A)
Assuming the electrons start from rest, their final kinetic energy is equal to the electric potential energy lost while moving through the potential difference :
where
is the mass of each electron
v is the final speed of the electrons
is the charge of the electrons
is the potential difference
Solving the equation for v, the speed, we find
B) Centripetal acceleration, , in units of g: 3898 g
When the electrons cross the region of the magnetic field, they experience a magnetic force which is perpendicular to their trajectory: therefore they start moving in a circular motion. The acceleration they experience is not tangential, but centripetal, and it is given by
where v is the speed and r the radius of the trajectory.
We can equate the magnetic force exerted on the electrons to the centripetal force:
and isolate to find the centripetal acceleration:
And since , the acceleration can be rewritten as
c)
The radius of the circular trajectory can be found by using the formula for the centripetal acceleration:
Solvign for r, we find