(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.