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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.
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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

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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.

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Questions & Answers

what is the weight of the earth in space
peterpaul Reply
As w=mg where m is mass and g is gravitational force... Now if we consider the earth is in gravitational pull of sun we have to use the value of "g" of sun, so we can find the weight of eaeth in sun with reference to sun...
Prince
g is not gravitacional forcé, is acceleration of gravity of earth and is assumed constante. the "sun g" can not be constant and you should use Newton gravity forcé. by the way its not the "weight" the physical quantity that matters, is the mass
Jorge
Yeah got it... Earth and moon have specific value of g... But in case of sun ☀ it is just a huge sphere of gas...
Prince
Thats why it can't have a constant value of g ....
Prince
not true. you must know Newton gravity Law . even a cloud of gas it has mass thats al matters. and the distsnce from the center of mass of the cloud and the center of the mass of the earth
Jorge
please why is the first law of thermodynamics greater than the second
Ifeoma Reply
define electric image.obtain expression for electric intensity at any point on earthed conducting infinite plane due to a point charge Q placed at a distance D from it.
Mateshwar Reply
explain the lack of symmetry in the field of the parallel capacitor
Phoebe Reply
pls. explain the lack of symmetry in the field of the parallel capacitor
Phoebe
does your app come with video lessons?
Ahmed Reply
What is vector
Ajibola Reply
Vector is a quantity having a direction as well as magnitude
Damilare
tell me about charging and discharging of capacitors
Ahemen Reply
a big and a small metal spheres are connected by a wire, which of this has the maximum electric potential on the surface.
Bundi Reply
3 capacitors 2nf,3nf,4nf are connected in parallel... what is the equivalent capacitance...and what is the potential difference across each capacitor if the EMF is 500v
Prince Reply
equivalent capacitance is 9nf nd pd across each capacitor is 500v
santanu
four effect of heat on substances
Prince Reply
why we can find a electric mirror image only in a infinite conducting....why not in finite conducting plate..?
Rima Reply
because you can't fit the boundary conditions.
Jorge
what is the dimensions for VISCOUNSITY (U)
Branda
what is thermodynamics
Aniket Reply
the study of heat an other form of energy.
John
heat is internal kinetic energy of a body but it doesnt mean heat is energy contained in a body because heat means transfer of energy due to difference in temperature...and in thermo-dynamics we study cause, effect, application, laws, hypothesis and so on about above mentioned phenomenon in detail.
ing
It is abranch of physical chemistry which deals with the interconversion of all form of energy
Vishal
what is colamb,s law.?
Muhammad Reply
it is a low studied the force between 2 charges F=q.q`\r.r
Mostafa
what is the formula of del in cylindrical, polar media
Birengeso Reply
prove that the formula for the unknown resistor is Rx=R2 x R3 divided by R3,when Ig=0.
MAXWELL Reply
Practice Key Terms 3

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Source:  OpenStax, University physics volume 2. OpenStax CNX. Oct 06, 2016 Download for free at http://cnx.org/content/col12074/1.3
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