Motion of a Charged Particle in a Magnetic Field (CIE A Level Physics)

• When a charged particle enters a uniform magnetic field, it travels in a circular path
• This is because the direction of the magnetic force F will always be
  • perpendicular to the particle's velocity v
  • directed towards the centre of the path, resulting in circular motion

Circular motion of a charge in a magnetic field

In a magnetic field, a charged particle travels in a circular path as the force, velocity and field are all perpendicular

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

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

• Rearranging for the radius r gives an expression for the radius of the path of a charged particle in a perpendicular magnetic field:

• Where:
  
  • r = radius of the path (m)
  • m = mass of the particle (kg)
  • v = linear velocity of the particle (m s⁻¹)
  • B = magnetic field strength (T)
  • Q = charge of the particle (C)

• This equation shows that:
  • Faster moving particles with speed v move in larger circles (larger r): 
  • Particles with greater mass m move in larger circles: 
  • Particles with greater charge q move in smaller circles:  
  • Particles moving in a strong magnetic field B move in smaller circles: 

• The centripetal acceleration is in the same direction as the magnetic (centripetal) force
• This can be found using Newton's second law: