The Difficulty of Home-Testing Coulomb's Law

By Casual Physics Enjoyer September 07, 2026

I often find myself reflecting on how much I take for granted. One of my persistent struggles in the study of physics is the simple act of remembering physical laws.

My goal is to reach a level of intuition where applying a law of physics feels as natural as:

• Frying an egg.
• Constructing a sentence.
• Performing basic addition.

I imagine a world where I can manipulate physical reality with the same fluency as language. For instance: "Oh, my chicken is overcooked; no matter, I understand the heat equation, so I'll just decrease the temperature by X and ensure the chicken is more spherical next time!"

While I could easily query an LLM or look up Maxwell's equations, I am constantly struck by how the ancient Greeks uncovered so much about the universe with far fewer tools.

The Spirit of First Principles

I recall a moment in Brighton where my friend Cyrus and I challenged one another to calculate the Earth's radius from first principles, using nothing but the angle of the horizon. I find these challenges both entertaining and enlightening.

This mindset was reinforced by a piece of advice I encountered in R. Shankar's textbook, On Fundamental Physics II, while relaxing by a pool in Malaysia:

To achieve a profound understanding of physics, one must think critically about how a physical law can actually be tested and measured using real-world instrumentation.

Without this practical grounding, it is easy to get lost in "factors of $2\pi$" while performing mindless symbolic manipulations—a trap I frequently fell into as a theoretical physics student in the Cambridge Masters program.

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Deconstructing Coulomb's Law

Because I struggle to memorize Coulomb's law, I decided to explore how I could "feel" it and test it manually. However, electric charge is an abstract concept; you cannot simply "summon" a precise amount of it.

The Theoretical Framework

If we have two charged particles, $q_1$ and $q_2$, separated by a distance $r$, the force $F$ is expressed as:

$F = \frac{1}{4\pi\varepsilon_0}\,\frac{q_1 q_2}{r^2}$

To understand how one arrives at this, we can treat the force as a function: F = F(r, q1, q2).

While symmetry suggests the exponents should be the same, it isn't immediately obvious why $a=1$ in nature. I considered writing a full deep-dive on this rabbit hole, but it's out of scope for now.

Comparing Inverse Square Laws

A logical hypothesis is that this force follows an inverse square law, similar to the intensity of light or gravity.

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The Experimental Struggle

To verify the inverse square law at home, one could theoretically:

1. Charge two spheres equally.
2. Fix one in place.
3. Suspend the other by a string.
4. Measure the angle of deflection from the vertical to calculate the force.

While Coulomb used a high-precision torsion spring, I wanted a simpler method. However, charging metal spheres cleanly with household items is surprisingly difficult. I considered splitting a single charge between two objects via contact to ensure symmetry, but verifying that the charges were truly equal remained a problem.

Building a DIY Electroscope

Instead, I pivoted to building an aluminium foil electroscope.

Materials & Process:

• Insulated wire (from a breadboarding kit)
• Glass jar (with a hole drilled in the lid)
• Thin strips of aluminium foil
• A charged object (pen rubbed against hair)

The Setup:

1. The wire passes through the jar lid.
2. The bottom end is bent into a hook holding the foil strips.
3. The top end is capped with scrunched-up foil.

When I touch the external foil with a charged object, the internal foil strips separate due to electrostatic repulsion.

The Verdict: Currently, this method is qualitative rather than quantitative. The primary obstacle is charge decay, as humidity in the air bleeds the charge away from the objects. I am still searching for a more robust, repeatable way to create a stable charge to accurately measure the inverse square law.

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Community Discussion

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