Measuring masses and momenta

1
Measuring masses and momenta

• Measuring charged particle momenta.
• Momentum and Special Relativity.
• Kinetic energy in a simple accelerator.
• Total energy, mass and momentum.
• Measuring masses.

2
Motion of Charged Particle in a Magnetic Field

• Charge Q, magnetic field strength B.
• Velocity v, normal to magnetic field.
• Lorentz force F, normal to directions of B and v.
• Magnitude of force
• Circular path.

3
Measuring momentum

• Centripetal force
• Equate Lorentz and centripetal forces

4
Momentum and Special Relativity

• Measurementof momentumagainst speedfor an
  electron
• Must redefine momentum to keep conservation of
  momentum
• Relativistic momentum

5
Kinetic energy in a simple accelerator

• Remember two rules
• Work done _____ x ________.
• Change in K.E. work done.
• Build an accelerator to check this

electron gun
accelerator plates
velocity measurement
6
Kinetic energy cont.

• More measurements
• If want to keep K.E. work done,
  define where

7
Energy and mass

• Have seenso know E mc2 (ignoring K.E.).
• Putting it all together
• Remembering can show that

and
8
An aside, units

• We have
• Multiply p by c to get energyBut Q 1.6 x
  10-19 C for e, ? etc.
• Now c 3 x 108 m s-1 so
• Finally, express p in units of GeV / c

9
PC Exercise 2

• Use PC to do following experiment Side
  viewEnd view

?, ?, K or p
E known
e
e-
B field
?-, ?-, K- or p
?, ?, K or p
Measure r, hence get p
?-, ?-, K- or p
10
PC exercise 2 cont.

• Using known energy (from energy conservation) and
  momentum (from r measurement) calculate mass
• Compare with known particle masses, can you
  identify the particles?