# Millikan Oil drop lab experiment - equation for speed of drop

• Especial
In summary, the conversation discusses the recreation of the Millikan oil drop experiment using latex spheres to measure the charge of an electron. The equation for the speed of the drop is derived, taking into account air resistance and the application of an electric field. The voltage difference between the plates is used to find the electric field, which is assumed to be uniform. The viscosity of air can be determined using the zero field data. The charge on each sphere must be an integer multiple of the charge of a single electron. The electric field near the center of the plates can be calculated using the gap between the plates and their dimensions.
Especial
Millikan Oil drop experiment.
For my current lab, we are recreating the milian oil drop experiment to measure the charge of an electron. However, we are using 1-micron diameter latex spheres in place of oil drops.

Problem:
I am having difficulty deriving an equation for the speed of the drop. Only the linear part of air resistance is taken into account. Without an electric field the particle takes about 15 seconds to fall a distance of 15mm. With the current applied, different spheres travel at different velocities dependent on their charge. And the same sphere moves faster when the field is applied in the direction of gravity.

Attempt at solution:
v1 is rising against gravity
v1 = [qE - mg] / (6*pi*eta*r)
where eta is viscosity of air
and
v2 is when field is reversed and aids gravity
v2 = [qE + mg] / (6*pi*eta*r)

---> How do I find qE if I know the voltage difference between the two plates is 50V. What about 100V or 150V?

---> How do I measure the viscosity of air to use in the equation for v1 and v2?

---> Does the charge “q” on each sphere have to be an integer multiple of e, the charge of a single electron?

Last edited:
Especial said:
---> How do I find qE if I know the voltage difference between the two plates is 50V. What about 100V or 150V?
How is the electric field related to the voltage across the capacitor plates? Remember, the field between the plates may be assumed to be uniform.
Especial said:
---> How do I measure the viscosity of air to use in the equation for v1 and v2?
Especial said:
---> Does the charge “q” on each sphere have to be an integer multiple of e, the charge of a single electron?
Yes.

So apparently the gap between the plates d is 15 mm. I assume the dimensions of the plates are larger than 15 mm. In that case the electric field near the center of the plates can be taken to be E = V/d across the full width of the gap.

mike.Albert99 said:
So apparently the gap between the plates d is 15 mm. I assume the dimensions of the plates are larger than 15 mm. In that case the electric field near the center of the plates can be taken to be E = V/d across the full width of the gap.
Correct.

## 1. What is the purpose of the Millikan Oil drop lab experiment?

The purpose of the Millikan Oil drop lab experiment is to determine the charge of an electron by observing the motion of oil droplets in an electric field.

## 2. How does the equation for the speed of the drop relate to the charge of the electron?

The equation for the speed of the drop, v = mg/6πηr, is used to calculate the charge of the electron (e) by measuring the mass (m), viscosity of air (η), and radius (r) of the oil droplet. This equation was derived by Robert Millikan and is a fundamental part of his oil drop experiment.

## 3. Can the Millikan Oil drop lab experiment be used to determine the mass of an electron?

No, the Millikan Oil drop lab experiment does not directly determine the mass of an electron. However, by combining the results of this experiment with other experiments, such as the Thomson's cathode ray tube experiment, the mass of an electron can be determined.

## 4. What are some sources of error in the Millikan Oil drop lab experiment?

Some sources of error in the Millikan Oil drop lab experiment include air currents disrupting the motion of the oil droplets, variations in the electric field strength, and measurement errors in the mass and radius of the droplets. These sources of error can affect the accuracy of the results.

## 5. How is the Millikan Oil drop lab experiment relevant in modern science?

The Millikan Oil drop lab experiment is still relevant in modern science as it provided a way to accurately measure the charge of an electron, which is a fundamental constant in physics. This experiment also demonstrated the quantization of electric charge, which has implications in fields such as quantum mechanics and particle physics.

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