Electric Potential⚠ unverified
Physics / Electromagnetics · Compute the electric potential due to a point charge
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| q | q | C | 1.0 | Source point charge |
| r | r | m | 1.0 | Radial distance from the charge |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | V | V | Electric potential, in volts (V). Returns 0.0 when ``r`` is not positive |
The science & history
Understanding the Parameters
- $q$ — positive $q$ → positive $V$ outside; superpose algebraically for many charges.
- $r$ — potential falls as $1/r$ (slower than $E \sim 1/r^{2}$).
- $V$ — scalar; field relates by $\mathbf{E} = -\nabla V$.
Derivation (Approaching a Proof)
Work to move $q_{\mathrm{test}}$ from $\infty$ to $r$ against the field of $q$:
$$W = \int_{\infty}^{r} k\frac{q q_{\mathrm{test}}}{r'^{2}}dr' = k\frac{q q_{\mathrm{test}}}{r}.$$
Potential $V = W/q_{\mathrm{test}} = k q/r$. Differentiating recovers $E = k q/r^{2}$ (Electric Field point charge).
History
Potential formalised electrostatic energy and simplified multi-charge problems; the volt is the SI unit of potential difference.
Related Concepts: Electric Field point charge, Coulomb's Law force, Energy Electric Field, Capacitor Energy
Notes: Registry calculator electric-potential (unverified). Point charge, free space, $V(\infty)=0$.