Charged particles in magnetic fields

A positron produced a track in a detector, as shown.

(Source: © Science Source/SCIENCE PHOTO LIBRARY)

Which of the following is the direction of the magnetic field in this detector?

Complete the particle equation for this decay.

Explain whether the conservation laws of charge and baryon number are obeyed for this decay.

The table summarises the charges for three types of quark.

The sigma particle has one strange quark within its structure.

State why the neutron does not leave a track.

The initial momentum of the positive pion is 1.1 10^–19N s. The scale of the diagram is 1 cm represents 15 cm.

Determine the magnitude of the magnetic flux density acting perpendicularly to the tracks.

Particle accelerators produce beams of high speed charged particles which are used to investigate particle collisions. New particles are created during the collisions.

In the Large Hadron Collider (LHC), protons are maintained in a circular path by the force exerted on the protons due to a magnetic field.

The magnetic flux density required to maintain the protons in a circular path increases as the kinetic energy of the protons increases.

Explain why.

Calculate the magnetic flux density required to maintain the protons in the LHC when the protons are travelling at a speed of 3.0 10⁷m s^–1.

circumference of LHC = 27 km

A maximum of 13 600 GeV of energy is available to create a new particle.

Calculate the theoretical maximum mass, in kg, of the new particle.

*(b) Fifty years ago, fixed‑target collision experiments were carried out at the Stanford Linear Accelerator Centre (SLAC). In these experiments, high speed particles were made to collide with a stationary target.

Currently, colliding beam experiments are carried out at SLAC. In these experiments, high speed particles travelling in opposite directions are made to collide head‑on.

For a given total energy in the collision, colliding beam experiments allow particles to be created with a larger mass than could be created in a fixed‑target experiment.

Explain why colliding beam experiments allow a new particle with the larger mass to be created. You should consider how the conservation of energy and the conservation of momentum apply to each type of collision.

The decay of a positive muon produced a positron, an electron neutrino and a muon antineutrino. The diagram shows the tracks formed in a particle detector.

A muon belongs to a family of particles called leptons.

State two features that all particles in the lepton family have in common.

Write a nuclear equation for the decay of the muon (μ) described above.

Describe the role of the magnetic field in a particle detector.

Explain how the diagram gives evidence that a particle or particles, other than the positron, were produced in this decay.

A delta particle decays into a proton and a pion.

The diagram shows tracks in a particle detector formed when the delta particle decays.

State why it can be concluded from the diagram that the delta particle is neutral.

Deduce the charge on the pion.

Complete the particle equation for the decay of the delta (Δ⁰) particle.

State why the delta particle must be classified as a baryon based on the evidence of its decay.

Explain how the momentum of the proton compares with the momentum of the pion.

The mass of the delta particle is 1232 MeV/c².

Calculate the mass of the delta particle in kg.

The mass of the proton is 939 MeV/c² and the mass of the pion is 139 MeV/c².

Explain why the sum of the masses of the two particles after the decay is not equal to the mass of the delta particle.

Questions 4 and 5 refer to the information below.

A demonstration is carried out using a beam of electrons in an evacuated tube.

When electrons hit a fluorescent screen, light is emitted. A piece of metal, in the shape of a Maltese cross, stops electrons and produces a shadow on the screen as shown.

5 The screen is viewed by an observer at point X in the diagram above. A magnetic field is directed at the beam of electrons. This causes the shadow to move upwards on the screen in the direction OM.

In which of the following directions is the magnetic field acting as seen by this observer?

A negatively charged pion decays into a muon and an antineutrino. The diagram shows tracks in a particle detector formed in such an event.

Deduce whether the antineutrino is charged, giving two reasons for your decision.

Write a particle equation to represent this decay.

According to the standard model, the pion and muon are classified within two different groups of particles.

State which group each particle belongs to and describe the two groups.

The momentum of the pion just before it decays is 9.1 × 10⁻²⁰N s.

Determine the magnetic flux density of the magnetic field which acts in the detector and state its direction.

Scale of diagram 1 cm represents 10 cm

Use a vector diagram to determine the momentum of the antineutrino.

The initial momentum of the muon is 1.59 × 10⁻¹⁹N s.

A negatively charged pion decays into a muon and an antineutrino. The diagram shows tracks in a particle detector formed in such an event.

Deduce whether the antineutrino is charged, giving two reasons for your decision.

Write a particle equation to represent this decay.

According to the standard model, the pion and muon are classified within two different groups of particles.

State which group each particle belongs to and describe the two groups.

The momentum of the pion just before it decays is 9.1 × 10⁻²⁰N s.

Determine the magnetic flux density of the magnetic field which acts in the detector and state its direction.

Scale of diagram 1 cm represents 10 cm

Use a vector diagram to determine the momentum of the antineutrino.

The initial momentum of the muon is 1.59 × 10⁻¹⁹N s.

At the end of the 19th century, J.J. Thompson used electric and magnetic fields to deflect beams of charged particles. A photograph of his apparatus is shown.

Electrons were accelerated through a potential difference to produce a beam of high-energy electrons. The beam was then deflected in perpendicular directions by the magnetic and electric fields. The final position of the beam on the screen was determined by the charge and mass of the electrons.

Explain how electrons from the source become a beam of high-energy electrons.

An electron is travelling left to right and enters a region of uniform magnetic field as shown below. The direction of the magnetic field is perpendicular to the direction of travel of the electron.

The magnetic field deflects the electron in the direction up the page.

Explain the direction of the magnetic field that would produce this deflection.

Explain why the electron would travel in a circular path if no other forces acted on it.

In a modern version of Thompson’s experiment, a uniform electric field of electric field strength E is applied so that the electric and magnetic forces on the electrons are equal and in opposite directions.

