Hemel Hempstead Private Tuition: Coulombs Law

Coulomb's Law, A Level Physics, measuring the force between two charged polystyrene spheres. Given lots of different equipment and access to the Internet, students had to come up with ways to measure the force between the two spheres.

Measuring Invisible Forces: Coulomb’s Law in the A-Level Physics Lab

If you’ve ever rubbed a balloon on your jumper and stuck it to the wall, congratulations—you’ve seen Coulomb’s Law in action (albeit in a slightly chaotic way).

But how do we go from balloon static to the precise mathematical description of electric forces between charges?

Let’s explore Coulomb’s Law, how students can research it, and—most excitingly—how it can be measured in the A-level Physics laboratory with some clever kit and a steady hand.

🧲 What is Coulomb’s Law?

Coulomb’s Law describes the electrostatic force between two point charges. In simple terms:

Like charges repel, unlike charges attract—and the strength of that force depends on the size of the charges and how far apart they are.

Mathematically, it’s written as:

F = k \frac{|q_1 q_2|}{r^2}

Where:

$F$ is the electrostatic force between the charges,
$q_1$ and $q_2$ are the magnitudes of the two charges (in Coulombs),
$r$ is the distance between the centres of the charges (in metres),
$k$ is Coulomb’s constant ( $8.99 \times 10^9 \, \text{Nm}^2/\text{C}^2$ ).

Notice the inverse square law: if you double the distance between charges, the force drops by a factor of four.

🔍 Researching Coulomb’s Law

Students preparing to study or demonstrate Coulomb’s Law can approach the research in three main ways:

1. Theoretical Background

Start with a textbook or a reliable online source (like Physics Classroom, HyperPhysics, or Khan Academy). Look for:

The historical context (Charles-Augustin de Coulomb’s torsion balance in 1785),
The equation and what each term means,
How electric field and force relate to charge and distance.

2. Simulations

Interactive tools like the PhET “Electric Forces and Fields” simulator allow students to change charges and distances and see the force vectors in real time. This helps visualise the law in action before touching any lab equipment.

3. Historical Experiments

Research the torsion balance Coulomb used. It’s a delicate device with a bar suspended by a fibre, showing the torque created by repulsive or attractive electric forces. Most school labs don’t have one, but understanding it helps grasp how Coulomb verified the law.

🧪 Measuring Coulomb’s Law in the Lab

This is where theory meets experiment—and it’s a challenge because electrostatic forces are small and sensitive to environmental interference (like moisture in the air or your hand waving nearby).

Here are a few methods suitable for A-level:

Method 1: Using a Modern Coulomb Torsion Balance Kit

Some A-level labs are equipped with a Pasco Coulomb’s Law apparatus or similar kits. These often contain:

A torsion balance with a lightweight conducting sphere,
A second charged sphere brought near to interact electrostatically,
A scale or angular measurement to track the force,
A way to measure distance between charges.

Students follow a method like:

Charge the spheres (using a Van de Graaff generator or charging rod),
Measure the angle of twist in the torsion wire (proportional to force),
Measure distance between charges,
Repeat with different distances and/or charge magnitudes.

Plotting $F$ against $1/r^2$ should give a straight line, proving the inverse-square relationship.

✅ Top Tip: Do this in a dry room with minimal air currents. Keep mobile phones away.

Method 2: Parallel Plate Repulsion

If a torsion balance isn’t available, students can try a basic version using:

Two lightweight foil disks or spheres on insulating threads,
A known charge transferred by rubbing or induction,
A ruler or protractor to measure repulsion distance.

While not precise, it demonstrates the principle qualitatively. A graph of repulsion distance versus applied charge gives students a sense of the relationship between force and charge.

Method 3: Use a Top Pan Balance

If equipment is limited, assess understanding using simulations where:

Students set up charges and vary the distance,
One sphere is placed on a balance and the other is suspended above and moved down. The change in Mass is recorded.
Plot force vs distance graphs and analyse gradients.

Whilst this method is not precise, the students can see the force changing, and if they can work out the charge on the sphere using some type of charge meter, then this will work.

📊 Analysing Results

After collecting data:

Plot $F$ vs $1/r^2$ – the graph should be linear if Coulomb’s Law holds.
Use the gradient to calculate $k$ , and compare with the theoretical value.
Discuss sources of error: inconsistent charging, movement of air, inaccurate distance readings, etc.

Extension for keen students: Try to calculate the charge on one of the spheres by rearranging Coulomb’s Law. This introduces the idea of using experimental data to estimate charge—a great link to later studies in fields and electronics.

🧠 Final Thoughts

Coulomb’s Law is one of those elegant physics laws: deceptively simple, yet deeply powerful. It’s the electric version of Newton’s Law of Gravitation—and just as fundamental to our understanding of the universe.

By researching the theory, experimenting carefully, and analysing results critically, A-level students not only grasp the concepts—they develop the skills of real scientists.

Tuesday, 15 April 2025

Coulombs Law