Short on time? This page is the recap. For the explanations, the figures and the worked examples, use the full study guide.
Recap
- A charged object (the source) sets up an electric field in the space around it. The field is a vector at every point.
- Measure it with a test charge q₀: a charge small enough not to disturb the source charges. E = F/q₀, in N/C.
- E has the direction of the force on a positive charge. A negative charge feels a force opposite to E.
- E points away from isolated positive charges and towards isolated negative charges.
- Superposition: the net field is the vector sum of the fields of each source.
- Vector field maps draw arrows on a grid (length = magnitude). Field lines are tangent to E, start on + and end on −, are denser where E is stronger, and never cross.
- k = 1/(4πε₀) = 8.99 × 10⁹ N·m²/C²; e = 1.60 × 10⁻¹⁹ C.
Key relationships
| Situation | Relationship | Notes |
|---|---|---|
| Definition | E = F/q₀ | q₀ small; E does not depend on q₀ |
| Force on a charge q | F = qE | Opposite to E if q < 0 |
| Point charge q | E = kq/r² = q/(4πε₀r²) | E ∝ q and E ∝ 1/r² |
| Several point charges | E_net = E₁ + E₂ + … | Add x- and y-components |
| Conductor in equilibrium | E = 0 inside; E ⊥ surface just outside | Excess charge on the surface |
| Insulator | E inside can be non-zero | Charge can sit inside and on the surface |
| Outside a spherically symmetric sphere | E = kQ/r² (r ≥ R) | As if Q were a point charge at the centre |
Assumptions behind the results
- Source charges are at rest (electrostatics).
- Point charges have negligible size compared with the distances involved.
- The test charge is small enough not to move the source charges.
Mistakes to avoid
- Adding magnitudes. Fields are vectors: resolve, then add.
- Wrong distance. Use the distance from each source to the point.
- Wrong direction for a negative source. E points towards it.
- Forgetting the sign of q in F = qE. A negative charge is pushed against E.
- Treating field lines as paths. They show the force direction, not the velocity.
- “E = 0 inside any charged sphere.” Only for a conductor in equilibrium.
Quick self-check
- What is E at 0.30 m from a +1.0 nC point charge? (99.9 N/C, about 100 N/C, away from the charge)
- You move three times farther from a point charge. What happens to E? (It becomes 1/9 as large)
- Find the force on a −3.0 nC charge in a field of 2.0 × 10⁴ N/C pointing east. (6.0 × 10⁻⁵ N, west)
- Where is the excess charge on a charged metal block in equilibrium? (On its surface; E = 0 inside the metal)
- On a field-line diagram, lines are twice as close together at point X as at point Y. Where is E stronger, and which way does it point at X? (At X; along the tangent to the line through X, in the arrow direction)
Next: practice questions.