Circular Path of Particles

• What path does a charged particle take in a uniform magnetic field?

  Circular path

  
• Why does a charged particle travel in a circular path in a magnetic field?

  The magnetic force is always perpendicular to velocity

  
• What does the magnetic force provide for a charged particle in circular motion?

  Centripetal force

  
• What is the equation for centripetal force?

  F = mv²/r
• What expression relates centripetal force to magnetic force on a charged particle?

  mv²/r = BQv
• How do you rearrange the equation for the radius of a charged particle's path?

  r = mv/BQ
• What does the variable 'r' represent in the equation r = mv/BQ?

  Radius of the path
• What happens to the radius of the path if the speed of the particle increases?

  The radius increases
• How does mass affect the radius of the path of a charged particle?

  Greater mass results in a larger radius
• What effect does a greater charge have on the radius of the path?

  It results in a smaller radius
• How does a stronger magnetic field affect the radius of the path?

  It results in a smaller radius
• What direction does centripetal acceleration have in relation to the magnetic force?

  Same direction as the magnetic force
• What is a cyclotron?

  A type of particle accelerator
• What does a cyclotron utilize to create a spiral path?

  Circular trajectory of charged particles

  
• What are some medical applications of cyclotrons?

  Produce tracers and high-energy radiation
• What are the components of a cyclotron?

  Two hollow semicircular electrodes, magnetic field, electric field
• What is the function of a cyclotron?

  1. Charged particles enter the dees
  2. Magnetic field applied perpendicular to path
  3. Electric field applied in gaps between dees
  4. Particles accelerate and spiral outwards
  5. Particles leave at desired speed

  
• What happens when charged particles enter the dees of a cyclotron?

  They move in a circular path

  
• What role does the electric field play in a cyclotron?

  Accelerates particles between the dees
• What energy do particles gain when crossing the gap between dees?

  QV (charge times voltage)
• What is the charge-to-mass ratio of an electron?

  1.76 × 10¹¹ C/kg
• How do you calculate the radius of the circular path of an electron in a magnetic field?

  Use r = mev/eB
• What is the radius of the circular path of an electron with given values?

  2.7 mm
• What are the key equations related to circular motion in a magnetic field?

  • F = mv²/r (centripetal force)
  • mv²/r = BQv (equating forces)
  • r = mv/BQ (radius of path)
• What should you refresh your knowledge on for circular motion in magnetic fields?

  • Equations of circular motion
  • Data sheet sections