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Not 100% sure either but I think it means that even though the kinetic energy is close to zero, the electron would still sort of be drift to the detector as the detector has a positive charge and the electron is negatively charged, thus attracting it towards the detector based on charge. I could be wrong though. Don't think it will be something we need to worry about too much for now though hopefully!
I think Professor Lavelle said that this "partial positive charge" only applied when the ejected electron had a kinetic energy of 0 or close to 0. Since the kinetic energy is so low, the only way the electron could reach the detector is by attraction since the electron is negatively charged and the detector is positively charged. In cases where the kinetic energy is greater than 0, the electron would hit the detector on its own.
In most circumstances, when an electron is emitted it will have extra energy as a result of the energy difference between the threshold energy and the energy of the photon. This will result in the electron being launched into the detector, which allows for the electron to be detected. It is possible, however, to have a photon match the threshold energy perfectly and therefore cause the ejected electron to just float off. If this were to occur, an arisen issue would be that it does not have enough "fly away" to hit the detector. To solve this issue so that we could still detect that emitted electron, the detector has a slightly positive charge that attracts that electron and *boom* detected.
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