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The elementary electric charge is the smallest unit of electric charge, possessed by a single electron. This fundamental charge is denoted by the symbol "e" and has a value of approximately \(1.6 \times 10^{-19}\) Coulombs (C). It serves as a building block for understanding the structure of matter, as it is the charge carried by elementary particles like electrons and protons.

In the context of Millikan's experiment, determining this elementary charge was crucial. The experiment revealed that the charge on oil droplets was always a whole number multiple of this elementary charge. This discovery helped affirm that electric charge is quantized and not just a continuous property. This idea of quantization of charge was pivotal in advancing the field of atomic physics and developing modern electronics.

The experimental setup in Millikan's oil drop experiment was both clever and meticulously designed. It consisted of a chamber equipped with several essential components:

• An **atomizer**, to produce fine oil droplets.
• Two parallel **metal plates**, to apply an electric field.
• A **voltage source**, connected to the plates to generate the electric field.
• A **microscope**, fitted with a vertical measuring scale, to observe and measure the movement of the oil droplets.

The spray of the oil droplets was directed into the space between the metal plates. By adjusting the voltage across these plates, the strength of the electric field could be controlled precisely. This setup allowed Millikan and his team to observe how charged droplets behave under the influence of the electric field and gravitational force.

An electric field is a region around charged particles or objects within which a force is exerted on other charged particles. In Millikan's experiment, the electric field played a crucial role by influencing the motion of the charged oil droplets.

The electric field was generated by applying a voltage across the two parallel metal plates. Depending on their charge, the oil droplets would either be pulled towards one of these plates or pushed away. By carefully adjusting the voltage, Millikan achieved a balance between the gravitational pull on a droplet and the force exerted by the electric field.

It is at this balance point that the droplet suspended in mid-air, allowing for measurements needed to calculate the droplet's charge. The precise control over the electric field allowed for detailed analyses and accurate calculations in the experiment.

The charge of an electron, found to be \(1.6 \times 10^{-19}\) Coulombs, is a fundamental constant in physics and critical for the understanding of atomic and subatomic processes. Millikan's oil drop experiment provided one of the first accurate measurements of this value.

By observing the behavior of just a few oil drops in an electric field, Millikan determined that each drop carried a charge that was a multiple of the charge of an electron. This integral value indicated that charge is quantized.
Millikan's careful experimental procedures confirmed that the amplitude of electric charge of electrons is constant and universal. This finding is fundamental to electronic devices, understanding chemistry, and various fields within physics, supporting the underpinnings of much of modern science and technology.