Understanding Coulomb's Law
Coulomb's Law is a fundamental principle of physics that describes the force of attraction or repulsion between two stationary, electrically charged particles. Just as gravity governs how masses interact, Coulomb's Law governs how charges interact.
1. The Core Principle
The law states that the electrical force between two point charges is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them.
2. The Mathematical Formula
To calculate the electrostatic force ($F$), we use the following equation:
Variable Breakdown:
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$F$: The electrostatic force (measured in Newtons, N).
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$k$: Coulomb’s constant ($\approx 8.99 \times 10^9 \text{ N}\cdot\text{m}^2/\text{C}^2$).
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$q_1, q_2$: The magnitudes of the two charges (measured in Coulombs, C).
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$r$: The distance between the centers of the two charges (measured in meters, m).
3. Key Characteristics
The Inverse Square Law
Because $r$ is squared in the denominator ($1/r^2$), the force changes drastically with distance:
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If you double the distance ($2r$), the force becomes $1/4$ as strong.
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If you triple the distance ($3r$), the force becomes $1/9$ as strong.
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If you halve the distance ($1/2r$), the force becomes 4 times stronger.
Direction of Force
Coulomb's Law is a vector quantity, meaning it has both magnitude and direction:
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Repulsion: Like charges ($+$ and $+$) or ($-$ and $-$) push away from each other.
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Attraction: Opposite charges ($+$ and $-$) pull toward each other.
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The force always acts along the straight line joining the two charges.
4. Comparison: Electric Force vs. Gravitational Force
Coulomb's Law looks very similar to Newton's Law of Universal Gravitation ($F = G \frac{m_1 m_2}{r^2}$), but there are major differences:
| Feature | Electrostatic Force (Coulomb) | Gravitational Force (Newton) |
| Source | Electric Charge ($q$) | Mass ($m$) |
| Nature | Can be attractive or repulsive | Only attractive |
| Strength | Very strong (e.g., holds atoms together) | Relatively weak (only noticeable with huge masses) |
| Medium | Affected by the surrounding medium | Not affected by the medium |
5. Pro-Tips for Problem Solving
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Unit Conversion: Charges are often given in micro-Coulombs ($\mu\text{C}$). Always convert them to Coulombs ($1 \mu\text{C} = 10^{-6} \text{ C}$) before plugging them into the formula.
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Distance Matters: Ensure $r$ is in meters (m), not centimeters or millimeters.
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Absolute Values: When calculating the magnitude of the force, ignore the positive/negative signs of the charges. Use the signs afterward to determine if the force is attractive or repulsive.
Quick Check
If you have two charges and you increase the magnitude of one charge by a factor of 3, what happens to the total force?
Answer: Since the force is directly proportional to the product of the charges, the total force will also increase by a factor of 3.
Would you like to try a practice problem to see how the numbers fit into the formula?
Understanding Electric Fields
An Electric Field is a region of space around a charged object where other charged objects experience a force. If you place a tiny "test charge" near a larger charge, it will move because of the electric field.
Think of it like a "field of influence." Just as the Earth has a gravitational field that pulls on masses, a charge has an electric field that pushes or pulls on other charges.
1. Representing the Field: Field Lines
To visualize an invisible electric field, we use Electric Field Lines. These lines follow specific rules:
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Direction: They always point away from positive ($+$) charges and toward negative ($-$) charges.
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Strength: The closer the lines are to each other, the stronger the field is in that area.
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No Crossing: Field lines never intersect.
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Termination: They start on positive charges and end on negative charges (or extend to infinity).
2. Electric Field Strength ($E$)
Electric Field Strength (also called Electric Field Intensity) is a quantitative measure of how powerful the field is at a specific point. It is defined as the force per unit charge.
The Mathematical Formula
If you place a small test charge $q$ in an electric field and it feels a force $F$, the field strength $E$ is:
Where:
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$E$: Electric Field Strength (measured in Newtons per Coulomb, N/C or Volts per meter, V/m).
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$F$: Electrostatic Force (Newtons, N).
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$q$: Magnitude of the test charge (Coulombs, C).
Important: $E$ is a vector quantity. Its direction is the same as the direction of the force exerted on a positive test charge.
3. Field Strength of a Point Charge
For a single point charge $Q$, the field strength at a distance $r$ away is calculated using Coulomb's Law:
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Directly Proportional: If you increase the charge $Q$, the field gets stronger.
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Inverse Square Law: If you move twice as far away ($2r$), the field strength drops to one-fourth ($1/4$).
4. Uniform Electric Fields
A Uniform Electric Field has the same strength and direction at every point. This is usually created by two parallel metal plates with opposite charges.
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The field lines are parallel and equally spaced.
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The strength is calculated as $E = V/d$, where $V$ is the potential difference and $d$ is the distance between plates.
5. Summary Reference Table
| Concept | Definition / Detail |
| Electric Field | The "aura" or region around a charge where force is felt. |
| Field Direction | Out of positive, into negative. |
| Field Strength ($E$) | Force per unit charge ($F/q$). |
| Standard Units | N/C (Newtons per Coulomb). |
| Vector Nature | Has both magnitude and a specific direction. |
Pro-Tip for Students: The "Test Charge" Trick
Whenever you are asked which way an electric field points at a certain spot, imagine placing a tiny positive particle there.
