Faraday’s E&M Fields

Example 4: Your Parents’ Old TV

The Question:

1. If the field in a TV tube is 40,000~V/m and the region where the field is concentrated is 0.5 meters long (which is more than a factor of 10 too large), what is the voltage?
2. What is the energy of a single electron accelerated through your parents’ old TV picture tube?

Here’s a cross section of a cartoonish old TV tube. At the left, electrons are “boiled” away from a heater and experience a negative charge and so are accelerated to the right. They pass through a grid that’s positively charged and are now free to roam…at very high speeds.

The “magnet” rectangles are really a cross section of coils carrying currents which bend the electron beam (stay tuned, so to speak) and the electronsa are pointed at the phosphorescent screen where when they hit, they make light that you, on your couch on the right can see looking to the left at the screen.

The Answer:

1. We know the length of the tube, so we can calculate the voltage:

2. The kinetic energy, as we’ve seen, depends on the field, but now with knowing the voltage, we can use $U=qV$ to calculate it. The magnitude of the negative charge is that of a single electron, so $q=e=1.6 \times 10^{-19}$ C and we find (remembering that 1 V is 1 J/C):