# CIE A Level Physics复习笔记20.1.8 Motion of a Charged Particle in a Magnetic Field

### 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: ∝ 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: ∝ 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   