(455) Millikan's experiment [IB Physics SL/HL]

Millikan's Experiment Overview

  • Conducted by Millikan and Fletcher in 1909.

  • Focused on charged particles in an electric field.

  • Used oil drops to avoid issues with water evaporation affecting mass.

Experimental Setup

  • Charged positively using oil drops.

  • Placed between two parallel plates: bottom plate positively charged, top plate negatively charged.

  • Direction of electric field: upward towards the top plate.

Forces Acting on Oil Drops

  • Gravitational Force (F_g): Acts downwards, calculated as ( F_g = m \cdot g ).

  • Electric Force (F_e): Acts upwards, given by ( F_e = E \cdot Q ).

  • Net forces lead to possible accelerations or constant velocities depending on electric field strength.

Key Relationships

  • When in equilibrium (constant velocity, no acceleration): ( F_e = F_g )

  • Leads to: ( E \cdot Q = m \cdot g )

  • Rearranging gives charge: ( Q = \frac{m \cdot g}{E} )

Electric Field Calculation

  • Electric field between plates: ( E = \frac{V}{D} ) ( \Rightarrow ) ( Q = \frac{mgD}{V} )

  • (V): potential difference, (D): distance between plates.

Quantization of Charge

  • Charges of particles are observed to be multiples of the elementary charge (i.e., ( 1.6 \times 10^{-19} \text{C})).

  • Implies charge is quantized (exists in specific countable amounts).

Application in Exams

  • Understanding forces when moving oil drops through fluids:

    • Buoyant Force (F_b): Upward force acting against gravity.

    • Viscous Drag Force (F_d): Opposes motion of the drop.

  • At constant speed, net force is zero: ( F_{up} = F_{down} ).

  • General Force Equilibrium:

    • Upwards Forces: ( F_e + F_b )

    • Downwards Forces: ( F_d + F_g )

Important Equations and Forces

  • Electric Force: ( F_e = E \cdot Q )

  • Buoyant Force: ( F_b = \rho \cdot V \cdot g )

  • Viscous Drag Force: ( F_d = 6 \pi \cdot ext{viscosity} \cdot r \cdot v )

Conclusion

  • Millikan's experiment provided evidence for the quantization of electric charge, demonstrating how elementary charge is foundational in physics.