The electron was discovered in 1897 and the $e/m$ ratio was measured at that time ,but the charge $e$ itself was measured in 1911. Why was it not possible to measure it earlier?
[Physics] Why is it easier to measure the specific charge of an electron over the charge
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Best Answer
Because $e/m_e$ appears in macroscopic equations, but $e,m_e$ individually do not.
The force equation for a general electron in an electromagnetic field is $F=e(...)$. This makes acceleration proportional to $\frac{e}{m_e}$.
Acceleration is not that hard to measure, especially if you measure it in the form of deflection. Piping electrons from a beta emitter into a calibrated magnetic field will give you a deflection in their path, and this can be measured by having them strike a phosphor screen.
So, $\frac{e}{m_e}$ is easy to measure.
On the other hand, it is hard to measure $e$ and $m_e$. To do so we would need to create a system where the force is acting only on the electron, but it is attached to a larger, measurable mass. This replaces the $m_e$ in $F=m_ea=e(...)$ with a larger $m$, and now from experiment we can measure $e$.
That's exactly what Millikan did when he measured $e$. He took oil drops with charges that were small multiples of $e$. The mass of the drops could be calculated from their behavior in freefall1, and the electrostatic force required to balance them is measured.
1. While Galileo's ball drop experiment tells us that the behavior of a falling body doesn't depend on mass; this is no longer applicable when we consider viscosity, and thus by carefully monitoring the behavior we can determine the mass of a falling drop.