CIE A Level Physics复习笔记20.1.8 Motion 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_B will always be perpendicular to its velocity v
  • F_B 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 F_B 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

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