• A charged particle in uniform?magnetic field?which is perpendicular to its direction of motion travels in a?circular?path
• This is because the?magnetic force?F?is always perpendicular to its velocity?v
  • F?will always be directed towards the centre of orbit

   

A charged particle travels in a circular path in a magnetic field

• The magnetic force?F?provides the?centripetal force?on the particle
• The equation for centripetal force is:

• Where:
  • F?= centripetal force (N)
  • m?= mass of the particle (kg)
  • v?= linear velocity of the particle (m s–1)
  • r?= radius of orbit (m)

   

• Equating this to the magnetic force on a moving charged particle gives the equation:

• Rearranging for the radius?r?obtains the equation for the radius of the orbit of a charged particle in a perpendicular magnetic field:

• The product of mass?m?and velocity?v?is momentum?p
  • Therefore, the radius of the charged particle in a magnetic field can also be written as:

• 
• ?Where:
  • r?= radius of orbit (m)
  • p?= momentum of charged particle (kg m s–1)
  • B?= magnetic field strength (T)
  • q?= charge of particle (C)

• This equation shows that:
  • Particles with a larger momentum (either larger mass?m?or speed?v) move in larger circles, since?r ∝?p
  • Particles with greater charge?q?move in smaller circles:?r?∝?1 /?q
  • Particles moving in a strong magnetic field?B?move in smaller circles:?r?∝?1 /?B