Moving Charges in a Magnetic Field

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Force on a charged particle

A magnetic field will create a force on a charged particle. This is called the Lorentz force.

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Lorentz force

  • The Lorentz force always acts perpendicular to the velocity of a particle.
  • This means that the force acts as a centripetal force.
    • Particles in magnetic fields undergo circular motion.
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  • We know that the centripetal force is given by
    • Fc=mv2/r{F_c}=mv^2/r
  • If the particle is travelling in a magnetic field perpendicular to the field lines it must be acted upon by the Lorentz force
    • F=qvBF=qvB
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Calculation 2

  • If we equate the two forces we get
    • qvB=mv2/rqvB=mv^2/r
  • We can then rearrange to get the radius of the circle
    • r=mv/qBr=mv/qB

Particle Accelerators

A cyclotron is a method of accelerating particles.

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  • A cyclotron is made up of two semi-circular plates separated by a gap with a potential difference across it.
  • A magnetic field is applied so that it is perpendicular to the semi-circles.
  • Charged particles follow a circular path parallel to the plates due to the magnetic field.
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  • A positive particle reaches the gap every half rotation.
  • The voltage drop accelerates the particle towards the negative terminal across the gap.
  • The voltage across the gap is varied on every half rotation so that the particle speed is always increased.
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  • The radius of the circular motion is given by
    • r=mv/qBr=mv/qB
  • As the velocity of the particle increases, the radius of its circular motion increases.
  • The particle spirals out of the machine at a very high speed.

Jump to other topics

1Measurements & Errors

2Particles & Radiation


4Mechanics & Materials


6Further Mechanics & Thermal Physics (A2 only)

7Fields & Their Consequences (A2 only)

8Nuclear Physics (A2 only)

9Option: Astrophysics (A2 only)

10Option: Medical Physics (A2 only)

11Option: Engineering Physics (A2 only)

12Option: Turning Points in Physics (A2 only)

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