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Millikan's Experiment
Relationship Between Charge, Current, and Time
Basic Electrical Relationships
Relationship Between Charge (Q), Current (I), and Time (t)
\[ Q = I × t \]
Where:
Q: Electric charge (Coulomb)
I: Current intensity (Ampere)
t: Time (seconds)
Relationship with Elementary Charge
\[ Q = n × e \]
Where:
e: Elementary charge
\[ e = (1.6 × 10^{-19})\;C \]
n: Integer (number of electrons)
Millikan's Experiment to Determine the Elementary Charge
In 1909, Robert Millikan, a professor at the University of Chicago, with the assistance of Professor Harvey Fletcher, determined the approximate value of the elementary charge of an electron. The method he used is called the "oil drop experiment."
The experiment relied on studying charged oil droplets in an electric field:
Purpose of the Experiment
To determine the charge of an electron by studying the motion of oil droplets in an electric field.
\[ q = \frac{(m × g)}{E} \]
Where:
Concept
Symbol
Description
Mass
m
Amount of matter in the body (unit: kilogram)
Droplet Charge
q
Electric charge of the droplet (unit: Coulomb)
Electric Field Intensity
E
Force of the electric field acting on the charge (unit: Newton/Coulomb)
Gravitational Acceleration
g
Acceleration due to gravity (unit: m/s²)
Electric field intensity (Newton/Coulomb)
Important Notes:
- Electric charge is quantized (discrete values)
- Value of elementary charge
\[ (e) ≈ 1.602 × 10^{-19}\;C \]
- Robert Millikan won the Nobel Prize in 1923 for this discovery
Fundamental Equations
Gravitational Force
\[ F_g = mg \]
Where
\[ m = \frac{𝜌}{V} = \frac{𝜌}{\frac{4}{3}𝜋r^3} \]
\[ F_g = mg = \frac{𝜌}{V} \cdot g = \frac{𝜌}{\frac{4}{3}𝜋r^3} \cdot g \]
m
ρ
r
g
Mass Density Droplet Radius Gravitational Acceleration
Electric Force
\[ F_e = qE \]
Where:
\[ q \] Droplet charge
\[ E \] Electric field intensity
Relationship Between Electric Field Intensity and Potential Difference
Relationship Between Electric Field Intensity and Potential Difference
Fundamental Equations:
Electric field intensity (E) = Potential difference (V) ÷ Distance between plates (d)
\[ E = \frac{V}{d} \]
Symbols Explanation:
Symbol
Description
Unit (SI)
E
Electric field intensity
Volt/meter (V/m)
V
Potential difference between plates
Volt (V)
d
Distance between plates
Meter (m)
Calculation Method:
- Determine the potential difference between the plates (V)
- Measure the distance between the plates (d)
- Divide the potential difference by the distance to get the electric field intensity
Practical Example:
If the potential difference between two parallel plates is 12 volts and the distance between them is 0.03 meters:
\[ E = \frac{V}{d} = \frac{12V}{0.03m} = 400 V/m \]
Important Notes:
- This equation applies only to uniform electric fields between parallel plates
- Field intensity is directly proportional to potential difference and inversely proportional to distance
- The direction is always from the positive plate to the negative plate
Experimental Steps:
- Spray oil droplets charged by friction
- Expose them to an adjustable electric field
- Measure the voltage needed to suspend the droplet in air
- Calculate the charge from the equilibrium: electric force = gravitational force
- Repeat the experiment for multiple droplets and find the greatest common divisor (e)
Conclusion
When the electric force equals the gravitational force:
\[ qE = mg \]
\[ q = \frac{mg}{E} \]
After repeating the experiment, it was observed that the charge
\[ q \]
is always an integer multiple of an elementary charge
\[ e \]
\[ q = ne \]
Where \[ n = 1, 2, 3, ... \]
The value of the elementary charge (electron charge) was determined:
\[ e ≈ 1.602 \times 10^{-19} \, \text{C} \]
Millikan's Oil Drop Experiment Simulation
Millikan's Oil Drop Experiment
Used Formulas:
1. Electric field
\[ (E) = \frac{V}{d} \]
2. Volume of spherical oil droplet
\[ V = \frac{4}{3}πr³ \]
3. Mass (m) = Density (ρ) × Volume (V)
4. Charge
\[ (q) = \frac{(m × g × d)}{V} \]
5. Number of electrons
\[ (n) = \frac{q}{e} \]
(where e = 1.6 × 10⁻¹⁹ Coulomb)
Millikan's Experiment |
Basic Electrical Relationships
Relationship Between Charge (Q), Current (I), and Time (t)
\[ Q = I × t \]Where:
Q: Electric charge (Coulomb)
I: Current intensity (Ampere)
t: Time (seconds)
Relationship with Elementary Charge
\[ Q = n × e \]Where:
e: Elementary charge \[ e = (1.6 × 10^{-19})\;C \]
n: Integer (number of electrons)
Millikan's Experiment to Determine the Elementary Charge
In 1909, Robert Millikan, a professor at the University of Chicago, with the assistance of Professor Harvey Fletcher, determined the approximate value of the elementary charge of an electron. The method he used is called the "oil drop experiment."The experiment relied on studying charged oil droplets in an electric field:
Purpose of the Experiment
To determine the charge of an electron by studying the motion of oil droplets in an electric field.
