Millikan's Oil Drop Experiment

In Millikan's oil drop experiment, an oil drop with mass m and charge q is suspended in mid-air by balancing the downward force of gravity with the upward electric force.

Key Concepts:
- Oil drop mass (m)
- Oil drop charge (q)
- Electric field magnitude (E)
- Coefficient of viscosity (n)
- Radius of the oil drop (r)
- Terminal velocity (v2)
- Acceleration due to gravity (g)

Explanation:

1. Applying the Electric Field:
- In the experiment, an electric field of magnitude E is applied.
- The electric field exerts an upward force on the oil drop due to its charge q.
- This upward force opposes the downward force of gravity.

2. Balancing Forces:
- Initially, the oil drop accelerates upwards due to the applied electric field.
- As it accelerates, the upward electric force increases until it balances the downward force of gravity.
- At this point, the oil drop reaches a constant velocity called the terminal velocity (v2).

3. Equation for Force Balance:
- The force balance equation can be written as:
qE = mg + 6πnrv2

where:
- qE is the upward electric force
- mg is the downward force of gravity
- 6πnrv2 is the viscous drag force

4. Determining the Charge:
- By measuring the terminal velocity (v2) of the oil drop, we can determine the charge (q) using the equation above.
- The terminal velocity can be measured by timing the oil drop as it falls a known distance.
- Substituting the measured values into the equation allows us to calculate the charge.

5. Determining the Mass:
- Once the charge is determined, we can calculate the mass (m) of the oil drop using the equation:
qE = mg

Solving for m gives:
m = qE/g

6. Determining the Radius:
- The radius (r) of the oil drop can be determined using the equation for the viscous drag force:
6πnrv2 = mg

Solving for r gives:
r = (9ηv2)/(2gρ)

7. Measuring the Acceleration due to Gravity:
- The experiment can also be used to measure the acceleration due to gravity (g) by measuring the terminal velocity and substituting the other known values into the equation for r.

Summary:
- In Millikan's oil drop experiment, an oil drop is suspended in mid-air by balancing the upward electric force with the downward force of gravity.
- By measuring the terminal velocity, the charge, mass, radius, and even the acceleration due to gravity can be determined.
- This experiment played a crucial role in determining the charge of an electron and contributed to the development of modern atomic theory.