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If it would be pushed away, the field points away.
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If it would be pulled in, the field points in.
Would you like to see how we calculate the "Net Electric Field" when there are two or more charges acting on the same spot?
Understanding Electric Potential Energy
Electric Potential Energy ($U$) is the energy stored in a system of charges due to their positions relative to each other. It is the electrical equivalent of gravitational potential energy. Just as an object held above the ground has the potential to fall, a charge placed near another charge has the potential to move due to the electrostatic force between them.
1. The Core Concept
When a work ($W$) is done to move a charge against an electric field, that work is stored as potential energy.
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Conservative Force: Like gravity, the electrostatic force is conservative. This means the work done in moving a charge between two points depends only on the initial and final positions, not the path taken.
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The Zero Point: Usually, we define the potential energy to be zero when the distance between charges is infinite ($r = \infty$).
2. Potential Energy of a Two-Point Charge System
For two point charges, $q_1$ and $q_2$, separated by a distance $r$, the electric potential energy is calculated using the following formula:
Where:
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$U$: Electric Potential Energy (measured in Joules, J)
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$k$: Coulomb's constant ($\approx 8.99 \times 10^9 \text{ N}\cdot\text{m}^2/\text{C}^2$)
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$q_1, q_2$: Magnitude of the charges (in Coulombs, C)
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$r$: Distance between the centers of the charges (in meters, m)
Note on Signs: > * Like charges (both $+$ or both $-$): $U$ is positive. You must do work to push them together; they "want" to fly apart.
Opposite charges ($+$ and $-$): $U$ is negative. The system is "bound," and you must do work to pull them apart.
3. Potential Energy in a Uniform Electric Field
If a charge $q$ is placed in a uniform electric field $E$ (like between two large charged plates), the change in potential energy as it moves a distance $d$ along the field lines is:
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If a positive charge moves with the field, it loses potential energy (spontaneous).
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If a positive charge is moved against the field, it gains potential energy (requires external work).
4. Relation to Electric Potential ($V$)
It is easy to confuse Electric Potential Energy ($U$) with Electric Potential ($V$).
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Electric Potential ($V$): The potential energy per unit charge ($V = U/q$). It is measured in Volts (V).
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Electric Potential Energy ($U$): The total energy of the charge ($U = qV$).
5. Summary Table
| Feature | Description |
| Symbol | $U$ or $PE_{elec}$ |
| Unit | Joules (J) |
| Scalar/Vector | Scalar (It has no direction, only magnitude/sign) |
| Dependence | Depends on the magnitude of charges and the distance between them |
| Work Relation | $W_{ext} = \Delta U$ (Work done by external force increases energy) |
Quick Check: Conceptual Logic
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If you bring two electrons closer together, does the potential energy increase or decrease?
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Answer: It increases. Because they repel, you have to "squeeze" them together, doing work on the system.
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If an electron moves toward a proton, does the potential energy increase or decrease?
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Answer: It decreases. The system "wants" to do this naturally, converting potential energy into kinetic energy.
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Great choice. In the QCAA (Queensland Curriculum and Assessment Authority) Physics syllabus for Unit 3, Coulomb’s Law is a cornerstone of Electromagnetism.
The formula we'll be using is:
Where:
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$F$ is the electrostatic force (Newtons, $N$)
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$k$ is Coulomb's constant ($\approx 8.99 \times 10^9 \, \text{N m}^2 \text{C}^{-2}$)
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$q_1, q_2$ are the charges (Coulombs, $C$)
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$r$ is the separation distance (metres, $m$)
Practice Questions: QCAA Style
I’ve designed these to mirror the "Check your understanding" and "Data test" style questions you'll see in Grade 11.
Question 1: Recall and Apply (Simple)
Two point charges, $q_1 = +3.0 \times 10^{-6} \, \text{C}$ and $q_2 = -5.0 \times 10^{-6} \, \text{C}$, are placed $0.20 \, \text{m}$ apart in a vacuum.
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A) Calculate the magnitude of the electrostatic force between them.
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B) State whether the force is attractive or repulsive.
Question 2: The Square-Inverse Law (Conceptual)
Two charged spheres exert a force of $12 \, \text{N}$ on each other. If the distance between the spheres is tripled ($3r$), calculate the new electrostatic force without using the value of $k$.
Question 3: Solving for Distance (Rearranging)
The repulsive force between two identical positive charges of $2.5 \times 10^{-4} \, \text{C}$ is measured to be $45 \, \text{N}$. Calculate the distance separating the two charges.
Helpful Reminders for QCAA Exams:
Watch your units: Often, questions will give charges in microCoulombs ($\mu\text{C}$) or distances in centimetres ($\text{cm}$). You must convert these to Coulombs and Metres before plugging them into the formula.
$1 \mu\text{C} = 1 \times 10^{-6} \, \text{C}$
$1 \text{cm} = 0.01 \, \text{m}$