\[ q = \frac{(m × g)}{E} \]Where:
| Concept | Symbol | Description |
|---|---|---|
| Mass | m | Amount of matter in the body (unit: kilogram) |
| Droplet Charge | q | Electric charge of the droplet (unit: Coulomb) |
| Electric Field Intensity | E | Force of the electric field acting on the charge (unit: Newton/Coulomb) |
| Gravitational Acceleration | g | Acceleration due to gravity (unit: m/s²) |
Important Notes:
- Electric charge is quantized (discrete values)
- Value of elementary charge \[ (e) ≈ 1.602 × 10^{-19}\;C \]
- Robert Millikan won the Nobel Prize in 1923 for this discovery
Fundamental Equations
Gravitational Force
\[ F_g = mg \]
Where
-
\[ m = \frac{𝜌}{V} = \frac{𝜌}{\frac{4}{3}𝜋r^3} \]
\[ F_g = mg = \frac{𝜌}{V} \cdot g = \frac{𝜌}{\frac{4}{3}𝜋r^3} \cdot g \]
| m | ρ | r | g |
|---|---|---|---|
Electric Force
\[ F_e = qE \]
Where:
-
\[ q \] Droplet charge
\[ E \] Electric field intensity
Relationship Between Electric Field Intensity and Potential Difference
Fundamental Equations:
Electric field intensity (E) = Potential difference (V) ÷ Distance between plates (d)\[ E = \frac{V}{d} \]
Symbols Explanation:
| Symbol | Description | Unit (SI) |
|---|---|---|
| E | Electric field intensity | Volt/meter (V/m) |
| V | Potential difference between plates | Volt (V) |
| d | Distance between plates | Meter (m) |
Calculation Method:
- Determine the potential difference between the plates (V)
- Measure the distance between the plates (d)
- Divide the potential difference by the distance to get the electric field intensity
Practical Example:
If the potential difference between two parallel plates is 12 volts and the distance between them is 0.03 meters:
\[ E = \frac{V}{d} = \frac{12V}{0.03m} = 400 V/m \]Important Notes:
- This equation applies only to uniform electric fields between parallel plates
- Field intensity is directly proportional to potential difference and inversely proportional to distance
- The direction is always from the positive plate to the negative plate
Experimental Steps:
- Spray oil droplets charged by friction
- Expose them to an adjustable electric field
- Measure the voltage needed to suspend the droplet in air
- Calculate the charge from the equilibrium: electric force = gravitational force
- Repeat the experiment for multiple droplets and find the greatest common divisor (e)
Conclusion
When the electric force equals the gravitational force:
\[ qE = mg \] \[ q = \frac{mg}{E} \]After repeating the experiment, it was observed that the charge \[ q \] is always an integer multiple of an elementary charge \[ e \]
\[ q = ne \]
Where \[ n = 1, 2, 3, ... \]
The value of the elementary charge (electron charge) was determined:
\[ e ≈ 1.602 \times 10^{-19} \, \text{C} \]
Millikan's Oil Drop Experiment
Used Formulas:
1. Electric field \[ (E) = \frac{V}{d} \]
2. Volume of spherical oil droplet \[ V = \frac{4}{3}πr³ \]
3. Mass (m) = Density (ρ) × Volume (V)
4. Charge \[ (q) = \frac{(m × g × d)}{V} \]
5. Number of electrons \[ (n) = \frac{q}{e} \] (where e = 1.6 × 10⁻¹⁹ Coulomb)
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