Motion of a Charged Particle in a Uniform 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 FB will always be perpendicular to its velocity v
- FB 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 FB 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
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 circle path of the electron.
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
