Electricity and magnetism

Electric charge and Coulomb’s law

Explore the force between two point charges: flip a charge’s sign to distinguish attraction from repulsion, then verify the inverse-square law $F = k|q_1q_2|/r^2$ .

Middle school

Equipment

Two virtual point charges q₁ and q₂ on a perspective canvas
Sliders “Điện tích q₁”, “Điện tích q₂”, and “Khoảng cách r”
Button “Đổi dấu q₂” to flip charge q₂ negative
Readout F ∝ |q₁q₂|/r² and the F/F₀ versus r/r₀ graph

Procedure

Observe attraction and repulsion
In figure 1, keep «Điện tích q₁» and «Điện tích q₂» positive and read the line “F ∝ … Same signs: repulsion” — the force arrows are collinear and opposed. Click «Đổi dấu q₂» to make q₂ negative: the arrows turn toward each other and the readout switches to “Opposite signs: attraction”. Drag the canvas to rotate and inspect the force pair from other angles.
Verify dependence on the charges
Hold «Khoảng cách r» fixed at 1.20 m. Raise «Điện tích q₁» from 3 to 6 units and re-read “F ∝ …” — the relative force doubles. Then vary «Điện tích q₂» and confirm the force is proportional to the product $|q_1q_2|$ ; record pairs of values and compare with $F = k\,|q_1q_2|/r^2$ .
Verify the inverse-square law
In figure 2, drag the «Khoảng cách r» slider from 0.60 to 1.20 r₀ and read “F/F₀ = 1/(r/r₀)² = …”: doubling r quarters the force. Try several more r values to see the measured point follow the curve $F \propto 1/r^2$ , then predict F/F₀ at r = 0.90 r₀ before reading the result.

Simulation

Experiment history

In the mid-eighteenth century, natural philosophers such as Jean-Antoine Nollet guessed that electric force weakens with distance, and Henry Cavendish measured the inverse-square law with a hollow conducting sphere — though his result remained unpublished until James Clerk Maxwell recovered it a century later. In 1785, Charles-Augustin de Coulomb used a torsion balance to measure directly the repulsion and attraction between charged spheres, reporting to the French Academy of Sciences. Coulomb concluded that the force is proportional to the product of the charges and inversely proportional to the square of their separation,

F = k|q_1q_2|/r^2

with

k \approx 8.99\times10^9\,\mathrm{N\,m^2/C^2}

. His torsion balance could resolve forces of a few ten-millionths of a newton, and this quantitative method set the pattern for electrical measurement. The unit of charge and the law itself still bear his name as foundations of electrostatics.

Related physicists

Charles-Augustin de Coulomb James Clerk Maxwell

Equipment

Procedure

Simulation

Experiment history

Related physicists

Related library topics