Coulomb's Law | Engineering Calculator API

Coulomb's Law API

Formula

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

where

$k = \frac{1}{4 \pi \varepsilon_0 \varepsilon_r} = \frac{K_E}{\varepsilon_r}$

Description

This endpoint computes values using Coulomb's Law for the electrostatic force between two charges. The API can solve for any unknown variable given sufficient inputs and supports both single-distance and multi-distance comparisons.

It supports:

• Solving for $F$, $q_1$, $q_2$, $q_1 \cdot q_2$, or $r$
• Comparing forces at two distances $r_i$ and $r_f$
• Custom dielectric media using $\varepsilon_r$
• Signed forces (repulsive $+$, attractive $-$)

Parameters

Behavior

• If both q1 and q2 are provided, q_product is computed automatically.
• If q_product and one charge are provided, the other charge is derived.
• If both r_i and r_f are provided, the API returns forces at both distances along with change and ratio.
• If solving for a single unknown, all other required values must be provided.
• If all values are provided, the API verifies consistency.

Derived Quantities

When sufficient data is available, the API also computes:

• Electric potential energy
  $U = k \cdot \frac{q_1 q_2}{r}$

• Electric field from each charge
  $E = k \cdot \frac{|q|}{r^2}$

Example Summary Output

• Solving for force:
  $F = k \cdot \frac{q_1 q_2}{r^2}$

• Solving for distance:
  $r = \sqrt{\frac{k |q_1 q_2|}{|F|}}$

• Multi-distance comparison:
  $F(r_i) \rightarrow F(r_f)$ with change $\Delta F$ and ratio

Notes

• $r \neq 0$
• $F \neq 0$ when solving for $r$
• Sign of force depends on charge polarity when signed=true