- 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 will always be perpendicular to its velocity v
- F will always be directed towards the centre of the path in circular motion
A charged particle moves 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:
- F = centripetal force (N)
- 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 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:
- 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
- The centripetal acceleration is in the same direction as the centripetal (and magnetic) force
- This can be found using Newton's second law:
F = ma
An electron with a 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 of the electron.
Make sure you're comfortable with deriving the equation for the radius of the path of a particle travelling in a magnetic field, as this is a common exam question.
Similar to orbits in a gravitational field, any object moving in circular motion will obey the equations of circular motion. Make sure to refresh your knowledge of these equations.