A charged particle of mass 
and charge 
is travelling with velocity 
in a vacuum. It enters a region of uniform magnetic field of flux density 
, as shown in the figure below.
The magnetic field is normal to the direction of motion of the particle. The path of the particle in the field is the arc of a circle of radius 
.
Explain why the path of the particle in the field is the arc of a circle.
Show that the radius is given by the expression
A thin metal foil is placed in the magnetic field in (a). A second charged particle enters the region of the magnetic field. It loses kinetic energy as it passes through the foil. The particle follows the path shown in the figure below.
The path of the particle has different radii on each side of the foil. The radii are 
and 
. Determine the ratio
for the particle as it passes through the foil.
