• 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_B?will always be perpendicular to its velocity?v
  • F_B?will always be directed towards the centre of the path

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

• The magnetic force?F_B?provides the?centripetal force?on the particle
• Recall the equation for centripetal force:

• Where:
  • m = mass of the particle (kg)
  • v = linear velocity of the particle (m s^-1)
  • r = radius of the orbit (m)
• Equating this to the 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:

• This equation shows that:
  • Faster moving particles with speed?v?move in larger circles (larger?r):?r?∝?v
  • Particles with greater mass?m?move in larger circles:?r?∝?m
  • 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

Step 1:?Write down the known quantities

Magnetic flux density, B = 6.2 mT

Electron speed, v = 3.0 × 10⁶?m s^-1

Step 2:?Write down the equation for the radius of a charged particle in a perpendicular magnetic field

Step 3:?Substitute in values