Notes on the Oil Drop Experiment Lecture

Overview of the Oil Drop Experiment

• Experimental study of charged oil drops.
• Key focus on mass, density, and forces acting on the oil drop.

Definitions and Variables

• m: Mass of the oil drop
• ρ (rho): Density of the oil drop
• σ (sigma): Density of the air
• g: Acceleration due to gravity
• V: Volume of the oil drop, calculated as ( \frac{4}{3} \pi r^3 )
• Weight of the oil drop (W): ( W = \frac{4}{3} \pi r^3 \rho g )

Forces Acting on the Oil Drop

• Thrust Force: Calculated using the density of air and gravity.
  • ( \text{Force} = \sigma V g )
• Gravity Force: Weight of the oil drop.

Equations in Motion

1. Balance of Forces:
   • Sum of upward forces = Sum of downward forces.
   • ( F_{upward} = F_{electric} + W )
   • ( W = F_{gravity} )
2. Electric Field Effect on Oil Drop:
   • Upward force due to electric field acting on negatively charged oil drop.
   • Force due to electric field: ( F_e = F + W )
3. Total Charge on the Oil Drop (q):
   • ( q = 6 , \pi , \eta , (b_1 + b_2) / (E , k) )

Key Calculations

• Radius formula under gravity:
  • ( r = \sqrt{\frac{9 \eta V_1}{2g(\rho - \sigma)}} )
• Charge measurement:
  • Total charge measured in multiples of the charge of an electron:
  • ( q = n \cdot 1.6 \times 10^{-19} , C )
• Total Charge Relation:
  • Total charge is integral multiple of electron charge.

Conclusion

• The experiment demonstrates the quantization of electric charge through the behavior of oil drops in an electric field.
• Results show that the charge measured on the droplets is always a multiple of the elementary charge (charge of an electron).
• Important for understanding the nature of electric charge and atomic structure.