Charge and electric fields
Why it matters
Charge and electric-field models explain electrostatic forces, sensing and the foundations of circuits.
Prerequisites
Course 2.1 and the preceding canonical classes where applicable.
Concept and explanation
Charge q is a conserved signed property measured in coulombs. Like signs repel and unlike signs attract. The electric field E at a point is force per positive test charge, E=F/q₀; it exists independently of the chosen test charge. Conductors allow mobile charge; ideal insulators strongly restrict it.
Key terms
charge; conservation; conductor; insulator; Coulomb force; electric field; superposition
Notation and reading strategy
q in C; r in m; F in N; E in N/C. Choose axes before adding vectors. Field arrows show vector direction; field lines are representations, not physical paths.
Physical model
System: point charges in vacuum or air approximation. Geometry: positions on stated axes. Known charges and separations; unknown force or field. Assume stationary point charges and k=8.99×10⁹ N·m²/C².
Mathematical development
Coulomb magnitude F=k|q₁q₂|/r². Vector direction follows the line joining charges. For several sources, E_total=ΣE_i by vector components. Force on q is F=qE, so a negative q reverses the field direction.
Learning objectives
- Distinguish charge, force, field and potential.
- Use Coulomb’s law and vector superposition with units and direction.
Worked examples
Worked example 1
Physical situation, given and goal: Two +2 μC charges are 0.30 m apart. Find force magnitude and direction.
Representation, law, development, calculation, units and direction: F=8.99×10⁹(2×10⁻⁶)²/(0.30)²=0.400 N. Each force points away from the other charge.
Verification, interpretation and limitations: N·m²/C²·C²/m²=N; doubling r would reduce F by four. Point-charge approximation limits the model.
Worked example 2
Physical situation, given and goal: A +3 μC source lies at x=0. Find E at x=0.20 m.
Representation, law, development, calculation, units and direction: E=kq/r²=8.99×10⁹(3×10⁻⁶)/(0.20)²=6.74×10⁵ N/C toward +x.
Verification, interpretation and limitations: Positive-source symmetry gives outward direction; E does not depend on a test-charge value.
Common mistake and counterexample
Incorrect: electric field equals electric force. Field is force per unit positive test charge; force also depends on the affected charge. Validate with F=qE and units.
Guided practice
Reconstruct Worked Example 2 without looking, label every quantity and unit, then compare each mathematical and directional step.
Knowledge Check and Summary
- Charge is conserved in an isolated system.
- Field is vector force per positive test charge.
- Coulomb interaction follows inverse square.
- Field lines are not physical objects.
Mastery criterion: 4/4 correct with model, units, sign/direction and independent validation. Correct any miss, explain why, then complete a fresh equivalent check.
Related Laboratory
Next class: Voltage and current