8.6 Interpreting Particle Tracks

• Particle detectors that count particles, like Geiger-Muller tubes, are useful but they cannot distinguish different types of particle
• Modern detectors can show the paths of charged particles, from which physicists are able to interpret the characteristics of the particle

• The curvature of the particle tracks gives an indication of its momentum
  • A smaller radius means the particle has a smaller momentum
  • A larger radius means the particle has a larger momentum

• This is due to the equation for the radius of a charged particle in a magnetic field:

• Where:
  • r = orbital radius of charged particle (m)
  • p = momentum of charged particle (kg m s^–1)
  • B = magnetic field strength (T)
  • Q = charge of particle (C)
  • m = mass of the particle (kg)
  • v = velocity of the particle (m s^-1)

• If the radius of a track is decreasing (i.e., it is spiralling closer inwards) 
  • This means the particle's momentum is decreasing
  • This is because r ∝ p
  • Therefore, the velocity of the particle is decreasing
  • Hence, the kinetic energy of the particle is also decreasing, due to ionising other particles in its path

The radius and direction of particle tracks is used to determine momentum and charge. Creation and annihilation is also observable

• The direction of a track's curvature gives an indication of the particle's charge
  • Fleming's Left Hand Rule can be used to determine the sign of the particle's charge

• Sometimes, particle tracks appear to start out of 'nowhere'
  • This indicates particle-antiparticle creation
  • These paths are in opposite directions because the particle-antiparticle pair is oppositely charged
  • Therefore, the magnetic force on them is oppositely directed
  • However they have the same radius because they each have the same mass (and hence, momentum)
• Therefore charge, energy and momentum are always conserved in interactions between particles

Part (a)

Step 1: Comment on the source of the tracks

• • The red and yellow tracks begin together out of 'nothing'
  • This indicates an uncharged particle is creating charged particles

Step 2: Comment on the radius of the tracks

• • Both the red and yellow tracks have the same radius
  • This indicates both particles have the same momentum, and mass, which is true for creation of a particle-antiparticle pair

Step 3: Comment on the direction of the tracks

• • Both tracks spiral in opposite directions
  • This indicates each particle is oppositely charged, because the (centripetal) magnetic force acts on them in the opposite directions

Part (b)

Step 1: Determine the direction of particle velocity and centripetal force

• • The centripetal force on each particle must be toward the centre of orbit
  • The tracks begin from a point and spiral away from each other, so the particle velocity must be as indicated in the image below:

Step 2: Apply Fleming's Left Hand Rule for the red track

• • Fleming's Left Hand Rule gives the direction of the magnetic force on a positively charged particle in a magnetic field
  • The first finger should point into the page, along the direction of the magnetic field
    • On the red track, the thumb should point toward the centre of orbit (the direction of the force)
    • The second finger points downward, but the actual particle velocity is upward
    • Therefore, the red track must indicate a negatively charged particle

Step 3: Check Fleming's Left Hand Rule for the yellow track

• • The first finger should again point into the page
    • On the yellow track, the thumb should also point toward the centre of orbit (the direction of the force)
    • The second finger points downward, which is in agreement with the actual particle velocity
    • Therefore, the yellow track must indicate a positively charged particle