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

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

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:

 Motion of a Charged Particle in a Uniform Magnetic Field equation 1

  • 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:

Motion of a Charged Particle in a Uniform Magnetic Field equation 2

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

Motion of a Charged Particle in a Uniform Magnetic Field equation 3

  • 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

Motion of a Charged Particle in a Uniform Magnetic Field Worked Example equation 1

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

Motion of a Charged Particle in a Uniform Magnetic Field Worked Example equation 2

Step 3: Substitute in values

Motion of a Charged Particle in a Uniform Magnetic Field Worked Example equation 3Motion of a Charged Particle in a Uniform Magnetic Field Worked Example equation 4

 

 

 

 

 

 

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