Electric Field (point charge)⚠ unverified
Physics / Electromagnetics · Electric field magnitude due to a point charge
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| q | q | C | 1e-06 | Source charge |
| r | r | m | 0.1 | Distance from charge |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| E | E | V/m | Electric field |
The science & history
Understanding the Parameters
- $q$ — larger charge → stronger field; sign sets direction (magnitude ignores sign here).
- $r$ — field falls as $1/r^{2}$.
- $E$ — force per unit positive test charge: $\mathbf{F} = q_{\mathrm{test}}\mathbf{E}$.
Derivation (Approaching a Proof)
By definition $\mathbf{E} = \mathbf{F}/q_{\mathrm{test}}$. Substituting Coulomb’s force on $q_{\mathrm{test}}$ due to $q$ and cancelling $q_{\mathrm{test}}$ yields $E = k q/r^{2}$. Related potential: $V = k q/r$ (Electric Potential) with $E = -\nabla V$ radially $E = |dV/dr|$.
History
The field concept (Faraday, Maxwell) rephrases Coulomb action-at-a-distance as a local property of space; point-charge $E$ is the first textbook example.
Related Concepts: Coulomb's Law force, Electric Potential, Energy Electric Field, Parallel-Plate Capacitance
Notes: Registry calculator electric-field-point-charge (unverified). Free-space point charge.