Edexcel A Level Physics

Revision Notes

8.5 Radius of a Charged Particle in a Magnetic Field

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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

Circular motion of charged particle, downloadable AS & A Level Physics revision notes

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:

7.8.5 Centripetal Force Equation

  • Where:
    • F = centripetal force (N)
    • m = mass of the particle (kg)
    • v = linear velocity of the particle (m s1)
    • r = radius of orbit (m)

 

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

Centripetal & Magnetic Force Equation

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

Radius of Magnetic Circular Path Equation

  • 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:

r equals fraction numerator p over denominator B q end fraction

  • 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

Worked example

An electron with charge-to-mass ratio of 1.8 × 1011 C kg-1 is travelling at right angles to a uniform magnetic field of flux density 6.2 mT. The speed of the electron is 3.0 × 106 m s-1.

Calculate the radius of the circular path travelled by the electron.

Circular Magnetic Field Worked Example

Exam Tip

Make sure you're comfortable with deriving the equation for the radius of the path of a charged particle travelling in a magnetic field, as this is a common exam question. 

Crucially, the magnetic force is always perpendicular to the velocity of a charged particle. Hence, it is a centripetal force and the equations for circular motion can be applied. 

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