Positive ions are travelling through a vacuum in a narrow beam. The ions enter a region of uniform magnetic field of flux density 
and are deflected in a semi-circular arc, as shown in the figure below.
The ions, travelling with speed 
, are detected at a fixed detector when the diameter of the arc in the magnetic field is 
.
By reference to the figure above, state the direction of the magnetic field.
The ions have mass 
and charge 
. Show that the magnetic flux density is 
. Explain your working.
Ions of mass 
with the same charge and speed as those in (b) are also present in the beam. In order to detect these ions at the fixed detector, the magnetic flux density is changed. Calculate this new magnetic flux density.
that keeps the ions in the circular path is equal to the magnetic force 
acting on them:
.
