University of Wisconsin Green Bay

In a cathode ray tube, electrons are "boiled" off of a filament and accelerated through a potential difference. They then strike a fluorescent screen and so can produce non-permanent images. Cathode ray tubes are used, for example, in televisions and computer monitors. Suppose you want to build a cathode ray tube that will accelerate electrons to a speed of 7.5 x 107m/s. How great a potential difference do you need? Should the potential be higher at the filament or the screen?

  • In this problem, you are asked to find the change in electric potential of an electron given a specified change in its speed. Electric potential is a measure of electric potential energy, just as height is a measure of gravitational potential energy. This is a Conservation of Energy problem.

    If non-conservative forces are either known or small and if energy is converted from one form to another between the locations, then any time you compare speed of an object at two different points, conservation of energy is the most direct way to understand the problem.

    In this case, you start out with stored energy due to the location of the electron in an electric potential and convert it to kinetic energy.

  • Any time you understand the motion of an object by looking at its energy, you begin with the Conservation of Energy equation.

  • The electron needs to be accelerated through a potential difference of 16 J/C. The electric potential is higher at Point 2 - the screen.

  • In this problem, you are asked to find the potential difference required to accelerate an electron from rest to 7.5 x 107m/s. The energy conversion chain for this motion is

    electric potential energy→kinetic energy

    as reflected in the second line of the equation above.

    You should notice that although electric potential is higher at the ending point, electric potential energy is lower. PEE = qV and q is negative for an electron. So a higher V gives a more negative, or lower, PE. This makes sense—initial PE is converted to KE as the electron moves to the screen.