1984B4. An electron from a hot filament in a cathode ray tube is accelerated through a potential
difference ε. It then passes into a region of uniform magnetic field B , directed into the page as shown. The mass of the electron is m and the charge has magnitude e.
a. Find the potential difference ε necessary to give the electron a speed v as it enters the magnetic field.
b. On the diagram, sketch the path of the electron in the magnetic field.
e. In terms of mass m , speed v , charge e, and field strength B , develop an expression for r , the radius of the circular path of the electron.
d. An electric field E is now established in the same region as the magnetic field, so that the electron passes through the region undeflected.
i. Determine the magnitude of E .
ii. Indicate the direction of E on the diagram
