Electric field magnitude from $q_1$: $E = k_e \dfrac{|q_1|}{r^2}$. Potential energy: $U = k_e \dfrac{q_1 q_2}{r}$.
$F > 0$ means repulsion (like signs); $F < 0$ means attraction (opposite signs).
FAQ
How is the Coulomb force similar to gravity?
Both follow the inverse-square law and describe two-body interactions. However, the electric force can be attractive or repulsive and is far stronger than gravity.
Why do like charges repel?
Like charges produce electric fields pointing in the same direction, creating a net force pushing them apart. Opposite charges create fields that attract.
What are everyday examples of Coulomb force?
Static electricity (plastic rubbing hair), electron-nucleus binding in atoms, and all chemical bonds are manifestations of the Coulomb force.
How is the Coulomb force different from the magnetic force?
Coulomb force acts between stationary charges; magnetic force acts between moving charges (currents). Relativistically they are aspects of the same electromagnetic interaction.
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I can see the simulation updating, but what exactly is being calculated here?
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Great question! The simulator solves the governing equations in real time as you move the sliders. Each parameter you control directly affects the physical outcome you see in the graph. The key is to build an intuitive feel for how each variable influences the result — that's how engineers develop physical judgment.
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So when I increase this parameter, the curve shifts significantly. Is that a linear relationship?
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It depends on the model. Some relationships are linear, but many engineering phenomena are nonlinear. Try moving the sliders to extreme values and see if the output changes proportionally — if the graph shape changes, that's a sign of nonlinearity. This hands-on exploration is exactly what simulations are best for.
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Where is this kind of analysis actually used in practice?
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Constantly! Engineers run these calculations during the design phase to quickly screen parameters before investing in expensive physical tests or detailed finite element simulations. Getting comfortable with these simplified models is a real engineering skill.
Enter charge Q1 magnitude in Coulombs using the vQ1 input (range: -100 to +100 µC)
Enter charge Q2 magnitude using vQ2 input with the same units
Set separation distance R in meters using vR (range: 0.01 to 10 m)
Click simulate to compute electrostatic force F = k|Q1×Q2|/R² where k = 8.99×10⁹ N·m²/C²
Observe force magnitude and direction visualization; repulsive forces shown in red, attractive in blue
Worked Example
Two point charges in a vacuum: Q1 = +5 µC (5×10⁻⁶ C), Q2 = -3 µC (−3×10⁻⁶ C), separated by R = 0.25 m. Force calculation: F = (8.99×10⁹ × 5×10⁻⁶ × 3×10⁻⁶) / (0.25)² = 2.157 N attractive. The visualizer displays this as a 2.157 N pull along the line connecting the charges, with Q1 drawn toward Q2 (opposite charge attraction per Coulomb's Law).
Practical Notes
Very small separations (under 0.02 m) generate extreme forces; use caution with high-magnitude charges to avoid numerical instability
In air versus vacuum: multiply force by 0.0001 for relative permittivity εr ≈ 1.0006 correction (negligible for most engineering)
Charge distribution: treat inputs as point charges; results become inaccurate for extended charge geometries—use superposition for multiple charge configurations
Sign convention: same sign charges repel; opposite signs attract; simulator handles both automatically
🎬 Watch it in motion
Electric Field Lines | out of plus, into minus #Shorts
Electric Dipole | the field two opposite charges weave #Shorts
