Charged Particles in Magnetic Fields

This is part of the HSC Physics course under the topic Charged Particles, Conductors and Electric and Magnetic Fields.

HSC Physics Syllabus

  • 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`

 

Charged Particles Interacting with Magnetic Fields

This video analyses the interaction between moving charged particles and uniform magnetic fields. 

Force on Charged Particles in Magnetic Field

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 to:

    `F_m=qv_(_|_)B`

     

    Right Hand Palm Rule

    The direction of magnetic force acting on the charged particle is determined by the right-hand palm rule. The diagram below shows the rule for a positively charged particle. For a negative particle, the thumb must point in the opposite direction to the particle's motion.

     

    Uniform Circular Motion in Magnetic Fields 

    Since the magnetic force always acts perpendicularly to the charged particle's velocity, it provides the centripetal force necessary for uniform circular motion. This is why a charge moving at constant speed in a uniform magnetic field undergoes uniform circular motion.

    By equating force due to magnetic field and centripetal force:

    $$F_m=F_c$$
    $$qvB = \frac{mv^2}{r}$$
    $$qB = \frac{mv}{r}$$
     
    We can derive an expression for the radius of circular motion:
     
    $$r = \frac{mv}{qB}$$

    This equation shows that the radius is directly proportional to the charge's mass and speed, and inversely proportional to its charge and the strength of the magnetic field.

    Calculation Example

    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. 

    (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. 

    (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. 

     

    Previous section: Work Done on Charges in Electric Fields

     Next section: Comparing Charged Particles in Magnetic Fields to Electric Fields