Definition of E
(E1.4.1) E1.4 · The Electric Field →The field at a point is the force a small positive test charge would feel there, divided by that charge.
| electric field | N/C = V/m | |
| force on the test charge | N | |
| test charge | C |
Test charge small enough not to move the sources it is measuring.
Put a test charge q₀ at the point and measure the force on it. Double q₀ and the force doubles, so the ratio is independent of the test charge:
Define that ratio as the field, a property of the point rather than of the test charge:
Strictly, take the limit of a vanishing test charge so it cannot disturb the sources:
E = 200 N/C along +x, q = −3 nC:
The sign places the force along −x, opposite to the field. The relation F = qE is the definition rearranged, not a separate law.
Electron in E = 100 N/C:
1 µg grain carrying 1000e in the same field:
Negligible for elementary particles, dominant for macroscopic ones.
E exists whether or not anything is there to feel it. Splitting the problem this way — sources make the field, field acts on charges — is what makes electromagnetism tractable.