student activity (answers)
12.2 The Australian synchrotron – reading comprehension –
answers to student worksheet
Questions
1. What is a synchrotron? [1 mark]
A particle accelerator that is optimised to produce electromagnetic waves.
2. An electron moving in a circular path at constant speed is accelerating. Why? [2 marks]
The direction of the velocity is changing. Acceleration is the rate of change of velocity:
therefore the velocity changes if either the speed or direction changes.
3. The centripetal force required for the circular trajectories of particles in a circular storage ring
would be supplied by the magnetic force from large magnets. Derive an expression for the radius
of curvature (r) of the path of an electron of mass (m), charge (q), in a magnetic field (B), while
moving with speed (v). (Assume the direction of the B field is perpendicular to v)
[3 marks]
Fc  Fmag

mv 2
 qvB
r
r

mv
qB
4. The name ‘synchrotron’ derives from the fact that the created magnetic field must be synchronised

to increase as the speed of a particle increases while it is moving in a curved path of fixed radius
(r). Explain why, with reference to your answer in Question 3 and also the information from the
passage.
[3 marks]
According to the equation r = mv/qB we see that if v increases, then B must increase to
maintain constant r.
Furthermore, Einstein’s formula for the increase in mass with velocity, indicates that m also
increases, therefore B must be increased even more in order maintain constant r.
Section 12.2
Page 261
5. Calculate the speed of the 3 gigaelectron volt kinetic energy electrons in the Australian
Synchrotron. Express your answer to two decimal places. [5 marks]
3 GeV = 3 ×1.6 × 10-19 J
mo = 9.11 × 10-31 kg
Ek  mc 2 mo c 2


mo
1
v2
c2
 mo c 2
rearrange

 m
2
o

1   


c 2 Ek  mo c 2 
v2

 m
2
v
o

 1  

2 
c
Ek  mo c 


2
9.11 1031

v  c 1  

9
19
31 2 
3 10 1.6 10  9.11 10 c 
= 3.00 × 108 m s-1

6. The electrons in a synchrotron are continually supplied with energy by electric fields. Without
continuous boosts in energy from the electric fields the electrons would slow down. Why? [2
marks]
The electromagnetic waves themselves carry away energy, which is emitted at the expense of
the kinetic energy of the particles. If the particles lose kinetic energy, they lose speed and so
would maintain their near circular trajectory.
Section 12.2
Page 262