Short on time? This page is the recap. For explanations, Figure 1 and the three worked examples, use the full study guide.
Recap
- A charged object sets up an electric field around it. Another charge placed in the field feels a force.
- The field at a point is the force per unit charge on a test charge: a charge small enough not to disturb the field.
- E is a vector. Near a lone positive charge it points outward; near a lone negative charge it points inward.
- The net field is the vector sum of the fields from each nearby charge.
- Vector field maps draw arrows (direction and size). Field lines are a simpler model: tangent gives direction, closer lines mean a stronger field, lines never cross.
- Conductor in equilibrium: E = 0 inside, excess charge on the surface, E perpendicular to the surface.
- Insulator: excess charge can be inside and on the surface; the field inside can be nonzero (qualitative only).
Key relationships
| Relationship | Symbols and units | Use it to |
|---|---|---|
| E = F_E / q | E in N/C, F in N, q in C | find E from a measured force, or the force from E |
| F_E = qE | keep the sign of q | get the direction of the force (opposite to E if q < 0) |
| E = k|q| / r² | k = 9.0 × 10⁹ N·m²/C², r in m | find the field of a point charge |
| E_net = E₁ + E₂ + … (vectors) | add x- and y-components | combine fields of up to four charges |
| E outside a charged sphere = k|Q|/r² | r from the centre, r ≥ R | treat a symmetric sphere as a point charge |
Assumptions behind the numbers
- Charges are point charges unless a size is given.
- Source charges stay fixed while you measure the field.
- Conductors are in electrostatic equilibrium (no charge moving).
Mistakes to avoid
- Adding magnitudes of fields that point in different directions. Use components.
- Giving an electron a force along E. Negative charges are pushed opposite to E.
- Using the test charge in E = k|q|/r². The q there is the source charge.
- Forgetting to square r, or measuring r to the surface of a sphere instead of its centre.
- Treating field lines as paths. They show the force direction, not the motion.
- Saying E = 0 inside any charged object. Only inside a conductor in equilibrium.
Quick self-check
- A +2.0 μC test charge feels a force of 0.012 N. What is the field there? (6.0 × 10³ N/C, in the direction of the force)
- The field 0.10 m from a point charge is 1200 N/C. What is it 0.20 m from the charge? (300 N/C)
- A metal sphere carries excess negative charge. Where is that charge, and what is the field at its centre? (On the outer surface; zero)
Next: practice questions.