Show that for electrons to be undeflected their velocity must be given by

where B is the magnetic flux density of the magnetic field.

The beam is produced by accelerating electrons through a potential difference of 250 V. The electric field strength is 1.4 × 10⁴V m⁻¹. The magnetic flux density is

Calculate the value of the specific charge e/m for the electron using this data.

In his original experiments, Thompson determined the specific charge of a range of particles. His results indicated that the specific charge of an electron is about 2000 times bigger than that for a hydrogen ion.

Deduce what conclusion can be made from this information.

At the end of the 19th century, J.J. Thompson used electric and magnetic fields to deflect beams of charged particles. A photograph of his apparatus is shown.

Electrons were accelerated through a potential difference to produce a beam of high-energy electrons. The beam was then deflected in perpendicular directions by the magnetic and electric fields. The final position of the beam on the screen was determined by the charge and mass of the electrons.

Explain how electrons from the source become a beam of high-energy electrons.

An electron is travelling left to right and enters a region of uniform magnetic field as shown below. The direction of the magnetic field is perpendicular to the direction of travel of the electron.

The magnetic field deflects the electron in the direction up the page.

Explain the direction of the magnetic field that would produce this deflection.

Explain why the electron would travel in a circular path if no other forces acted on it.

In a modern version of Thompson’s experiment, a uniform electric field of electric field strength E is applied so that the electric and magnetic forces on the electrons are equal and in opposite directions.

Show that for electrons to be undeflected their velocity must be given by

where B is the magnetic flux density of the magnetic field.

The beam is produced by accelerating electrons through a potential difference of 250 V. The electric field strength is 1.4 × 10⁴V m⁻¹. The magnetic flux density is

Calculate the value of the specific charge e/m for the electron using this data.

In his original experiments, Thompson determined the specific charge of a range of particles. His results indicated that the specific charge of an electron is about 2000 times bigger than that for a hydrogen ion.

Deduce what conclusion can be made from this information.

A current / and a magnetic field of flux density B are applied to a slice of semiconductor

Calculate the angle of the Earth’s magnetic field to the horizontal.

Electric and magnetic fields can be used in particle accelerators.

Which row in the table correctly describes the use of electric and magnetic fields in the particle accelerator indicated?

The discovery of the Higgs particle was an important contribution to our understanding of particle physics.

Describe the standard model for subatomic particles. You should identify the fundamental particles and the composition of the particles we can observe.

The mass of the Higgs particle is 2.2 10^–25 kg.

Calculate this mass in GeV/c².

The Higgs particle was discovered using the Large Hadron Collider (LHC) in 2012. Two beams of very high energy protons, moving in opposite directions, were made to collide.

Explain the need for such high energy collisions.

The beams of protons are contained within a ring of superconducting magnets.

Calculate the momentum of a proton in a beam.

magnetic field strength = 8.3 T circumference of the ring = 27 km

State the total momentum of the products of the collision between the two beams of protons.

The LHC accelerates protons until they gain energies of about 7 TeV.

A student used the equation E = to predict the energy of a proton in the beam, using the momentum calculated in (c)(ii), but found the energy was far higher than 7 TeV.

Explain why.

Proton beam therapy is being introduced in the UK as a new cancer treatment.

A beam of protons is accelerated by a cyclotron to an energy of 23 MeV and is then focused onto a tumour.

*(a) Explain how the cyclotron produces the high‑energy proton beam.

Conventional treatment may use X‑rays to deliver energy to a tumour.

The graph shows the variation of energy delivered with penetration below the skin for a beam of protons and a beam of X‑rays.

Deduce why the beam of protons could be a more effective treatment for tumours than a beam of X‑rays.

Developing new cancer treatments is expensive.

Give two possible reasons why money should be provided for the development of this new cancer treatment.

Mass spectrometry is a technique used to separate ions based on their charge to mass ratio.

The atoms in a sample are ionised and then accelerated and formed into a fine beam. This beam is passed into a region of uniform magnetic field and the ions are deflected by different amounts according to their mass.

Analysis of mass spectrometer data shows that chlorine exists in nature as two isotopes, chlorine-35 and chlorine-37.

State what is meant by isotopes.

In a mass spectrometer, chlorine-35 ions are accelerated through a potential difference of 8.50 kV to produce an ion beam.

Show that the speed of singly ionised chlorine-35 atoms is about 2.2 × 10⁵ m s⁻¹.

mass of an ion of chlorine-35 = 34.97 u

In most mass spectrometers the ions are passed through a velocity selector, after being accelerated, to produce a beam of ions of a particular velocity. The velocity selector consists of a pair of parallel plates, across which a potential difference (p.d.) is applied to create an electric field.

In one mass spectrometer the plates are 2.5 cm apart and a p.d. of 135 V is applied.

A magnetic field is also applied to produce a force on the ions in the opposite direction to the force from the electric field. For one particular speed the ions travel in a straight line and emerge from the selector.

Add to the diagram to indicate the directions of the electric field and the magnetic field.

The magnetic flux density applied to the velocity selector is 24.5 mT.

Deduce whether this magnetic flux density is suitable to produce a beam of chlorine-35 ions of speed 2.2 × 10⁵ m s⁻¹.

After passing through the velocity selector the ion beam enters a region of uniform magnetic flux density 0.35 T with the ions travelling at right angles to the field direction.

Explain why the ions travel in a circular path.

Calculate the radius of the circular path.

The diagram shows the path of the chlorine-35 ions in the field. Chlorine-37 ions enter the magnetic field with the same velocity.

1. Add another line to the diagram to show the path of these chlorine-37 ions.

2. Explain any differences in the paths.