A charged particle is accelerated from rest in a vacuum through a potential difference 
. Show that the final speed 
of the particle is given by the expression
where 
is the ratio of the charge to the mass (the specific charge) of the particle.
A particle with specific charge 
is moving in a vacuum towards a fixed metal sphere, as illustrated in the figure below.
The initial speed of the particle is 
when it is a long distance from the sphere. The sphere is positively charged and has a potential of 
. Use the expression in (a) to determine whether the particle will reach the surface of the sphere.
which is greater than 
