M6-S2: Charged Particles in Magnetic Fields

  • analyse the interaction between charged particles and uniform magnetic fields, including: (ACSPH083)

    • acceleration, perpendicular to the field, of charged particles
    • the force on the charge `F=qv_(_|_)B = qvBsintheta`

 

Force in Magnetic Fields

  • A moving charged particle experiences a force within an external magnetic field. The magnitude of the force is expressed by:
    `F_m=qvBsintheta`
     
    • When the angle between a charged particle’s motion and the magnetic field is 90º, the equation can be simplified as such:

    `F_m=qv_(_|_)B`

     

    • The direction of magnetic force acting on the charged particle can be determined by the right-hand rule.
      • Diagram shows rule for a positively charged particle. Force direction is simply reversed for a negative particle.

     

    Uniform Circular Motion in Magnetic Fields 

    • A charged particle undergoes uniform circular motion in the magnetic field if the angle is 90 degrees. 
    `F_m=F_c`
     
    `qvB=(mv^2)/r`
     
    `qB=(mv)/r` 

     

     

    Practice Question 1

    An electron is fired into a magnetic field, as shown in the diagram below.

    (a) On the diagram, sketch the path followed by the electron once it enters the magnetic field. (1 mark)

    (b) If the magnetic field has a strength of 0.05 T and the velocity of the electron is 300 m/s, calculate the force experienced by the electron once it enters the magnetic field. (1 mark)

    (c) An additional electric field can be applied to negate the magnetic force acting on that electron such that the particle can pass through both fields undeflected. Calculate the strength of the electric field that is required to achieve this and outline how the charged plates must be orientated. (2 marks)

      

    • compare the interaction of charged particles moving in magnetic fields to:

      • the interaction of charged particles with electric fields

      • other examples of uniform circular motion (ACSPH108)

     

    Charged Particle in Electric Field vs Magnetic Field

     

    Similarities

    Differences

    ·      Direction depends on nature of charge i.e. positive or negative

    ·      Magnitude of force is proportional to charge (q) of the particle and field strength (E and B)

    ·      Both are relatively greater than gravitational force. In other words, gravitational force is negligible when a particle is within either an electric or magnetic field

     

    ·      Type of force acting on the charged particle is different. Electrostatic force and magnetic force in electric and magnetic fields respectively

    ·      Stationary particle experiences force in an electric field but none in a magnetic field

    ·      Interaction with magnetic field can cause uniform circular motion

     

     

    • So far, circular motion is demonstrated in many other examples:
      • Car driving around a curved path
      • Satellite/planets orbiting in space
      • Rollercoaster travelling around a 360º track

     

    • The magnetic force F = qvB provides the centripetal force when a charged particle undergoes uniform circular motion
      • Direction of centripetal force is towards the centre of the motion
      • Linear velocity of the charged particle is constant in magnitude and orthogonal to the centripetal force
      • The charged particle will continue to undergo circular motion as no additional work is required (W = 0)

     

    Previous section: Charged Particles in Electric Fields

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