1. Home
  2. University physics volume 2
  3. Unit 2. electricity and magnetism
  4. Magnetic forces and fields
  5. Applications of magnetic forces

11.7 Applications of magnetic forces and fields  (Page 3/11)

<< Chapter < Page
  University physics volume 2     Page 3 / 11
Chapter >> Page >

Particles are accelerated to very high energies with either linear accelerators or synchrotrons. The linear accelerator accelerates particles continuously with the electric field of an electromagnetic wave that travels down a long evacuated tube. The Stanford Linear Accelerator (SLAC) is about 3.3 km long and accelerates electrons and positrons (positively charged electrons) to energies of 50 GeV. The synchrotron is constructed so that its bending magnetic field increases with particle speed in such a way that the particles stay in an orbit of fixed radius. The world’s highest-energy synchrotron is located at CERN, which is on the Swiss-French border near Geneva. CERN has been of recent interest with the verified discovery of the Higgs Boson (see Particle Physics and Cosmology ). This synchrotron can accelerate beams of approximately 10 13 protons to energies of about 10 3 GeV.

Accelerating alpha-particles in a cyclotron

A cyclotron used to accelerate alpha-particles ( m = 6.64 × 10 −27 kg , q = 3.2 × 10 −19 C ) has a radius of 0.50 m and a magnetic field of 1.8 T. (a) What is the period of revolution of the alpha-particles? (b) What is their maximum kinetic energy?

Strategy

  1. The period of revolution is approximately the distance traveled in a circle divided by the speed. Identifying that the magnetic force applied is the centripetal force, we can derive the period formula.
  2. The kinetic energy can be found from the maximum speed of the beam, corresponding to the maximum radius within the cyclotron.

Solution

  1. By identifying the mass, charge, and magnetic field in the problem, we can calculate the period:
    T = 2 π m q B = 2 π ( 6.64 × 10 −27 kg ) ( 3.2 × 10 −19 C ) ( 1.8 T ) = 7.3 × 10 −8 s.
  2. By identifying the charge, magnetic field, radius of path, and the mass, we can calculate the maximum kinetic energy:
    1 2 m v max 2 = q 2 B 2 R 2 2 m = ( 3.2 × 10 −19 C ) 2 ( 1.8 T ) 2 ( 0.50 m ) 2 2 ( 6.65 × 10 −27 kg ) = 6.2 × 10 −12 J = 39 MeV.
Got questions? Get instant answers now!

Check Your Understanding A cyclotron is to be designed to accelerate protons to kinetic energies of 20 MeV using a magnetic field of 2.0 T. What is the required radius of the cyclotron?

0.32 m

Got questions? Get instant answers now!

Summary

  • A mass spectrometer is a device that separates ions according to their charge-to-mass ratios by first sending them through a velocity selector, then a uniform magnetic field.
  • Cyclotrons are used to accelerate charged particles to large kinetic energies through applied electric and magnetic fields.

Key equations

Force on a charge in a magnetic field F → = q v → × B →
Magnitude of magnetic force F = q v B sin θ
Radius of a particle’s path in a magnetic field r = m v q B
Period of a particle’s motion in a magnetic field T = 2 π m q B
Force on a current-carrying wire in a uniform magnetic field F → = I l → × B →
Magnetic dipole moment μ → = N I A n ^
Torque on a current loop τ → = μ → × B →
Energy of a magnetic dipole U = − μ → · B →
Drift velocity in crossed electric and magnetic fields v d = E B
Hall potential V = I B l n e A
Hall potential in terms of drift velocity V = B l v d
Charge-to-mass ratio in a mass spectrometer q m = E B B 0 R
Maximum speed of a particle in a cyclotron v max = q B R m

Conceptual questions

Describe the primary function of the electric field and the magnetic field in a cyclotron.

Got questions? Get instant answers now!

Questions & Answers

distinguish between anatomy and physiology
Amina Reply
Anatomy is the study of internal structure of an organism while physiology is the study of the function/relationship of the body organs working together as a system in an organism.
adeyeye
distinguish between anatomy and physiology
Erny Reply
regional anatomy is the study of the body regionally
Ismail Reply
what is the meaning of regional anatomy
Aminat Reply
epithelial tissue: it covers the Hollow organs and body cavities
Esomchi Reply
in short way what those epithelial tissue mean
Zainab Reply
in short way what those epithelial tissue mean
Chizoba
What is the function of the skeleton
Lilias Reply
movement
Ogar
Locomotion
Ojo
support
Aishat
and body shape/form
Aishat
what is homeostasis?
Samuel Reply
what's physiology
AminchiSunday Reply
what is physiology
AminchiSunday
physically is the study of the function of the body
Najaatu
that is what I want ask
YAU
u are wright
YAU
pls what are the main treatment of hiccups
YAU
physiology is the study of the function of the body
Najaatu
hiccups happen when something irritates the nerves that course your diaphragm to contract
Najaatu
how did hypothalamus manege to control all activities of the various hormones
malual
what is protein
Abdulsalam
how can I treat pain a patient feels after eating meals
Namuli Reply
how do I treat a three year old baby of skin infection?
Okocha Reply
It depends on the type of infection. Bacterial, fungal, parasitic or viral?
schler
if you can share the sign ad symptoms of the skin infection then u geh the treatment cox they're different sign ad symptoms of skin infection with different treatment
Sa
the sign and symptoms of maleria
Abdulsalam
prostaglandin and fever
Maha Reply
yes
rayyanu
welcome sir
rayyanu
prostaglandin E2 is the final mediator.
Lemlem
prostaglandin E2 is the final mediator of fever.
Lemlem
yes
Agabi
good evening
Jediel
tissue.
Akoi
explain
Chizoba
Hi
Anya
,good evening
Anya
Discuss the differences between taste and flavor, including how other sensory inputs contribute to our  perception of flavor.
John Reply
taste refers to your understanding of the flavor . while flavor one The other hand is refers to sort of just a blend things.
Faith
While taste primarily relies on our taste buds, flavor involves a complex interplay between taste and aroma
Kamara
which drugs can we use for ulcers
Ummi Reply
omeprazole
Kamara
what
Renee
what is this
Renee
is a drug
Kamara
of anti-ulcer
Kamara
Omeprazole Cimetidine / Tagament For the complicated once ulcer - kit
Patrick
what is the function of lymphatic system
Nency Reply
Not really sure
Eli
to drain extracellular fluid all over the body.
asegid
The lymphatic system plays several crucial roles in the human body, functioning as a key component of the immune system and contributing to the maintenance of fluid balance. Its main functions include: 1. Immune Response: The lymphatic system produces and transports lymphocytes, which are a type of
asegid
to transport fluids fats proteins and lymphocytes to the blood stream as lymph
Adama
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply
<< Chapter < Page Page > Chapter >>
Practice Key Terms 3

Read also:

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, University physics volume 2. OpenStax CNX. Oct 06, 2016 Download for free at http://cnx.org/content/col12074/1.3
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'University physics volume 2' conversation and receive update notifications?

Ask