (a) the radius rd of the circular orbit for the deuteron and (b) the radius for the alpha particle.

a)

To determine
The radius rd of the circular path for the deuteron in terms of the radius of proton path rp .

Explanation

Given info: A proton (charge +e, mass mp ), a deuteron (charge +e, mass 2mp ), and an alpha particle (charge + 2e, mass 4mp ) areaccelerated from rest through common potential difference ΔV . The magnetic field is B . The particles velocities and the magnetic field are perpendicular to each other. The radius of the protons path is rp . The deuteron of the protons path is rd . The radius of the alpha particles path is rα .

Explanation:

Consider a particle which is accelerated from rest through a potential difference ΔV . Charge of the particle is q and mass is m .

From conservation of energy,

KEf+PEf=KEi+PEi

Since the initially the particle is at rest,

KEf+PEf=0+PEi

On re-arrangement,

KEf=PEiPEf       (1)

Since the potential energy of a charged particle is charge times potential,

12mv2=qViqVf=q(ViVf)=qΔV

On re-arrangement,

v=2qΔVm       (2)

Since the magnetic field supplies the centripetal acceleration,

qv

b)

To determine
The radius rα of the circular path for the alpha particle in terms of the radius of proton path rp .

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Additional Science Solutions

Find more solutions based on key concepts

Show solutions add

Which of these advantages do sports drinks provide over plain water? They taste good and so may lead people to ...

Nutrition: Concepts and Controversies - Standalone book (MindTap Course List)

What are common epigenetic changes?

Introduction to General, Organic and Biochemistry

How much energy is produced when the Sun converts 1 kg of mass into energy?

Horizons: Exploring the Universe (MindTap Course List)

A 75.0-kg firefighter slides down a pole while a constant friction force of 300 N retards her motion. A horizon...

Physics for Scientists and Engineers, Technology Update (No access codes included)