Radius of a Charged Particle in a Magnetic Field (Edexcel A Level Physics): Revision Note

Radius of a Charged Particle in a Magnetic Field

• 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