# Physics of cathode ray electroscopes: How to take the nonuniformity of the electric field between the deflection plates into account?

If you do deflection experiments using a cathode ray tube from a high school or college physics lab (like this), one usually gets a notable discrepancy between theory and experiment, if one assumes in the calculations that the electric field between the plates is uniform (and without fringe field). Take for example the measurement results shown in the German manual (p.3 left) for the tube linked above. First they apply an (not deeper motivated) "correction factor" of 0,75 to account for the nonuniformity of the electric field and then calculate for specific x positions the y position and compare it to the measurement. For example for an acceleration potential difference of 4 kV and a deflection p.e. of 5 kV they measure for x = 8 cm an y position of 2,3 cm compared to a calculated value of 2,7 cm. So the calculated value is 17 percent higher than the measured one.

Now in a cathode ray electroscope (at least in a most basic setting) you have almost the same setup, maybe 1 cm plate distance but correspondingly smaller plates. So my guess would be that the non uniformity of the electric field should result in a nonuniform scale on the screen of the oscilloscope, but usually the grid on the screen is equally spaced and each div corresponds to the same voltage unit (depending on the amplification factor).

So, why can the scale on the screen be equally spaced if the approximation that the electric field between the deflection plates is uniform is bad.

In textbooks I found so far they always assume (without further justification) that the electric field between the plates is uniform and neglect the fringe fields (for example here).

• Schematics are available on-line for various old CRT oscilloscopes. They have some fairly complex circuitry to get precise horizontal and vertical deflection. Commented Apr 27, 2022 at 14:26